## common misconceptions of cosmological horizons

This document contains comments about: "Expanding Confusion: Common misconceptions of cosmological horizons and the superluminal expansion of the universe" by Tamara M. Davis and Charles H. Lineweaver
To order to read the document select:http://arxiv.org/pdf/astro-ph/0310808v2.pdf

In order to study the size of the entire universe, using Friedmann's equation and based on the mainstream accepted cosmological parameters, please study this: Friedmann Lambda=0.01155 What this document shows:
1. First the path of a light ray (of events) emitted starting very close to the Big Bang. (blue line)
2. The size of the entire universe as a function of the age of the universe. (black line)
3. The Hubble sphere. (dashed black line)
When you compare the blue line with the black line you can see that of the entire universe we can only observe a tiny bit at present and that the size of the entire Universe is approximate 35 billion light-years

The cosmological parameters used in the Davis Lineweaver document are based on Omega(M)=0.3, Omega(Lambda)=0.7, H0=70 and age=13,5.
To calculated these parameter using Excel go to the link: Friedmann's equation operation
Based on: Lambda=0,01071, C=60 and age = 13,5 the simulated cosmological are: H0=69,96 Omega(m)=0,2986 and Omega(lambda) = 0,70014.

• The text in italics is copied from the article.
• Immediate followed by some comments

### 1. Introduction

The general relativistic (GR) interpretation of the redshifts of distant galaxies, as the expansion of the universe, is widely accepted. However this interpretation leads to several concepts that are widely misunderstood.
Those two sentences are to a certain extend in contradiction.
Probably the most common misconceptions surround the expansion of the Universe at distances beyond which Hubbleĺs law (vrec = HD : recession velocity = Hubbleĺs constant Î distance) predicts recession velocities faster than the speed of light.
I expect the biggest problem is the validity of this law and the applicability of this law.
In short based on which range of observations is this law demonstrated to be correct.
The reader should be aware that what this law should expres is the actual speed and the actual distance.
A related isssue is to what extend H is a constant.
The concept of the expansion of the universe is so fundamental to our understanding of cosmology and the misconceptions so abundant that it is important to clarify these issues and make the connection with observational tests as explicit as possible.
In a sense it is the other way around. It starts with observations. What we what to understand is the connection with the expansion of the universe at present.

### 2. Standard general relativistic description of expansion

Using Hubbleĺs law (vrec=HD), the Hubble sphere is defined to be the distance beyond which the recession velocity exceeds the speed of light, DHS = c/H.
The Hubble sphere is the dashed black line in document Friedmann Lambda=0.01155
The Black line is the size of the Universe with R/R0 = 1
For the objects using the mainstream cosmological parameters redshifts greater than z = 1.66 are receding faster than the speed of light. Distance is 13,7 Billion Light years. This is the point where the blue line crosses the dashed black line.
At the bottom line of the page we read:
In the Lambda-CDM concordance model all objects with redshift greater than z approx. 1.46 are receding faster than the speed of light.
That is correct using Friedmann's equation as explained above.
IMO there is a more important issue: is the friedmann equation correct to describe movement's approaching the speed of light. What additional observational proof is there.
Next we read:

### Page 4

This does not contradict SR because the motion is not in any observerĺs inertial frame.
This raises two questions:
1. What has SR to do with this whole problem?
2. What means: that is not in any observerĺs inertial frame?
See also: Common Misconception 4 - inertial frame Next we read:
No observer ever overtakes a light beam and all observers measure light locally to be travelling at c.
How do you know that when the recession velocity of the observer is higher the speed of light? i.e. when the redshift z of the observer is higher than approx 1.46
How is the speed of light measured by all observers?
The teardrop shape of our past light cone in the top panel of Fig. 1 shows why we can observe objects that are receding superluminally.
The blue line in the above mentioned document shows the events of what is observed.
The blue line is not a good indication why we can observe superluminal motion. It is the black line i.e. the worldline R/R0 = 1
Light that superluminally receding objects emit propagates towards us with a local peculiar velocity of c, but since the recession velocity at that distance is greater than c, the total velocity of the light is away from us.
That is the same mathematics as used to create the blue line. However, and that as an importany point, that does not mean that this is physical correct.
However, since the radius of the Hubble sphere increases with time, some photons that were initially in a superluminally receding region later find themselves in a subluminally receding region.
This is not the correct explanation. The reason is because the recession speed of the black line is roughly constant and equal to two times the speed of light. That means the local recession speed of a photon decreases when it moves (in opposite direction of the recession speed) towards the observer. At a certain distance the two speeds cancel and the distance stays constant. This is happening when the blue line becomes horizontal (roughly speaking half way between the black line and the observer). After that the photon starts to move towards the observer, faster and faster.
The objects that emitted the photons however, have moved to larger distances and so are still receding superluminally.
The oldest objects, yes. The most recently not. All of that is a function of the cosmological parameters.
Thus we can observe objects that are receding faster than the speed of light.
This is tricky. We can observe fast receding objects as they were in the past, when they were in there infancy. Not how they are at present.
Most observationally viable cosmological models have event horizons and in the Lambda-CDM model of Fig. 1, galaxies with redshift z approx 1.8 are currently crossing our event horizon.
These are the most distant objects from which we will ever be able to receive information about the present day.
The particle horizon marks the size of our observable universe. It is the distance to the most distant object we can see at any particular time.
The most distant objects we can see is the CMB radiation. The age is roughly 300000 years after the Big Bang and z=14 which is much larger as z = 1.8
Almost at the bottom of this page:
Instead photons we receive that have infinite redshift were emitted by objects on our particle horizon
The simulation discussed above shows a different result.
How older the universe, how older the earliest objects we can observe, how smaller the largest z values that will be observed.
The younger the universe, how larger the largest z values, that will be observed.
This reason is that dependend on the cosmological parameters the younger the universe the earlier you can observe. The limit is the moment of the Big Bang which shows the higest z value.
 In the text the discussion is about the observable universe. What is missing is something about the Universe with a capital U. This Universe is something completely independent of any human involvement. It is in effect all what happened after the Big Bang and has nothing to do with what we observe. Ofcourse what we observe should not be inconflict with the predictions of the laws that describe the Universe. This is the friedmann equation or something modified. A whole different question to answer the highest superluminal speeds involved in the entire Universe. The universe is assumed to be anisotropic and homogeneous. For a critial evaluation of this issue see: Comments about "Cosmological principle" in Wikipedia

### 3.1 Misconception #1: Recession velocities cannot exceed the speed of light

However, it is well-accepted that general relativity, not special relativity, is necessary to describe cosmological observations
As far as I know you need Friedmann's equation which is based on GR.
Moreover, we know there is no contradiction with special relativity when faster than light motion occurs outside the observerĺs inertial frame.
The document uses two concepts: observer's inertial frame and local inertial frame
See also:
Galaxies that are receding from us superluminally are at rest locally (their peculiar velocity, vpec = 0) and motion in their local inertial frames remains well de scribed by special relativity.
• The first (minor) question is that how do we know that they are receding superluminally.
• The second question is what has special relativity to do with their local inertial frame?
• IMO the motion of stars in such galaxies requires Newton's Law or GR and not SR.
See also: Common Misconception 4 - inertial frame
Equation (1) establishes the relation between V(t,z) and the parameters R0, dRt/dt and H(z).
These velocities are measured with respect to the comoving observer who observes the receding object to have redshift, z.
This raises the question how exactly are R(t) and H(z) calculated.

### Page 9

The particle horizon, not the Hubble sphere, marks the size of our observable universe because we cannot have received light from, or sent light to, anything beyond the particle horizon.
The Black line in the above mentioned document. The worldline for R = 1

### 3.4 Ambiguity: The depiction of particle horizons on spacetime diagrams

The particle horizon at any particular time is a sphere around us whose radius equals the distance to the most distant object we can see.
This is a rather difficult sentence.
At any moment in time we can observe many different galaxies and quasars, one of those which the higest z value is the most distant.
The problem is what is now the particle horizon? The distance of the galaxy from us in the past of what we see? or the distance at present?
How is what we see defined? Single photons are they included ?
The particle horizon has traditionally been depicted as the worldline or comoving coordinate of the most distant particle that we have ever been able to see
This is also a rather tricky sentence.
Part of the problem is that it requires the concept of worldline.

### Page 10

An alternative way to represent the particle horizon is to plot the distance to the particle horizon as a function of time
That may be possible, but first you must know what the particle horizon is.

### Page 18

The metric for an homogeneous, isotropic universe is the Robertson-Walker (RW) metric,
It is an important question to answer to what extend the universe at present is homogeneous and isotropic.
As explained above the size of the present day universe is roughly 35 billion light years and the recession velocity is 3c.
A different question is to what extend we agree that at a distance of 17.5 billion years the recession velocity is 1.5c
What this implies that space expansion implies simultaneous action (propagation).

### Common Misconception 1 - Superluminal motion

The biggest issue in the document is to what extend superluminal or faster than light speeds are possible.
This is a very tricky issue because if superluminal motion is possible the observers outthere assume that we also are undergoing superluminal motion. This argumentation is based on symmetrical considerations.
But if we are undergoing superluminal motion the observers diametrical are undergoing even more larger motions. etc etc.
Somewhere something is wrong in this reasoning....

### Common Misconception 2 - Absolute grid

Consider an Universe as a 3 dimensional grid, with a clock a each grid point. All the clocks have the same time and run synchronous.
Figure 1 shows a part of this grid. No vertical connections are drawn
 ``` o - o - o o A o o - o - o o - A - o A X A o - A - o o - o - o o A o o - o - o Figure 1 ```
In Figure 1 point X is the center of the grid. The nearest distance between two clocks is r. There are in 6 points at distance r from center. This are the points A. There are 12 + 8 points at larger distance.
We only consider the grid points at distance r. But also all the points at distance 2r, 3r, 4r etc.
Next we assume that the center X has a large mass and that all the clocks start to move at the same time towards the center. All the clocks coming from the same distance will arrive at the same time. The arriving time between the next group will decrease and the speed will increase. As such will the distance travelled at the last second also increase. When you divide that distance by the distance travelled in the first second you also get a parameter z.

The first complexity starts when space expansion is included. That means we still have a fixed "virtual" grid which a "virtual" clock attached to each grid point but there is also space expansion involved which implies that mass particles slowly move away with a radial speed linear with distance from the center
That means:
• at short distance the particles will move towards the mass at the center.
• at a certain distance they will be in equilibrium
• at a large distance they will move away from the mass at the center
The problem of course is how can such a configuration come into existance. What happened in order to create this situation.

### Common Misconception 3 - The length of a moving train

When you observe a train moving towards you the length seems longer as it really is. What you observe is in reality a vissible illusion: The train is not longer. To observe a simultion of this phenomena please select: VB Train operation.htm. The simulatation is written in Visual basic 5.0

The reason why this is mentioned, is because emission of light of a certain frequency is equivalent as sending a message of a certain length. This message is approaching you with is equivalent as the train approaching you and because the train seems (is observed) longer as it really is the same could have happened with the message.

This is only a thought..

### Common Misconception 4 - inertial frame

One very difficult concept to understand is the concept of inertial frame in relation to the (superluminal) expansion of space.
In the Wikipedia document http://en.wikipedia.org/wiki/Inertial_frame_of_reference the following is written:
In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame or inertial space) is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.
The issue is what has an inertial frame to do with the evolution of the universe, which is a physical process, or more specific if superluminal motion is evolved.
IMO nothing.
See also: Comments about Inertial frame of reference in Wikipedia.
IMO a reference frame is the same as the grid discussed above (See Common Misconception 2 - Absolute grid ) which we use to measure the positions and velocities of the galaxies, stars and planets studied but which has nothing to do with the trajectories followed by each in time.
That means the reference frame has nothing to do which the speeds of the objects, specific with superluminal motion.
This frame should be larger than the furthest galaxy measured. The link Friedmann Lambda=0.01155 introduced at the start of this document, which describes the entire universe is based on this reference frame.
That document uses the friedmann equation to describe the evolution of the universe and as such predicts superluminal motion. But that does not mean apriory that the predictions are correct.
The friedmann equation (a differential equation) includes certain parameters. If you want to use the friedmann equation than the first step should be to calculate these parameters based on observations within this frame. This is in fact very complicated.

Created: 22 September 2014

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