• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.

When we look at the CMB it comes from 46 billion comoving light years away. However, when the light was emitted the universe was much younger (300,000 years old).
This text is wrong. The CMB radiation we observe now comes from a distance of roughly 300000 * 3 = 1 billion light years when the "light" was emitted. The present distance maybe is 46 billion lightyears but probably less.
In that time light would have only reached as far as the smaller circles.
In that time the total diameter of the universe was 2 billion light years and expanding. That is the only physical important issue. We humans don't know what the state is of the universe at its outer border. What we only know that the state of the universe 300.000 after the Big Bang was highly uniform as indicated by the CMB radiation we receive at present.
The two points indicated on the diagram would not have been able to contact each other because their spheres of causality do not overlap.
That is of no physical significance.

### 1.1 Astronomical distances and particle horizons

When one looks out into the night sky, distances also correspond to time into the past.
A galaxy measured at ten billion light years in distance appears to us as it was ten billion years ago, because the light has taken that long to travel to the viewer.
This is not correct. The distance of a galaxy we observe now as of ten billion years ago is not 10 billion lightyears. It is true that light has travelled a distance of 10 billion lightyears. See also Reflection 1. Horizon Problem There are two distances involved the distance in the past when the light was emitted and the present distance. To calculate this distances select: friedmann's equation L=0.01155
The Yellow line is a good indication for the path that the galaxy followed.
At 3.7 years after the Big Bang the distance was roughly 7 billion light years.
At present the distance is roughly 22 billion light years.
If one were to look at a galaxy ten billion light years away in one direction, say "west", and another in the opposite direction, "east", the total distance between them is twenty billion light years.
Also here there are two distances involved.
At the moment of emission the distance was 14 billion Years
At the present the distance is 44 billion light years
This means that the light from the first has not yet reached the second, because the approximately 13.8 billion years that the universe has existed is not a long enough time to allow it to occur.
Light (The speed of light) has nothing to do with this problem. The reason of the problem is physical.

### 1.2 Causal information propagation

In accepted relativistic physical theories, no information can travel faster than the speed of light. In this context, "information" means "any sort of physical interaction".
The whole issue is that "all what changes" in any physical process has a finite speed. Photons as such have a finite speed.
Given the example above, the two galaxies in question cannot have shared any sort of information; they are not in "causal contact".
Again also here two different issues should be discussed: Their position at emission and the present position. For a physical explanation there is no real difference in the two.
One would expect [why?] , then, that their physical properties would be different, and more generally, that the universe as a whole would have varying properties in different areas.
If you look to different galaxies in the past they apparently have different features. For example see here: Galaxy rotation curves present and past
Anyway from a physical point of view there is nothing wrong that the universe appears everywhere the same. The same implies that we see galaxies everywhere but. The difference is that galaxies are in clusters.
I do not see the problem.

### 1.3 Homogeneity and isotropy

Contrary to this expectation, the universe is observed to be very close to isotropic, which also implies homogeneity.
It should be mentioned what we observe is the state of the universe in the past.
The cosmic microwave background radiation (CMB), which fills the universe, is nearly the same temperature everywhere in the sky, about 2.728 ± 0.004 K
The CMB we observe now is almost the state of the universe directly after the Big Bang. The radiation (light) has almost travelled a distance of 13.7 billion years and the whole issue is if the fluctuations we observe now are a good indication of the state at emission.
This (the difference in temperature) presents a serious problem; if the universe had started with even slightly different temperatures in different areas, then there would simply be no way it could have evened itself out to a common temperature by this point in time.
How do we know this? The whole issue is to what extend the CMB radiation we observe to day is a one to one image of the period, imate after the Big Bang, when it was emitted. I doubt that. A lot of the radiation we receive to day can be based on reflection.
This (the decoupling) is thought to have occurred about 300,000 years after the Big Bang.
Most probably at that time the universe was rather uniform.
The volume of any possible information exchange at that time was 900,000 light years across, using the speed of light and the rate of expansion of space in the early universe. Instead, the entire sky has the same temperature, a volume 10^88 times larger
The radius of the universe 300,000 years after the Big Bang was roughly 900,000 light years assuming space expansion of roughly 3*c. There after the universe expanded continuously until its present radius of 46 light years. The biggest issue the typical processes that everywhere took place.

### 2. Inflationary model

The theory of cosmic inflation has attempted to address the problem by positing a 10^-32 second period of exponential expansion in the first seconds of the history of the universe due to a scalar field interaction.
The expansion of the universe has nothing to do with a scalar field interaction. Such concepts should not be issued. The issue is physics not mathematics.
This scalar field is caused by something. The issue is what is this something.
According to the inflationary model, the universe increased in size by an enormous factor, from a small and causally connected region in near equilibrium. Inflation then expanded the universe rapidly, isolating nearby regions of spacetime by growing them beyond the limits of causal contact, effectively "locking in" the uniformity at large distances.
It should be remembered that the inflation period only happened in a very very short time. The influence as such is limited.
The theory predicts a spectrum for the anisotropies in the microwave background which is mostly consistent with observations from WMAP and COBE.
IMO it is impossible to demonstrate that the spectrum of the CMB radiation is in any way influenced by a rapid period (burst) of expansion.
However, in order to work, and as pointed out by Roger Penrose from 1986 on, inflation requires extremely specific initial conditions of its own, so that the cause of initial conditions is not explained: "There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process.
Also the initial conditions are very difficult to make acceptable.
A recurrent criticism of inflation is that the invoked inflation field does not correspond to any known physical field, and that its potential energy curve seems to be an ad hoc contrivance to accommodate almost any data obtainable.
The issue is much more about the true physical processes that caused such a burst of expansion throughout the universe.

### 3. Variable speed of light theories

Classically, varying speed of light cosmologies propose to circumvent this by varying the dimensionful quantity c by breaking the Lorentz invariance of Einstein's theories of general and special relativity in a particular way.
This is a very unclear sentence.

### 3.1 Petit model

According to this model, the cosmological horizon grows like R, the space scale, which ensures the homogeneity of the primeval universe, which fits the observational data.
If you want to force homogeneity you should assume that the average expansion speed decreases as a function of time. From a physical point of view, this has nothing to do with the speed of light.
In some sense there are two issues: The expansion speed and the speed of light.

### 3.2 Later models

The idea from Moffat and the Albrecht–Magueijo team is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions of the expanding universe have had time to interact at the beginning of the universe.
Interaction is a physical issue and has nothing to do with the speed of light.

### Reflection 1. Horizon Problem

Physical Phenomena should be explained starting from the environment and physical reactions that take place. The origin of Horizon Problem is the human point of view. We humans observe that there is a problem and the solution is the concept of inflation. We almost don't take care what the physical situation was in the past which can (within its own limits) could explain what we observe now.

The main stream opinion is that the Universe started with a Big Bang. This happend 13.7 billion years ago. At that same moment the Universe started to grow (expand) with a speed of slightly more than 3*c. There after the speed slightly slowed down and is now increasing again. This without considering inflation. To get an idea about this process please visit: friedmann's equation. This document shows that the present size of the universe is roughly 45 billion light years and what is the most important that of the total universe we can only observe a small bit, all in the past.

What this document also clearly shows is that what we observe now are events in the past.
 c = 60 Lambda = 0,01155 v0 = 3 The black line represents the outer edge of the universe. The black line is also called the 100% line. The blue line represents the trajectory of a photon that reaches us at present. The total length is 13.7 billion light years. The blue line starts where it crosses the the black line. This is roughly 300000 years after the Big Bang. That is the period of the CMB radiation. The pink line is the 80% line. It represents the evolution of the universe at 80% distance of the outer edge. The pink line crosses the blue line (an event) at 1 billion years after the Big Bang. That event happened at a distance of roughly 4 billion light years. That event is now at a distance of 28 billion lightyears. The yellow line is the 60% line. The pink line crosses the blue line (an event) at 2.5 billion years after the Big Bang. That event happened at a distance of roughly 6 billion light years. That event is now at a distance of 22 billion lightyears. When you study the blue line you can see that it reaches its maximum 4 billion years after the Big Bang. The distance is then 7 billion lightyears. This is the maximum we can observe.
There are (at least) two physical issues within the context of the Big Bang.

• The first issue is that we observe only a small fraction of the universe. This raises the issue to what extend based on our observations we can claim something for the whole universe.
• The second issue is that the average expansion speed of space is much larger than the speed of light. This is the physical reason of the horizon problem, which maybe is not a problem at all. The horizon problem has nothing to do with what we humans observe but all with the physical processes after the Big Bang, which in principle don't require any form of inflation (extra expansion).

### Reflection 2. Information and the speed of light.

All references to Information in the document should be modified, because it is misleading.
Within the concept of the Big Bang different era's are considered and the whole issue is to what extend there exixts a clear boundary between each.
The Book the Big Bang by Joseph Silk considers the following: Plank time, Inflation, Hadronic, Leptonic, Radiation, Matter and Decoupling. All of these Era's are charectorized by different processes which should take place in the whole of the expanding Universe.
Generally speaking photons are of no importance in these processes (or minimal). The speed of light is most important to make observations.

One question to answer is: can an observer outside the Universe (as created by the Big Bang) observe the Big Bang.
The issue is, if from the outside all the matter that caused the Big Bang is not something like a hugh black hole from which no light can escape? If that is the case an observer from the outside cannot visible observe the Big Bang.

### Reflection 3. Inflation theory versus Horizon problem.

The inflation theory was supposed to solve the Horizon problem. The Horizon problem is partly based on the observed uniformity in the Universe. This uniformity is considered a problem because how can different patches be similar when at present the distances between these patches is extremely large. The most probably reason is that all what exists has a common origin and evolved under more or less identical conditions.

A case in point to consider is the CMB radiation which was created during the Decoupling Era. At that time the Universe was very small. The question is: if at that period the Universe was already uniform? Specific the sphere at the out layer of the Universe? The next question is: if this uniformity was caused by inflation.
IMO I see no reason to suppose that.

Anyway, and that is the most important consideration, the current size of the Universe has nothing to do with this.

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Created: 8 June 2017

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