# What is the difference between coasting and static cosmology?

1. Feb 14, 2013

### Lino

Is the key difference between coasting and static cosmology models the presence of a linear acceleration, or are there other major differences?

Regards,

Noel.

2. Feb 14, 2013

### Garth

The static universe (as in Einstein's original model) is one which is not expanding at all.

As gravitational forces from objects in the universe would cause it to contract there has to be another force counteracting these, a dark energy. Einstein found that the cosmological constant could provide such a force and included it in his model. However it was soon shown that the model is unstable, and the slightest perturbation, a tendency to expansion or contraction, would grow into full blown expansion or contraction. Hubble's observations soon proved that the universe is in fact expanding.

The coasting model expands linearly, with no deceleration or acceleration.

This would happen in an empty universe (the original Milne model) with no gravitational fields , or if not empty (obviously as in the real universe) something would have to counteract the gravity forces.

A dark energy with an equation of state $\rho = -\frac{1}{3}p$ would achieve this (Kolb's model A coasting cosmology ).

Or, if anti-matter repels matter gravitationally then the universe could be split up into regions of matter and anti-matter with overall gravitational forces cancelling would also achieve this. (The Dirac-Milne universe)

Garth

3. Feb 14, 2013

### Lino

Thanks Garth. Guess I'll have to keep reading.

Regards,

Noel.

4. Feb 15, 2013

### Chalnoth

Note that this wouldn't counteract the gravity of matter. Rather, it limits to a coasting cosmology at late times. It only becomes coasting when nearly all of the energy density of the universe is of this kind of stuff. So there's really too much matter in our universe for this model to work.

5. Feb 15, 2013

### Lino

Thanks Chalnoth. Could you recommend any search words or links that are critical of a coasting cosmology (everything I read seems to be very positive)?

Regards,

Noel.

6. Feb 15, 2013

### Garth

Yes, I was keeping it perhaps a little too brief.

The coasting model with matter requires dark energy such that the total equation of state is $\rho_T = -\frac{1}{3}p_T$.

If the dark energy itself had an eos of $\rho = -p$, as with the cosmological constant, then $\rho_\Lambda = \frac{1}{3}\rho_M$.

Such an eos is suggested in Self Creation Cosmology (page722)

Where $\sigma$ is the (total density)/(total pressure), $\omega$ being already used for the Brans Dicke coupling constant.

Whether the theory can fit other observational constraints is another question.

Garth

Last edited: Feb 15, 2013
7. Feb 15, 2013

### Chalnoth

I'm not sure of any that have investigated this specifically, but this seems to me to be a good way of examining the issue:
http://lambda.gsfc.nasa.gov/product/map/current/params/wcdm_wmap9_spt_act_snls3.cfm

This is the list of parameters where they have taken the standard dark matter cosmology, but allowed the equation of state parameter $w$ to vary. This is model could easily include the coasting cosmology if $w \approx -1/3$.

The data used in this fit include WMAP (9-year data), SPT, ACT, and SNLS3. The estimate of the equation of state parameter with this combination of CMB and supernova data becomes:

$$w = -1.059 \pm 0.069$$

This is consistent with a cosmological constant ($w = -1$). So a coasting cosmology is completely ruled out, unless you can come up with a reason to believe that the other parameters used in the model are completely wrong (e.g. there really isn't any dark matter, though it's really really hard to fit the available evidence without dark matter), but even then you have to do the hard work to fit the new model with the available data, which is copious.

8. Feb 15, 2013

### Chalnoth

Right. But that's an unstable situation. It may have that density relationship for a short time when the universe transitions from decelerating to accelerating, but it won't stay there.

I guess I just have no interest in examining such exotic cosmologies in detail until they can demonstrate that they predict the power spectrum of the CMB (in detail), and in such a way that matches with near-universe estimates of expansion (e.g. BAO, supernova data). These alternative cosmologies are a dime a dozen, and they generally can't be used to predict a CMB power spectrum anything like the one we observe.

9. Feb 15, 2013

### Mordred

Here is one investigated paper of a Linear coasting model

http://arxiv.org/pdf/astro-ph/0306448v1.pdf

Classical Cosmology tests
Kolb[12] was probably first to demonstrate that data on Galaxy number
counts as a function of red-shift as well as data on angular diameter distance
as a function of red-shift do not rule out a linearly coasting cosmology. Unfortunately,
these two tests are marred by effects such as galaxy mergers and
galactic evolution. For these reasons these tests have fallen into disfavour as
reliable indicators of a viable model.
The variation of apparent luminosity of a “standard candle” as a function
of red-shift is referred to as the Hubble test. With the discovery of Supernovae
type Ia [SNe Ia] as reliable standard candles, the status of Hubble test has
been elevated to that of a precision measurement. Recent measurements by
the supernovae cosmology project [13] eliminated the “minimal inflationary”

Later researches as Chalnoth mentioned completely ruled out coasting models as far as i know. Leastwise I've never seen or heard of any recent articles on Coasting models

10. Feb 15, 2013

### Lino

Thanks all for the references and links.

Regareds,

Noel.