# What is the difference between coasting and static cosmology?

by Lino
Tags: coasting, cosmology, difference, static
 P: 259 Is the key difference between coasting and static cosmology models the presence of a linear acceleration, or are there other major differences? Regards, Noel.
PF Gold
P: 3,273
 Quote by 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.
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
 P: 259 Thanks Garth. Guess I'll have to keep reading. Regards, Noel.
P: 4,678

## What is the difference between coasting and static cosmology?

 Quote by Garth A dark energy with an equation of state $\rho = -\frac{1}{3}p$ would achieve this (Kolb's model A coasting cosmology ).
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.
 P: 259 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.
PF Gold
P: 3,273
 Quote by 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.
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)

 The presence of any matter or electromagnetic energy in the universe would force the solution of Equation (206) to assume Case 2: $\sigma = − \frac{1}{3}$ Equation(213)
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
P: 4,678
 Quote by 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.
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/..._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.
 Quote by Garth If the dark energy itself had an eos of $\rho = -p$, as with the cosmological constant, then $\rho_\Lambda = \frac{1}{3}\rho_M$.