## The Inflationary Universe - by Alan H Guth 1997 - Book review

This document contains comments about the book "The Inflationary Universe" - by Alan H Guth written in 1997.
The sub title is: My Quest for the Ultimate Nature of Reality
• The text in italics is copied from the article.
• Immediate followed by some comments

### page 9

Finally then we come to the key question: Given the present understanding of conservation laws, is there any hope for a scientific description of the creation of the universe.
Each law is a description of physical process. Conservation laws are mathematical descriptions of a specific aspect of closed processes subject of change. A conservation law does not describe the details of this change.
Next:
If the creation of the universe is to be described by physical laws that embody the conservation of energy, then the universe must have the same energy as whatever it was created from.
The first question to answer is what are the physical changes that took place when our universe came into existence.
A different problem to answer is: suppose we study one photon. Will this photon exists forever? You can try to answer this question using a conservation law. A much better approach is to start from the physical processes involved.
Next:
If the universe was created from nothing then the total energy must be zero.
That means the moment that our universe can into existence was a switch from nothing into something. Maybe there already was a huge "blackhole" before this moment.
Next:
Newton's description of gravity is often called an action-at-a-distance formulation, since gravity is interpreted as a force that one object exerts on a distant object.
A better name is: instantaneous-action-at-a-distance

### page 10

Most modern physics, however, think about gravity using an alternative formulation in which forces at a distance are avoided.
While maintaining the underlying content of Newton's Law, this newer formulation replaces the (instantaneous) action-at-a-distance with the notion of an (instantaneous) gravitational field.
In order to calculate this field you need point masses, which implies that the issue of instantaneous-action-at-a-distance is still relevant.

### Page 20

In the modern big bang theory, Hubble's law is interpreted as evidence that the universe is undergoing homogeneous expansion as illustrated in Figure 2.1
Hubble's Law is a description that the expansion of the (our) universe is homogeneous. It is no evidence that the universe is homogeneuos. Figure 2.1 is a graphical interpretation of this expansion but again is no evidence. I 'am not claiming that anything is wrong.

### Page 21

The expansion of the universe does not go unchecked, however, since every galaxy is attracting every other galaxy by the force of gravity. This attraction slows the expansion, although the slowing occurs at a rate that is too small for us to measure directly.
The current accepted mainstream notion is that the expansion is accelerating.

### Page 22

The ultimate fate of the universe, according to the BB theory depends on the average mass density of the universe
The ultimate fate of the (our) universe is a complex chemical process which most probably is not everywhere the same.
If this density exceeds a certain critical value that can be calculated from the expansion rate then gravity will eventually win out and the expansion of the (our) universe will be reversed.
IMO it is very implausible that this will happen for the whole universe in a uniform manner. The inflation theory makes this very unlikely.
If the mass density is precisely at the critical density then the (our) universe is called flat
I think it is more realistic to change the wording precisely at into: close to . Humankind will not realise that the world is almost flat. Anyway it is impossible to calculate the critical density
If omega is exactly equal to one, then the universe is flat.
In theory. In reality the word approximate should be added

### Page 23

If the pencil is perfectly balanced then the laws of classical physics imply that it will stand on its point forever
This behaviour has nothing to do with the laws of classical physics. It is the result of experiment with a pencil.
The problem is that you cannot use this experiment to describe the behaviour of the evolution of universe. That is a different experiment.
Next:
The situation of perfect balance corresponds to a value of omega equal to one - a mass density precisely equal to the critical density.
If omega is exactly one at any time then it will remain exactly one forever.
This is only true in theory. This assumes that the mass distribution is every where the same which is not true.

### The birth of modern cosmology - page 33

#### page 37

The problem is nonetheless fairly simple to understand: if masses were distributed uniformly and statically throughout space then everything would attract everything else and the entire configuration would collapse contracting without limit.
The problem is difficult at least if the problem is realistic.
As a thought experiment you can start with an initial state that masses are uniformly distributed. But this should also realistic. That means you have to answer the question what happened before. If you cannot answer that question than the answer: "the entire configuration will collapse" has no meaning.

#### page 43 Figure 3.2

Figure 3.2 The evolution of Friedmann universes.
If the cosmological constant is assumed to vanish (Lambda =0 or Omega (Lambda) = 0) models of the universe fall into three classes:
1. A mass density high enough to reverse the expansion leads to a closed universe.
2. In a low density universe called open the expansion continues forever and the velocity of any galaxy levels off at a constant value.
3. The mass density at the borderline between these two cases is called the critical density and the corresponding universe is called flat. A flat universe will expand forever but the velocity of any given galaxy will become smaller and smaller as time goes on.
Figure 3.2 describes a physical interpretation of the evolution of the universe The problem with a closed universe is that this is physical very unrealistic. A closed universe implies that the total universe is in some sort of equilibrium or balance. At some moment in the universe at the same time everywhere the expansion comes to a halt and starts to contract in harmony and finish in one point. Mathematically this is simple but physical unrealistic implying that the mathematical model (set of equations) is too simple.

The problem with both the flat and the open universe is what are called the density and the critical density of the universe.
The density is the total mass of the entire universe divided by the volume of the entire universe, which is a function of the radius of the entire universe. The critical density is a mathematical parameter to distinguish between (closed) flat and open. The real critical question is how to calculate this parameter based on observations IMO that is impossible.

#### page 44 Figure 3.3 The geometry

Figure 3.3 The geometry of Friedmann universes.
• A Closed geometry is the three dimensional analogue of a sphere. A triangle contains more than 180 degrees.
• An open geometry is the three dimensional analogue of a saddle-shaped surface. A triangle has less than 180 degrees.
• The third possibility is a flat geometry, the Euclidean geometry with which we are familiar, in which each triangle contains exactly 180 degrees, and the circumference of a circle is exactly pi times the diameter
Geometry is mathematics. The issue is not mathematics it is physics as discussed in page 43 Figure 3.2
In the case when the geometry is flat the evolution of the radius of the universe can be open, flat or closed. See also page 74

### Echoes of a scorching past - page 57

#### page 72 Figure 4.2 Power Spectrum as of 1975

Figure 4.2 Data on Cosmic background radiation spectrum as of 1975
Compare Figure 4.2 with Figure 4.4 (See page 78 and Figure 4.6 (See page 82

#### page 74 geometry

Why then, can we see the remnant radiation from the fireball of the Big Bang.
The problem is we cannot see remnant radiation from the fireball of the Big Bang at t=0. CMB radiation is later.
The answer to this question lies in understanding the geometry of the Big Bang.
What the author suggests is that the answer lies in what is discussed in page 44 i.e. in geometry. IMO it is not geometry: it is physics.
To answer this question you have to study: Friedmann Lambda = 0.01155
What this document shows is that space expansion is roughly equal to 3 times the speed of light. The black line shows the outer line of space expansion after the Big Bang. The blue line shows the path of the light ray that shows the oldest event that we can observe. This event happened at the black line.
On the contrary, the models of Friedmann and Lemaître were constructed to be completely homogeneous.
To assume that the Universe is homogenous and isotropic at each instant makes mathematically everything much simpler. But is such an assumption accordingly to the physical reality ?
A homogeneous universe makes gravitational waves and acoustic oscillations much more difficult to accept, which in a sense are density perturbations.
This means that the matter is assumed to have uniformly filled all of space at all times, right back to the instant of the Big Bang.
The first question to answer is what means: all of space?
Does this mean that "all of space" is closed and finite or is flat and infinite ?

This also implies that processes like nucleosynthesis happened instantaneous throughout the universe. See also page page 101 Nucleosynthesis.
What means all of space?

There is no edge and no center to the distribution of matter.
Does this imply that the universe is mathematical flat and infinite ?
Suppose that that is the case. What is the meaning of the wording: Space expansion? See also: page 177 flatness problem
It is hard to image what could possibly cause an explosion to happen simultaneously throughout the universe as the Friedman-Lemaitre models assume.
The Friedman's equation is a mathematical description of a certain process.
The problem is that a localized explosion cannot explain the observed uniformity of the CMB radiation
If there were a localized explosion that occurred in some particular direction in the sky, on the other hand, then one would expect that this direction would be clearly visible as a hot spot in the back ground radiation.
The big bang happened 350000 years before the events that caused the CMB radiation.

#### page 75

The inflationary universe can explain why the BB explosion occurred homogeneously throughout the observed universe, while at the same time the theory suggests that the observed universe is only a minute part of a vastly larger space that is far from homogeneous.
For more about the observed universe read this: Reflection 4 - The Observable Universe?
This are in fact two statements.
The issue This is a very tricky sentence because the sentence implies that the entire universe at present is not homogeneous.
Infact never was.
We must still understand how the intense heat of that explosion reduced to the faint reverberation at 3degress K that fills the universe today.
Okay.
The answer to this question hinges on the Doppler effect which was discussed in Chapter 3.
This has nothing to do with the Doppler effect.
Since Hubble's law tells us that the distant galaxy would be receding we expect that the light pulse would be redshifted when it reaches the earth
This is completely the other way around.
What is observed that light is redshifted. This is explained by assuming that the galaxy is receding and this is mathematical captured in Hubble's law.

#### page 78 Figure 4.4 Power Spectrum by the Berkeley-Nagoya rocket satellite

Figure 4.4 Cosmic background measurements by the Berkeley-Nagoya rocket experiment
Compare Figure 4.4 with Figure 4.2 (See page 72 ) and Figure 4.6 (See page 82 )

#### page 82 Figure 4.6 Power Spectrum by the COBE satellite

Figure 4.6 Cosmic background measurements by the COBE satellite
Compare Figure 4.6 with Figure 4.2 (See page 72 ) and with Figure 4.4 (See page 78 )

### Condensation of the primordial soup - page 85

#### page 86

Using the big bang equations to extrapolate back to 100000 years after the Big Bang we find that the temperature of the universe was about equal to the present temperature on the surface of the sun 5800 degrees K
This is no prove that the tempreture was actual 5800 degrees K.

#### page 86

The true history of the universe going back to t=0 remains a mystery that we are probably still far from unravelling.
This is a very honest statement The problem is that the inflation theory makes this mystery larger

#### page 89

Near the center:
The outlandish simplicity of the early universe is seen most clearly in the cosmic background radiation, the afterglow of the primeval heat.
The CMB radiation as observed in the form of radiation ("light" waves) is rather uniform, but that is no reason to assume that the processes that took place in the early universe are simple.
In fact they are very complex because in a very small time frame they changed drastically.
Thus the temperature of the early universe and presumably the density and pressure as well was uniform to this extraordinary accuracy.
Studying page 299 Appendix C Blackbody radiation this means that you can rewrite the above sentence as:
Thus the motion or the energy of the atoms and molecules in the early universe was extraordinary uniform.
The question ofcourse is if this is true.
Bottom of page 89:
Although we do not necessarily understand why the early universe was so uniform, the cosmic background radiation provides direct evidence that it was. (one of the great successes of the inflationary theory is a possible explanation for this simplicity.)
The cosmic background radiation is uniform to a large extend but that is no evidence that the universe at that moment was also uniform and homogeneous. The assumption that it is of course makes everything much simpler.
For most purposes one can approximate the early universe as being exactly uniform, greatly simplifying the calculation of its evolution.
If you do that you assume that there are no density perturbations. Infect the concept "thermal equilibrium density" disappears

#### page 90

The description of nucleoasynthesis can be started at 0.1 seconds after the big bang when temperature was 31.5 billion degrees Kelvin.
It is important to consider that the inflation period had "long ago" ended.
How do we know that at 0.1 seconds after the Big Bang the entire universe had the same temperature?

#### page 91

This temperature is so high that neither atoms nor even nuclei would have been stable - the random motion of the intense heat would have torn them apart, setting free the electrons, protons and neutrons.
Correct.
(The protons and neutrons themselves are stable at these temperatures, although at temperatures higher than 10^130K they too would be broken into their constituents called quarks)
From the evolution of the Big Bang point of view at temperatures higher than 10^130K what we had was a quark soup and when the temperature fall below this quark soup started to form protons and neutrons.
For every neutron there where 1.61 protons [1]
0.1 seconds after the Big Bang.
At this time there were 1.7 billion photons for every neutron.

#### page 92

At this time for every eight photons there were six electrons, six positrons, nine neutrino's and nine antineutrino's. There was also one electron for each proton, so that the mix was electrically neutral
The details should be interesting how this happened!
This level of detail is made possible by a wonderfully simplifying phenomenon called thermal equilibrium.
See for example: Wikipedia Thermal equilibrium
It should be remembered that temperature is a human based concept. Physical temperatures are related to the movement of the constituents of a fluid. This fluid is in thermal equilibrium when the movement is every where the same. See also Reflection 3 - Is our Universe uniform?
Suppose for example that the universe started out with only neutrons and no protons
This example is completely unrealistic.
Before there where protons and neutrons there was a quark soup. See page 123 . As a consequence of space expansion the movement (temperature) of the quarks decreased allowing the formation of both protons and neutrons.
This situation would not last long, as some of the neutrons would convert to protons by colliding with neutrino's or positrons in the hot cosmic soup as illustrated on the left side of Figure 5.2.
That means the universe started out with at least neutrons, positrons and neutrino's.

#### page 93

If enough time is allowed then the density of protons will grow until the rate of the proton-destroying reactions is equal to the rate of proton-creating reactions.
This seems to me very theoretical. IMO in only very mixed processes such an equilibrium can be reached.
The thermal equilibrium ratio of protons to neutrons at 31.5 billion degrees is 1.61, no matter where or when this situation might occur [1]
The problem is that because of space expansion the average temperature will decrease and so will this ratio change.
[1] The thermal equilibrium ratio of the protons to neutrons is equal to e^(mn-mp)c2/kT etc. mn and mp are the masses of neutron and proton etc.
General principles of quantum theory guarantee that the rates of the reactions shown in Figure 5.2 are related to each other in such a way that the equilibrium ratio of protons to neutrons is given by the formula quoted above.
Strong language. I doubt if it is that simple.

#### page 100

The frequent collisions assured that matter and radiation stayed at the same temperature, cooling together as the universe expanded.
The concept of temperature is an artificial mathematical concept. The whole issue is how uniform is the universe that means how uniform are matter and radiation mixed throughout the universe. Most probably this is not 100%.

#### page 101 nucleosysnthesis

The calculations of big-bang nucleosynthesis reached a new level of sophistication in 1967 when Robert V Wagoner, Fowler and Hoyle wrote an intricate computer code that incorporated 144 reactions etc
Each reaction at least incorporates a parameter called reaction rate which indicates how difficult (uncertain) this whole process is.

#### page 102

The graph shows how the depicted abundances depend on the density of protons in the universe
This density is unknown and changes as a function of the density of the quark gluon soup
The more protons and neutrons there are the more frequently they collide and the more helium 4 is produced.
Of course... Each reaction depends about the density of its input quantities, which makes the whole so difficult to predict.

#### page 103

Figure 5.5 (facing page) Big-bang nucleosynthesis .
The graph shows the predictions and observations for the quantities of the light chemical elements that were produced in the big bang.
The most important parameters are the initial conditions. Nothing is mentioned
The predictions (but not the observations) depend on the present mass density of protons and neutrons in the universe
The present predictions depend on the density of the protons and neutrons at the moment in order to start the sequence.
Lithium is produced by several reactions resulting in a more complicated curve on the graph.
Which makes the predictions more unreliable.
It is very difficult to astronomically estimate the density of protons and neutrons in the universe, so the nucleosynthesis calculations must be carried out for a range of possible values.
I understand that this is astronomically difficult. However this is in conflict with page 93 which indicates that the ratio is exactly known.

### Matters of Matter and Antimatter - page 105

#### page 108

If the fraction of unpaired quarks had differed appreciably from one in 30000000 then the nucleosynthesis process discussed in Chapter 5 would have been affected, producing a universe with a radically different chemical composition.
This is easy to claim but difficult to prove.
The nucleosynthesis process is much more affected by the ratio of the different quarks types. page 121
From the time that antiprotons were first produced in the Bevatron accelerator at Berkeley in 1955 physicists have found that antibaryons are produced only in combination with baryons.
A high-energy collision of two protons, for example, with a baryon number of 2, can result in a final state containing three protons and one anti-proton, which also has baryon number two.
2 = 3 - 1
However you can also think about the opposite reaction:
A collision of two anti-protons resulting in three anti-protons and one proton.
Since we believe that the observed universe has a baryon number of 10^78 the conservation of baryon number would imply that it always had a baryon number of 10^78

### The particle physics revolution of the 1970's - page 115

#### page 123 baryons and mesons.

Table 7.2 Table of strongly interacting particles.
The particles (hadrons) fall into two classes, baryons and mesons, where the baryons are on average heavier.
The mesons are also called non-baryons
In the universe current mainstream opinion is that 15% of all mass is baryonic and 85% non-baryonic.
Figure 7.1 The original quark model.
The particles called mesons are each composed of one quark and one anti-quark
Baryons are composed of three quarks. The baryon-number is either +1 or -1. For mesons the baryon-number = 0

### Grand unified theories - page 131

#### page 135

I was of course not yet aware that spontaneous symmetry breaking would figure prominently in the development of e new cosmology theory called the inflationary universe
GUTs also require spontaneous symmetry breaking and Higgs fields. Inflation theory uses the same concepts but this is different from GUTs.

#### page 139

In present-day particle theories, every fundamental particle is described as a bundle of energy of some field
That means the concept of particles, energy and fields are synonym.
The energy of the Higgs fields is concentrated into particles that are not surprisingly, called Higgs particles.
The same reasoning as above. The question arises how important this distinction is.

#### page 145

Grand unified theories not only provide a plausible description of fundamental particle interactions, but through the inflationary universe theory they can also help to explain the origin and structure of the universe around us.
GUTs also require spontaneous symmetry breaking and Higgs fields. Inflation theory uses the same concepts but this is different from GUTs.

### Combatting the magnetic monopole menace - page 147

#### page 148

The first is the creation of monopoles and the second is their annihilation. Henry and I understood neither
May be there is nothing to understand because they never existed as individual particles.
We finished the production problem by assuming that monopoles had an initial abundance approximately equal that of photons.
That is an easy "solution". How do you calculate the initial abundance of photons? You need the chemical reactions involved.
Accordingly to the standard Big Bang theory, at very early times all the known fundamental particles had the same abundance as photons to within about a factor of 2.
That is an easy assumption but is this true. Again you have to know the chemical reactions involved to create the fundamental particles.
Since we did not understand how monopoles would be produced we assumed that they would fall into the same pattern as everything else
This piece of text is very frank, but it keeps you wander.
For the annihilation we used a rough estimate based on the formula for the annihilation of electrons and positrons. Our result: The monopoles and antimonopoles that have not yet annihilated should be about 10000 times more abundant today than protons or neutrons.
If you do not know what annihilation really is how than can you trust your calculations.
IMO if they exist than monopoles are either positive or negative (magnetic) charged atoms. IMO if they exist than they already should exist before the Big Bang and they annihilated during space expansion.
Ken Wilson told us at lunch that he was not even convinced that monopoles are a valid prediction of grand unified theories.
Which leaves you thinking if there is a problem in the first place.

#### page 150

Since the monopoles would each have a mass about 10^16 times larger than a proton their enormous gravitational attraction would have caused the expansion rate of the universe to plummet.
The issue at hand is exactly what is a monopole and how are they produced.

#### page 152

The magnetic monopole is constructed from Higgs fields like those described in the previous chapter.
The word constructed is very misleading.
The simplest theory that gives rise to magnetic monopoles includes three Higgs fields which I will unimaginatively call Field A, B and C.
Unlike an electric or magnetic field which points in some particular direction in space a Higgs field has no directional properties.
This remark seems strange because considering the next page in order to describe a monopole you need three Higgs fields which combined have a directional property

#### page 153

Using this graph, the values of all three Higgs fields at any point of space can be represented by an arrow in three dimensions.
Which means that the three Higgs fileds combined have a directional property. It is important to consider that the arrow is not a physical concept.
To completely describe the Higgs field, however, we need to specify the values of all three Higgs fields at every point in space.
That seems logical. The problem is how does this field look consisting of n positif and negatif monopoles. That is nowhere discussed in this book.
There is an energy density associated with the Higgs fields and as discussed in the previous chapter the energy for the three fields is not the sum of an energy density for each of the individual fields.
As such the importance of the three fileds fades away.
Instead the energy density depends on the length of the Higgs field arrow.
The question to be answered is what is this arrow for a positive and negetative monopole IMO the "direction value" of the arrow can be both positif and negatif.

#### page 154 Figure 9.2

Figure 9.2 Energy density of a Higgs fields.
The graph shows the energy density of the three Higgs fields in the toy theory.
Figure 9.2 shows a complete arbitrary curve.
What Chapter 9 should demonstrate is the Higgs field of two or more monopoles.
In the vacuum the energy density is by definition at its lowest possible value.
This is easy to write but:
What is exactly a vacuum?
In our universe where is there a vacuum?
which specific condition decides: this is a vacuum and this is not a vacuum?
Does a vacuum contain monopoles or is a vacuum space when there are no monopoles (Higgs particles)?
The direction of the Higgs field arrow is therefore not fixed by energy considerations but is determined instead by random processes in the early universe.
We are discussing here the distribution of monopoles in early universe. The issue is what are the processes that created these processes in early universe. To claim that this are Higgs fields does not explain anything!
Since the vacuum has the least possible energy, the Higgs fields in the vacuum cannot vary from place to place.
This is the truth of a cow. (Translation of the Dutch expression: De waarheid van een koe. Which means even a cow can understand.)
The importance of course is to answer the question what exactly is a vacuum? How large is a vacuum and are all the vacuums connected.
The simplest definition in this context is that a vacuum is an area where there are no monopoles, but that is nowhere mentioned.

#### page 155

All three Higgs fields vanish at the center so the Higgs arrow has zero length and is not shown.
Easily written but what does that physical mean for the monople?
This creates a large energy density which contributes a large part of the enormous mass of the magnetic monopole.
How do you know that monopoles have a large mass? What is the definition of mass?

#### page 156

As discussed in the previous chapter, the Higgs fields were fluctuating wildly in the intense heat, just as molecules oscillate wildly at high temperatures.
It is not the Higgs field that is oscillating, it are the monopoles.
However the average value of the Higgs field at any point averaged over a brief interval of time was equal to zero.
The issue is what has this to do with the behaviour of the monopoles.
As the universe cooled below about 10^29 degrees K the Higgs fields underwent a phase transition in which the oscillations diminished and a nonzero average value was established.
The distance between all the monopoles increased.
Thus the random determination of the direction in which the Higgs arrow began to point was made indepently in many different small regions of space.
The Higgs field is always a one to one relation with position of all the monopoles in space.

#### page 157

The variation of the Higgs plural field from place to place requires energy and the energy density was decreasing as the universe expanded and cooled
It is very important to consider what we are studying: we are studying the three Higgs fields from magnetic monopoles
In fact what this sentence claims is that: When the universe expands the density of the monopoles decreases.
Next sentence:
The Higgs fields therefore smoothed out as the universe evolved, with the Higgs arrow in any region tending to allign with the Higgs arrow in neighboring regions.
It is not clear what the author physical means.
The following sketch provides an effort to make things clearer (or not)
 ``` P > ^ < P > > N < P > V ^ < P > V V ^ V < P > V ^ > N < P > N < V ^ < P > ^ V ^ < P > V < P > N > P > ```
The left part shows a region with all P monopoles
The right part shows a region with an equal number of P and N monoples.
This tendency of the Higgs field arrows to align, however, could proceed only in regions for which the neighboring regions showed some degree of consistency
What ever this means.
To estimate the amount of monopole production we must understand the degree of chaos in the Higgs fields that would result from the phase transition.
All these three concepts are very vague.
Phase transitions however are always complicated things and in this case we are trying to learn as much as possible without even knowing the details of the underlying particle theory.
All of this smells to speculation.

For more information go here: Reflection 5 - The monopole problem - Fields

### The Inflationary universe - page 167

For some general comments see : Reflection 1 - What is Inflation theory?

#### page 170

Even as the universe expands, the energy density of the false vacuum remains at a constant value, provided that we do not wait long enough for the false vacuum to decay.
Common sense tells me that when the universe expands the energy density should decrease.

#### page 171

Figure 10.2 A thought experiment to find the pressure of the false vacuum. etc
The energy must be supplied by the hand that moves the piston, so the hand must be pulling against a force.
You cannot use any thought experiment that tries to explain the processes that happened during the Big Bang.
Specific the use of words like chamber, piston and hand are out of the question.

#### page 176

The flatness problem, as you will recall from Chapter 2, concerns the quantity that astronomers call omega, the ratio between the actual mass density of the universe and the critical density. (The critical density, is the density that would put the universe just on the borderline between external expansion and eventual collapse)
When this happens the size of the Universe is constant, space expansion is zero and the Hubble constant is 0.
The issue is if this happens in the entire universe all synchronic at the same moment.
Yet the standard big bang theory offers no explanation of why omega began close to one ?
No theory explains why the Big Bang happened in the first place. No theory explains what specific exploded.

#### page 177 flatness problem

With inflation, however, the flatness problem disappears.
See specific Reflection 2
Accordingly to general relativity the mass density of the universe not only slows the cosmic expansion but it also causes the universe to curve.
Also Newton's Law describes such an behaviour. The critical issue is that this switch over period from expansion to contraction will not happen everywhere simultaneous.
then any mass density higher than the critical density causes the space to curve back on itself forming a partially closed universe as described in Chapter 3
There are two important considerations.
• On the surface of a sphere the sum of a triangle is more than 180 degrees. In principle this represents a static situation. However it is also possible that the sphere expands. Again at each instant the sum of a triangle stays more than 180 degrees. This is a geometric problem.
• A different problem is to study the radius of the universe starting from the Big Bang until present. With radius is meant the size of all space at a specific moment that is influenced by the Big Bang. This radius is the parameter that is calculated using Friedmann's equation, as a function of different cosmological parameters.
The radius can be also closed, flat or open. This is not a geometrical problem but a physical problem.
I do not understand why Alan Guth does not make a clear difference between the two.
Approximate at the center of the page:
In such a (closed) universe the sum of the angles in a triangle is more than 180 degrees.
Suppose our Universe is such an universe how would you measure the angles of such an triangle?
I expect that you start from an assumed flat surface and you draw a figure along the length of three straight rods of equal length, which ends meet. Generally speaking the angles should be identical and the sum of the angles should be 180 degrees. To test the second you divide a circle in 6 equal parts which gives you a standard angle of 60 degrees. Using this standard you can decide in principle if the universe is closed.
However does this also work in practice? In practice you do not know because there is no way to actual test this.
Next:

#### page 178

Figure 10.4 The solution of the flatness problem
The inflationary solution to the flatness problem is illustrated by this sequence of perspective drawings of an inflating sphere
Therefore as inflation drives the geometry of the universe towards flatness the value of omega is driven toward one.
Frame one shows a sphere, the outside of a closed universe with radius R.
Frame 2 shows a small section of the outside of a larger sphere with radius 3R.
Frame 3 shows a small section of the outside of a larger sphere with radius 9R.
Frame 4 shows a small section of the outside of a larger sphere with radius 27R.
But does that mean that the density of this universe is equal to the critical density?
Can inflation describe the future of the universe ? Reflection 2

#### page 181

Since the universe in the big bang theory has a finite age, there is a maximum distance that light could have travelled since the beginning of time.
The issue is much more that there is maximum distance that the (our) universe could have expanded since the big bang.
This distance is called horizon distance where the word "horizon" is used in the sense of a limitation on our knowledge.
The concept "horizon distance" should have nothing to do with our existence or knowledge. It should be a purely physical concept.

#### page 182

The CMB radiation shows us, among other things, that the universe at 300000 years was incredibly uniform, since the temperature of the radiation is found to be the same in all directions to an accuracy of about one part in 100000.
It is not the temperature to be found to be uniform but the frequency.
It is natural to ask therefore whether we can understand how this extreme uniformity was established.
It should be mentioned that CMB radiation shows information about a sphere. Not what is inside the sphere (nor outside).
The speed with which heat energy can be moved from one place to another, however, certainly cannot exceed the speed of light, and so the transfer of heat in the early universe is limited by the horizon distance.
IMO this implies that the horizon distance calculation cannot include processes faster than the speed of light
At 300000 years after the big-bang the horizon distance was about 900000 light-years
This distance is correct using friedmann's equation and assuming the standard cosmological parameters as described in Friedmann Lambda = 0.01155

However this distance also assumes that one way or another speeds faster than the speed of light are involved.
Next we read at page 182:
If we consider two photons arriving today from opposite directions in the sky, then we can use the mathematics of the Big Bang Theory to trace back the trajectories to 300000 years after the Big Bang. The calculation which takes into account the expansion of the Universe shows that the photons were emitted from two points about 90 million light-years apart as illustrated in Figure 10.5
That means 90 millions divided by 900000 = 100 times the horizon distance. (*)
I think this reasoning is misleading. The distance of the two points A and B 300000 years after the Big Bang was 2 * 900000 light years. The distance of the two points now is 2 * 35 billion light years.
For a better understanding select: Friedmann's equation - The path of a light ray This document gives an impression about the present size of the universe but what is more important the size of the universe based on when the events happened what we observe.

#### page 183 horizon problem

* Accordingly to the Big Bang theory the separation between points A and B in Figure 10.5 grew from 0 to 90 million light-years during a time interval of only 300000 years.
That is not true. The distance grew from 0 to 900000 lightyears.
Nonetheless the distance between two particles can increase due to the stretching of space between them, and general relativity places no restriction on how fast the stretching can occur.
The stretching of the expanding universe is roughly a factor of 3.
It should be remembered that all what happened after the Big Bang are all physical processes. General Relativity can only describe these processes.

#### page 184

The horizon problem is not a failure of the standard big bang theory in the strict sense, since it is neither an internal contradiction nor an inconsistency between observation and theory.
A difficult sentence.
One of the most salient features of the observed universe - its large scale uniformity - cannot be explained by the standard big bang theory; instead it must be assumed as an initial condition.
300000 years after the Big Bang the radius of the universe was at least 900000 light-years. At that distance chemical processes took place which emitted radiation at high frequency and temperature we now observe at low temperature and low frequency. The Big Bang explains this change in frequency (cooling) as stretching of space. Nothing more nothing less.
There exists no horizon problem
For more about the observed universe read this: Reflection 4 - The Observable Universe?
To understand how inflation eliminates the horizon problem, the first step is to recognize that the size of the presently observed universe is what it is, independent of one's theories of how the early universe evolved.
The issue is not the size of the presently observed universe because there is or exists not something as the "observed universe". What we observe is an image of the state of the universe of all what changed after the Big Bang.
Next:
Whether we believe in the standard big bang theory or inflation or even the steady state theory the most distant objects that we can detect are about 20-30 billion light-years away.
What Alan Guth should have added is: at present.
The seeds of the furthest objects we observe now is the microwave background radiation. The distance of the objects we observe now at the time when the events happened (super novae) and the distance of these same objects at present is a function of the cosmological model (parameters).
Next:
(There are presumably other objects even more distant than this, but since we cannot see this far, these objects are outside the observed universe)
The challenge of science is to investigate as much as possible what we know about our universe i.e. all what happened after the Big Bang. It is important to remark that of the present state of the universe we can only observe a tiny bit. All the rest is based on the cosmological model we use.
For more about the observed universe read this: Reflection 4 - The Observable Universe?
Next:
To trace the history of the presently observed universe we need to adopt a theory of how the universe evolved.
It is important to consider in many cases what we observe are supernovae which happened in the past. Each of these supernovae show an image of the state of the universe in the past, when the size of the universe was smaller than at present. As such the word "observed universe" is misleading.
During the brief period of inflation, however the inflationary theory describes an enormous burst of expansion that is not predicted by the other theory.
That is not taken into account by the other theory
When you perform a simulation of expansion of the universe using the friedman equation than you must assume that at t=0 the size of the universe increased with a certain amount. Other wise there is no universe. The interesting fact is that it almost does not matter how large this initial step: the size of the universe at present is almost the same and is much more a function of the cosmological parameters than of the initial step size.
For more information select: Friedmann's equation - Question 14 What is the influence of the parameter V0 (Which defines the first step size at t=0) compared to the inflation theory.
Almost at the end of page 184:
Nevertheless, it is clear, that before inflation the observed universe was incredibly small.
It is clear that at one moment the universe was clear (because we assume an expanding universe but it is not clear that inflation (fast expansion interval) has anything to do with this.
The biggest problem is why does he use "observed universe" in stead of "the universe" or "our universe" ?
Next is written:
There was plenty of time for such a small region come to a uniform temperature, by the same mundane (everyday) processes by which a hot cup of coffee cools to room temperature.
The second part is true but the logic in the comparison raises certain questions:
1. Why does he use the word temperature, which is a human based process. You should describe this with terminology relevant for the processes involved.
2. What we are discussing is the time extremely shortly after the big bang, the state of which is purely speculation. Most probably many different processes happened simultaneous. It is very difficult to assume that all the changes which happened, happened everywhere synchroneous, simulataneous in harmony.
Next, at the bottom of page 184:
Then, once the uniformity was established in this very small region, the process of inflation stretched it to become large enough to encompass the entire observed universe.

#### page 185

Thus the uniformity in temperature throughout the observed universe is a natural consequence of inflation.
This is easy to write, but the details are lacking. With details I mean, the description of the physical processes that took place.
Anyway the use of the word: Observed Universe is very misleading. Inflation, when its happens, has nothing to do with the observed universe. It should describe the evolution all that happens (in our Universe) after the Big Bang (Our BB).
For more about the observed universe read this: Reflection 4 - The Observable Universe?

#### page 186 - entire universe

Applying this reasoning to the sample numbers shown on Figure 10.6 we find the entire universe (our universe) is expected to be at least 10^23 times larger than the observed universe.
The concept of size of the observed universe is not clear. However such a huge universe also raise a serious problem when our universe is supposed to be closed, because such an universe is supposed to decrease in time and shrink to a point. Such a process for how larger the universe presently is, is physical impossible.
At the same time what we should try to study is the entire universe i.e. all what was changes after the Big Bang.

### The aftermath of discovery - page 189

#### page 193

Although inflation seemed a panacea for all cosmology's ills. there was still an important unresolved issue: how exactly does inflation end?
How exactly does inflation start?
The complication however is that inflation must end. The energy of the false vacuum must be released to produce the "ordinary" matter that populates the universe today.
The picture emerges, that matter is converted to false vacuum at the start of inflation and back to matter at the end of inflation. During inflation false vacuum also produces bubbles. Remarkable.

### The new inflationary universe - page 201

#### page 208

The Higgs fields that drive the inflation are a theoretical invention, so the nature of these inflation fields cannot be deduced from known physics.
The processes that drive inflation should be properly understood. That is important. The inflation filed as such is of much less importance.
The secret of new inflation is to choose a special shape for the energy density graph of the inflationary Higgs fields
The question to answer is if during the period of inflation there are different inflationary Higgs fields involved: One before, one during and one after.

#### page 209

The desired shape which might be called a flattened Mexican hat, is illustrated in Figure 12.1
Figure 12.1 shows a Mexican hat. Inside almost in the center lies a small ball.
The question to answer is: what is the meaning of the ball?
I expect that the ball resembles the Universe. But if that is the case the Higgs field is much larger as the Universe, which is impossible.
The evolution of the Higgs field can again be visualized as the motion of a ball rolling on the hill of the energy diagram.
The question to answer is what has the evolution of the Higgs field to do with the size of the Universe.

#### page 210

In the original inflation theory, with the dented Mexican energy diagram the phase transition follows the paradigm of boiling water.
With the emphasis on dented. See page 211
If the energy density of the Higgs fields is described by the flattened Mexican hat diagram, however, then this scenario is totally different.
It is easy to draw these two different hats...
As shown in figure 12.2(f) the Higgs field throughout this huge region oscillates and converts its energy to a hot soup of particles, exactly as required for the standard hot big bang model.
This text is very interesting because mainstream opinion is now the LCDM model (Lambda Cold Dark Matter model)
All of the successes of the original theory are preserved by the new inflationary universe and the graceful exit problem disappears completely.
This looks like a Win Win situation. But is this correct?

#### page 211

 ``` x x X x x x x x x x x x x x x x x x AB x x x x x x X C Figure 10.1 Figure 12.2(a,b,c) Old Inflation ``` ``` x x X x x x xDx x x E x x x x x X F Figure 12.2(d,e,f) New Inflation ```
Figure 10.1 from page 168 shows the dented mexican Hat. Figure 12.2 shows the flattened Hat.
The letter A shows the position of the ball in Figure 12.2(a). B = Figure 12.2(b) etc.
The letter D shows the position of the ball in Figure 12.2(d). E = Figure 12.2(e) etc.

### Wrinkles on a smooth background - page 213

#### page 213

One of the great virtues of the inflationary theory is its explanation of the large scale uniformity of the universe.

#### page 215

In the new inflationary theory, on the other hand, the randomness off bubble formation is not a factor.
What are bubbles? Where are those bubbles?
In this version of the theory the entire observed universe is assumed to lie deep in a single bubble, so any bubble collisions are far too remote to have any observable effects.
Apparently there are more versions.....
The issue is not the observed universe but the state of all what changed after the Big Bang i.e. the entire universe. See also page 186 entire universe
For more about the observed universe read this: Reflection 4 - The Observable Universe?

#### page 216

Hawking discovered that quantum effects cause black holes to emit radiation with the same spectrum as a hot object, the blackbody spectrum discussed in Chapter 4.
I expect it is much more: Hawking proposed.
The temperature of the black hole depends on its mass, with the temperature becoming higher as the mass becomes smaller *
(* The temperature is found by dividing a number by the mass of the black hole)
This means that how smaller the black hole how larger the temperature.
Studying page 299 Appendix C Blackbody radiation this means that how smaller the Black hole the larger the movement of the atoms and molecules.

#### page 217

In the inflationary theory, perturbations created by quantum processes on subatomic distance scales are rapidly stretched to the size of galaxies or even larger than the observed universe.
This same process will make the scenario that the universe will collapse or is closed very unlikely. See also page page 22

#### page 218

In other places the Higgs field will roll a smidgen slower, prolonging inflation and its associated production of matter. The result would be a slightly nonuniform distribution of matter at the end of inflation. as illustrated in Figure 13.1
Figure 13.1 means nothing. The issue is how the Higgs field does this in detail or is this something we wish?
page 213

### Observational clues from deep below and far beyond - page 237

#### page 237

Inflation, we discovered, must be driven by a field with an extremely flat energy density diagram or else the resulting density perturbations would be too large.
The inflation theory is characterised by two discontinuous events: One to start a extremely small period of rapid expansion and one to stop this period. The biggest problem is to explain these two events.
At that time the unification of the weak and electromagnetic forces was the major open question in particles physics and theorists had thrashed out a bewildering array of theories that accomplished this goal.
The unification of the electro and magnetic forces is an unification of both forces and fields. The one causes the other (to change) and vice versa.
For more information about the current state of what is called the Electroweak interaction see Wikipedia: Electroweak interaction. In short at the start of the Big Bang the four fundamental forces of nature did not exist.

#### page 238

Since inflation is so successful in explaining the origin of matter, the flatness of the early universe and the large scale uniformity of the universe it seems reasonable to just accept the smallness of the observed density perturbations as a measurement of the energy density diagram of the inflation.
I have great doubts of this whole reasoning.
Water can boil and freeze but do we really know how this happens at these precise instances (environment) ?

#### page 241

Paul Steinhardt handed me a piece of paper that he had been given by the COBE team.
The graph on the piece of paper is shown as Figure 14.1
For a detailed discussion see this: Critical evaluation of Power Spectrum calculation in the book "The Inflationary Universe"
The key point, however, is simple: The agreement between the data and the predictions of inflation was nearly perfect.
The undulations of the small triangles indicating the data points followed faithfully the shaded gray band that showed the consequences of the scale-invariant density perturbation spectrum predicted by inflation.

#### page 242 Figure 14.1

Figure 14.1 shows two types of information:
• Computed points shown as small triangles with the estimated uncertainty shown as a vertical line extending above and below the point. In the range from 0 to 180 degrees roughly 36 computed points are shown with 5 degrees interval.
• For all these points the gray band shows the theoretically predicted range of values corresponding to the scale-invariant spectrum of density perturbations arising from inflation.
Page 242 does not give the information how this theoretically predicted range is calculated and what exactly inflation has to do with this. To be more specific you need two bands: one with and one without inflation. .

### The eternally existing self-reproducing inflationary universe - page 245

#### page 245

A cosmological theory lives or dies on the basis of the description it predicts for the observable universe.
A cosmological theory should describe the evolution of the entire universe. This should be supported by what is observed.
In a certain sense it is the other way around: based what is observed we make a prediction what the description is of the entire universe. Future observations should support these predictions. If not than the theory should be adjusted.
Regarding the concept of Observable Universe read this: Reflection 4 - The Observable Universe?
While we can never expect to test the predictions of inflation for the region beyond the observable universe there is no way that we can prevent ourselves from thinking about it.
We should always be carefull about theories which make additional predictions that cannot be observed i.e. proved.
The driving force behind inflation, you will recall, is a peculiar state of matter called false vacuum.

#### page 246

I will call such a region a "pocket universe"
Such a name is very misleading
The pocket universe on the other hand is only a minute fraction of all that exists so in that sense it is only a "pocket"
Of all that exists is the entire universe. That is what we should study.

### Wormholes and the creation of universes in the laboratory - page 253

This whole chapter is rather speculative
If meringue is made by beating egg whites and sugar how do you make a universe?
First of all you need a good definition of what you mean with a universe and what with two universes. .
Secondly suppose some claims: "Eureka I have made a universe." what are the tests or experiments to test this claim.
All of this is rather speculative
Since the inflationary theory implies that the entire observed universe can evolve from a tiny speck it is hard to stop oneself from asking whether a universe can in principle be created in a laboratory.
The Big Bang presupposes that (our) entire universe evolved (predated) from a tiny speck.
The next step is to try to create in a laboratory the earliest conditions of the universe
For more about the observed universe read this: Reflection 4 - The Observable Universe?

#### page 254

If the recipe for the standard big bang universe were written in a Cookbook how would it read? To begin the universe at an age of one second the ingredient list include 10^89 photons 10^89 electrons 10^89 positrons 10^89 neutrinos 10^89 antineutrinos 10^79 protons and 10^79 neutrons.
Unfortunately the quarck soup is not discussed.
anti-matter: anti-protons and anti-neutrons are not discussed
The ingredients should be stirred vigorously to produce a uniform batter which should then be heated to a temperature of 10^10 degrees K.
Mixing is a typical human task. It is much more realistic to assume that the soup after 1 second was not uniform. That the density distribution was not homogeneous.
If inflation is driven by the physics of grand unified theories a patch of false vacuum 10^-26 centimeters across is all the recipe demands
This is easy to write but physical very difficult to accept.
While the mass required for the previous recipe was 10^32 solar masses, the mass in this case is only 10^-32 solar masses.
This is easy to write but physical very difficult to accept.
Both tremendous large and tremendous small numbers are difficult to accept.

#### page 255

So, in the inflationary theory the universe evolves from essential nothing at all, which is why I frequently refer to it as the ultimate free lunch.
The most difficult part of the Standard Big Bang theory is how did it all began. For the inflation theory this is the same.
Does this mean that the laws of physics truly enable us to create a new universe at will?
The laws of physics are descriptions of physical existing processes.
If we tried to carry out this recipe unfortunately, we would immediately encounter an annoying snag: since a sphere of false vacuum 10^-26 across has a mass of one once, its density is a phenomena 10^80 grams per cubic centimeter!
The snag or unbelievable "fact" is in the claim that a sphere of 10^-26 has a mass of one ounce.
In this context, I will discuss whether the laws of physics in principle allow such an advanced civilization to create a universe.
Physics has nothing to do with advanced civilizations
Laws are descriptions of the specific circumstances of identical processes.
Newton's Law is a description how objects (masses) move in "vacuum".

#### page 256

So, to complete the construction it would be necessary to rapidly sweep away the ordinary matter leaving only the inflation field in its false vacuum state.
What is ordinary matter? How do you remove that?
Once a patch of false vacuum is created the evolution is independent of how it was created.
Seems to me an empty statement.
The false vacuum is characterized by having a huge energy density which cannot decrease as the volume expands and a huge but negative pressure.
This huge energy density is explained because a false vacuum is extremely small.
This seems to be in conflict with the concept of a free lunch.

### Epiloque - page 277 - new inflation

Vey shortly after new inflation was proposed, Andrei Linde proposed yet another variant called chaotic inflation
While new inflation depended on having a plateau in the energy density diagram as in figure 12.1 on page 209 the chaotic model showed that such a plateau is not necessary at all.
When you design a a new law which invalidates an other old law you should clearly indentify what is wrong with the physical observations of the old law compared with the observations (predictions) of the new law.
If the ball that represents the values of the field starts high enough up the hill at the side of the bowl then sufficient inflation can occur as the ball gently rolls to the point of minimum energy density.
It does not look very scientific when you try to explain something global using a concept like a field while in practice it is impossible to measure this field.

#### page 278 - extended inflation inflation

In the late 1980s Paul Steinhardt and Daile La invented yet another version of inflationary cosmology called extended inflation which differed from the previous successful models chiefly in the way that inflation ends.
If you propose a new model with a different ending as an old model than either one is wrong.
The ending of extended inflation, however, closely resembled that of the original inflationary model (See page page 167 ) Many small bubbles of normal matter would form in the midst of the false vacuum, vey much like the boiling of water.
The picture is that matter is created out of almost nothing. See also page 254

#### page 282 - open inflation

Open inflation is similar in many ways to new inflation, except that one assumes that the amount of inflation that occurs as the inflation field rolls down the hill in the energy density diagram is limited and insufficient to drive the universe to flatness,
Reading this text you get a clear indication how simple everything is.

#### page 287

The universe in which we live has all the expected earmarks of inflation:
1. It contains a vast quantity of matter and energy
2. it is undergoing uniform expansion.
3. the early universe is known to have been extraordinary close to the critical density
4. the universe is homogeneous on very large scales
5. the nonuniformities observed on smaller scales are compatible with the nearly scale-invariant spectrum of perturbations that is predicted by inflation.
IMO it is very difficult to claim that the points 1-4 are typical of the inflation theory.
For a comment about #3 see below.
For a critical evaluation of the spectrum see here: Critical evaluation of Power Spectrum calculation in the book "The Inflationary Universe"
Next he writes:
• To me, the most impressive piece of evidence for inflation is the flatness problem - the closeness of the mass density of the early universe to the critical value.
That means that omega(m) = 1 and that Lambda or omega(Lambda) are equal to zero
These are parameters of the friedmann equation which describes the evolution of the earth.
The problem is that the mainstream point of view is that Lambda is not zero and that the density of the universe is not equal to the critical density. See: Friedmann L=0.01155
The question is how do you measure the mass density at the early universe and the critical density?

### Newton and the infinite static universe - page 295

Newton wrote in December 1692:
But if the matter was evenly disposed throughout an infinite space, it could never convene into one mass; but some of it would convene into one mass and some into another so as to make an infinite number of great masses scattered at great distances from one to another throughout all that inifite space. And thus might the sun and fixed stars be formed supposing the matter were of lucid (clear) nature.
There is nothing wrong with this description.
When you take fish food (granules), you grind these granules into powder and you throw this powder into a pond. What you will see is that the tiny particles will create something like a film of dust particles on top the water. Next adjacent particles will move towards each other and form larger particles. This process will repeat until all initial particles are amalgamated into larger structures. Also these structures will almalgamate in larger ones.

#### page 297

The failure of Newton's reasoning is an illustration of how careful one has to be thinking about infinity
The only thing to decide who is right or wrong is by performing an experiment.
From the modern viewpoint an infinite distribution of matter under the influence of Newton gravity would unquestionably collapse.
If you start with an uniform (infinite) distribution of matter why should it all collapse? This has nothing to do in principle with any Law.
The following text is modified:
Suppose that two spheres of mass A and B have the same density of matter and that sphere B has the same radius of sphere A. Suppose further that each sphere consist of a distribution of particles such as stars. Since the stars will not start to press against each other when the spheres begin to contract there will be no pressure forces to resists the contraction.
The critical question to answer is why will each of the spheres collapse?
If a sphere collapses the sphere did not exist in the first place. So what is the problem ?
The problem is in the initial conditions . For a sphere of particles to exist in empty space the particles should have a speed to resist gravity. In fact the speed of all the particles should such that the total energy (a vector) should be zero.
The same problem exist if you want to demonstrate the viral theorem.
Next:
It can be shown that gravity will cause both spheres to collapse in exactly the same amount of time (independent) of their radius.
That is one question. A more important issue is that the sphere will not exist in the first place.

### Blackbody Radiation - page 299

Starting with thermal equilibrium it is well known today that temperature is really just a measure of the random motion of atoms and molecules. To make this notion quantitative one would like to know how to relate the average energy of these random motions to the temperature
What this means that instead of using the word temperature (which is a human based concept) it is much more appropriate to use the wording: (random) motion of atoms and molecules.
When you consider the BB it is this motion (around some arbitrary point for each atom or molecule considered) which decreases in time

### Reflection part 2 - Problems solved?

The inflation theory is supposed to have solved certain cosmological problems but at the same time it creates also new problems.
The problem is that when a theory solves a problem how do you know in the first place that there was a problem because you have solved it?

• One case in point is the flatness problem. See page 177 flatness problem
Inflation also solves the flatness problem.
The problem is what exactly is the flatness problem ?
• From one point of view this is a geometric, mathematical problem. As discussed in page 44 .
• From an other point of view assuming that geometry is flat it is a physical problem. In such a view our universe can also be open, flat and closed as a function of the total mass of the universe.
IMO Inflation has nothing to do with this.

• A different case is the horizon problem. See page 183 Horizon problem
Inflation also solves the horizon problem.
The horizon problem is to some extend a communication problem related to the size and the uniformity of the universe. Both are in conflict with each other. By introducing inflation the problem is solved...
As claimed above the inflation theory also creates new problems.
• At page 75 is written (most probably) that the entire universe (at present) is far from homogeneous. That is most probably true. See also Reflection 3 - Is our Universe uniform?
• page 186 entire universe shows that as a result of inflation the size of the entire universe is 10^23 larger than the observed universe. This impressive expansion already happened immediate after the Big Bang page 185 however Figure 10.6 does not show this difference between the standard theory and the inflation theory.
• What is the impressive physical mechanism that caused this expansion and which mechanism caused it to stop. The tools (capabilities) should already be available immediate after the Big Bang. The inflation theory is something like a second Big Bang. The characteristic of every explosion is that it causes inhomogeneities. The characteristic of rest is that it causes homogeneities.

A much more interesting problem is the following:
When you study the chemical processes during the evolution to a large extend it is an open system. It is not a closed system which are the chemical processes happening in chemical production plants here on earth. There is also no feedback involved. Feedback means that the output (final state) flows influences the input flows. Feedback loops exists in rotating stars which eject material in the rotating axis and collect material in the plane perpendicular to this axis.
Starting from the assumption that we have an open system how is it possible that throughout the entire universe we almost have every where the same chemical elements from the periodic table as the building blocks for the stars and galaxies. This question is interesting because the primary building blocks are the same (quarks) but the places were these present day processes take place are far apart and no communication is involved between them.

### Reflection 3 - Is our Universe uniform?

Uniformity of our universe implies that the distribution of all the different constituents of the Universe during its entire evolution is every where the same. That means: in place and time.
Uniformity is closely related to Thermal equilibrium which implies that temperature is every where the same. See also page 92
Both concepts IMO are not realistic in an expanding universe because they require instantaneous communication (at least larger than space expansion)
This is difficult direct after the start of the Big Bang where the universe was relative small but the physical changes big.
This is also difficult much later because the Universe became much larger.
Part of the problem is what you can call a mixing problem.

For nucleosynthesis this implies that the reactions representative should all happened everywhere simultaneous in order that the universe stays uniform and homogeneous.

### Reflection 4 - The observable Universe

Throughout the book at many places the concept "The observable Universe" is used. This concept is very misleading because it gives an idea that there exist an universe we can observe.
See For example page 75 , page 184 , page 185 , page 215 , page 245 and page 253
What the standard Big Bang assumes is that our Universe started from a tidy speck which "exploded" and expanded. At this initial point the Universe had an extreme high temperature and cooled down until a temperature of 2.7 degrees K. During the whole evolution the composition of the universe changed uniform until at present.

The important point is that from the entire universe we can only observe a tidy part how the situation is at present. The further away the earlier we can again only observe a tidy part of the universe how the state was at that moment. The furthest away is 300000 year after the Big Bang but also of that moment we can only observe a small part of the entire universe, most of it will be inside this sphere.

What is important that you can not speak of the observable universe with the idea that it is an entity, something that exists. The individual objects we observe galaxies quasars and supernovae are entities. As a total collection they are not an entity because each of them is observed at a different age.

### Reflection 5 - The monopole problem - Fields

In Chapter 9 Combatting the magnetic monopole menace the magnetic monopele "problem" in relation to the inflation problem is discussed.

There are two types of monopoles: Positif charged and negatif charged.
If there are monopoles than a piece of iron should contain many, all scatered throughout the piece at random locations. When the piece is magnetized all positif charged should move to one region and the negatif charged into the oposite direction.

At present there no monopoles. The standard Big Bang theory claims that in the early universe there should be many monopoles. Without inflation there still should be many. The huge stretching of space (inflation) solves this issue.

Part of the solution discussed are Higgs fields. The problem by introducing fields is that they do not solve anything physical, because the fields them self also should be explained.
The Higgs fields are subdivided into 3 types: X,Y and Z and together they define an arrow.
The problem is that the book not clearly discusses

• what the differences are between a field of a positif monopole versus a negatif monopole.
• How the fields of each type are created
• How the fields are annihilated

The worst is that may be the whole monopole problem has nothing to do with inflation because there were never any monopoles or if there were they are all collected inside iron atoms and molecules.