# Does the empty Milne Universe have a horizon problem?

1. Jun 22, 2011

### johne1618

I have a question about the horizon size of the empty Milne Universe.

The empty Milne Universe expands linearly with time. This implies that the horizon size for the Milne Universe is given by:

d_H = Integral [ t=t_early to t_0 ] ( dt / t )

d_H = log t_0 - log t_early

Thus the horizon size for the Milne Universe diverges as t_early -> 0.

Does this mean that there is no "horizon problem" for the Milne Universe?

It seems that the Milne model doesn't require the theory of inflation to explain the uniformity of the cosmic microwave background.

Last edited: Jun 22, 2011
2. Jun 22, 2011

### BillSaltLake

If it's really empty, then the temperature of the CMB is always zero and the matter density is always zero. If you're going to assume a zero-zero universe, then there's no mystery as to why it's a "uniform" zero-zero.

3. Jun 23, 2011

### Chalnoth

H.L. Mencken once said, "There is always an easy solution to every human problem--neat,
plausible, and wrong."

This one is wrong, and it is clear that it is wrong because the Milne universe is an empty universe, with no matter or energy whatsoever.

That said, no, the Milne universe has no horizon problem, because the Milne universe has no horizon.

4. Jun 23, 2011

### Garth

The correct answer is simply "the Milne universe has no horizon problem".

If one carries out an Einstein 'gedankenexperiment' or 'thought experiment' and place in the Milne Universe test particles and a test observer of negligible mass and 'test-photons' of negligible energy so that they do not affect the nature of the universe's space-time then the universe would have a horizon.

However as all the way back from 't=0' it would have expanded away from the observer at the same rate that the universe expanded then there is no horizon problem, everything within the observable universe would have always been casually connected.

This is an important fact to remember as a linearly expanding universe, or 'coasting cosmology', model would have no horizon, smoothness or flatness problems normally associated with the standard model and therefore not require Inflation to correct them.

As there seems to be a problem in getting Inflation to work consistently it may be just as well to keep this feature of the Milne Universe at the back of one's mind. (Such a model would also readily explain certain Cosmological Coincidences.)

To obtain such a model you would need an equation of state $p = - \frac{1}{3}\rho c^2$ .

As DE is introduced ad hoc to make the standard LCDM model fit, then perhaps this alternative version of DE ought also to be considered.

[Note, the Coasting Cosmology model includes the Milne Model (when p and $\rho$ are both zero), but it is not restricted to it. The CC model need not be empty as the above equation of state for DE compensates for the presence of mass/energy to keep the model expanding linearly.]

Just a thought,
Garth

Last edited: Jun 23, 2011
5. Jun 23, 2011

### Chalnoth

This equation of state is the equation of state given by cosmic strings. Turns out not to work there, because it predicts an extremely different spectrum of perturbations on the CMB (it would have no peaks, for one, just a smooth distribution).

6. Jun 23, 2011

### Garth

Hi Chalnoth!

I am not saying "this is the answer" just that, given the lack of the confirmed detection of a Higgs Particle or Inflaton to make Inflation work, the lack of a confirmed detection of a DM particle and the ad hoc nature of DE, we need "to keep this feature of the Milne Universe at the back of one's mind."

Actually some would contend that the Coasting Cosmology model does predict the observed CMB power spectrum: A Concordant “Freely Coasting” Cosmology, fits the SNe Ia data Cosmological Constraints on a Power Law Universe (out to z=1), and yields a viable alternative BBN scenario Nucleosynthesis in a Simmering Universe . (Note the increased time for BBN means the baryon density increases to explain all of present DM as originally baryonic in nature (A problem with the model is present deuterium has to be created through another process (something like - spallation in Type III hypernovae shock fronts??) while on the other hand the lithium problem is eased). The problem it leaves is, "Where is all this unobserved baryonic DM today?"

Until we have a confirmed detection of the Inflaton/Higgs and DM particles I feel IMHO that this model should be kept in mind - at least on the back burner.

Garth

Last edited: Jun 23, 2011
7. Jun 23, 2011

### Chalnoth

Why? It's ruled out observationally, in a number of ways.

As for what you linked, first note that the "coasting cosmology" paper you linked was never published.

The supernova paper is quite old, and more recent constraints rule out a coasting cosmology.

The BBN paper was also never published (and quite old...before WMAP!), but anyway there's no way to explain the even/odd ringing of the CMB peaks without non-baryonic dark matter.

8. Jun 23, 2011

### Garth

Because, in answer to the OP question,"the Milne Model does not have a horizon problem".

I agree that not enough work has been done on the coasting model and published in reputable journals. Once the detection of the Higgs/Inflaton and DM particles have been confirmed then we will be able to forget the CC model, but until then it might be as well to keep the thought "on the back burner".

Garth

9. Jun 23, 2011

### Chalnoth

Agree? Pretty sure that's the opposite of agreeing with me. I'm saying the Milne model is wrong. Quite enough work has been done on it, and it's time to move on.

10. Jun 23, 2011

### bapowell

Why must one wait for the detection DM particles before accepting that data has provided strong evidence for the presence of dark matter? How would we even know that such and such particle discovered at the LHC was a DM particle? Even if it shared all the requisite properties of dark matter, this would still be only indirect evidence. We already have plenty of indirect evidence for dark matter, e.g. the Bullet Cluster. And as Chalnoth says, the acoustic peaks in the CMB and even the degree of clustering of LSS are all strong pieces of evidence in favor of non-baryonic dark matter.

Studying the early universe is a lot like solving a murder mystery, but one does not need to find the murder weapon (discover the inflaton) to determine that a murder has taken place (that inflation happened.)

11. Jun 23, 2011

### Garth

I haven't denied the existence of Dark Matter, I have only said that we don't know what it is.

I think the Bullet Cluster and other studies show that something is definitely there, but what?

In the standard model, when DE is not operating in the BBN epoch, we are restricted to $\Omega_{baryonic} = ~ 0.04$ and so in that model DM cannot be baryonic in nature, however in the coasting model (R = ct) the various eprints on the physics arXiv by the Indian team suggest that it would be much greater, with estimates around 24%. Obviously more work has to be done to verify these results, but if, and only if, they hold up then the observed DM might be baryonic in nature.

What grounds have you for stating Inflation has happened?

(Except to solve the horizon, smoothness and density problems of GR, which would not exist in a linearly expanding model.)

Garth

Last edited: Jun 23, 2011
12. Jun 23, 2011

### bapowell

No real grounds yet, although I think the fact that Harrison-Zeldovich is essentially ruled out at 95 % CL is interesting. Superhorizon correlations in the E-mode polarization spectrum are also indicative of inflation -- AFAIK, no causal mechanism can generate them.

But my point is simply that we don't need to observe the inflaton itself to be satisfied that inflation has occurred, if sufficient indirect evidence is available. And such evidence should soon be rolling in from Planck and other ground-based observatories. For example, if we confirm that the spectrum of primordial density perturbations is in fact Gaussian and adiabatic, and we discover a tensor signal in the CMB (of the correct tilt), then I would throw my hat in with inflation, with or without an inflaton in my back pocket.

13. Jun 23, 2011

### Chalnoth

You'll note that those results were put on the arxiv before WMAP. And again: never published. Usually there's a reason for that.

14. Jun 23, 2011

### Garth

Actually some are published:

Cosmological constraints on a power law universe (Physics Letters B, Volume 624, Issues 3-4, 29 September 2005, Pages 135-140) (Geetanjali Sethia, Abha Devb and Deepak Jain, Univ. Delhi)
While nearby out to z = 0.3: Is cosmic acceleration slowing down? (Phys. Rev. D 80, 101301(R) (2009)) (Arman Shafieloo (Oxford) Varun Sahni (Pune, India), and Alexei A. Starobinsky (Russia/Japan))

You say above
Given that we are now discussing the linearly expanding costing cosmology model (no one is saying the universe is empty as in the specific case of the Milne model) can you substantiate with published references the work that shows that it (with $\Omega_{baryonic} \simeq 0.3$ or greater) is wrong?

I'm not saying the CC model is the right one, just that there are grounds for questioning aspects of the standard LCDM model and being open to viable modifications of it.

Garth

Last edited: Jun 23, 2011
15. Jun 23, 2011

### Chalnoth

Take your pick. I mean, there's CMB studies, or more recent supernova observations, or baryon acoustic oscillation studies. Consider, for example, this plot:
http://supernova.lbl.gov/Union/figures/Union2_Om-Ol_slide.pdf

A "coasting cosmology" is down there at the origin, 0,0, which is ruled out at well over 3 sigma even by supernovae alone. The combination with other data completely kills that possibility.

That's fine. But the Milne cosmology is not a viable modification.

16. Jun 23, 2011

### Garth

No - the empty Milne model is down there at (0,0) the generalized version of it, the CC model has positive $\Omega_M$ and $\Omega_{\Lambda}$ that diagram, taken from IMPROVED COSMOLOGICAL CONSTRAINTS FROM NEW, OLD, AND COMBINED SUPERNOVA DATA SETS Figure 15 (I believe), assumes the prior that $\omega = -1$, whereas the CC model requires an equation of state $\omega = -\frac{1}{3}$

The determination of $\omega = -1$ itself had the prior that the universe was flat.

Its not Milne cosmology but Kolb cosmology that I am intrigued by.
Garth

17. Jun 23, 2011

### Chalnoth

If you'll look at Kolb's original paper, he was proposing that this might be motivated by a cosmic string dominated universe:

But we now know that cosmic strings cannot be a dominant form of energy density of the universe, because they produce a wildly-different spectrum of perturbations on the CMB.

There's also the point to be made that we now have a good handle of how much matter there is out there, and if we allow the properties of whatever remains to vary, then we get something that behaves pretty much like a cosmological constant.

So you can throw that idea into the dustbin of history as well. Potentially interesting in its day. But still wrong.

18. Jun 24, 2011

### Garth

So let us discover the DM particle/s, explain the DE/DM density coincidence, get Inflation to work and be confirmed by the laboratory (LHC?) detection of the Inflaton/Higgs particle (or find a theory without a horizon problem) and then we will know what we are talking about!

Best regards,
Garth

19. Jun 24, 2011

### Chalnoth

There is basically no way for the LHC to produce an inflaton particle. Our best bet for understanding inflation is through CMB polarization studies, and, potentially, direct measurements of the gravitational wave background further down the road.

20. Jun 24, 2011

### bapowell

I disagree with this. Even if it was possible, discovering a heavy scalar at the LHC that could be the inflaton would provide no further direct evidence for inflation than the primordial perturbations in the CMB already do. Any heavy scalars produced at the LHC are not going to come with a sticker on them that says "Hello, my name is Inflaton."