Perfect cosmological principle in co-moving co-ordinates

[johne1618]

To quote cosmologist Ned Wright:

The Steady State model of the Universe was proposed in 1948 by Bondi and Gold and by Hoyle.

Bondi and Gold adopted the "Perfect Cosmological Principle", and added the assumption that the Universe was the same at all times to homogeneity (the same in all places) and isotropy (the same in all directions).

If the Universe is the same at all times, it is argued that the value of the Hubble parameter must be a constant H_0, so

H = \frac{\dot{a}}{a} = H_0

leading to an exponential cosmology

a(t) = e^{H_0 (t - t_0)}

where t_0 is the present age of the Universe.

This model is an expanding model that does not change its appearance over a time interval from -\infty to +\infty.

However this model has been discredited as there is good evidence of a Big Bang Universe with a finite age.

But perhaps one could save the Perfect Cosmological Principle by saying the Universe should look the same at all times in co-moving cordinates.

Now we have

H = \frac{c}{R_H}

where R_H is the Hubble radius.

Therefore if the Universe is to look the same at all times in co-moving co-ordinates then R_H must be co-moving and so

R_H = a(t) R_0

where R_0 is constant.

Therefore we have

\frac{\dot{a}}{a} = \frac{c}{a R_0}

As H_0 = c/R_0 we have

\frac{\dot{a}}{a} = \frac{H_0}{a}

with solution

a(t) = H_0 t

This model is static in co-moving co-ordinates with a finite lifetime.

 

[twofish-quant]

Congratulations you've used reinvented the Milne model!

You can search the forums for lots of detail on the problems with Milne. The short answer is 1) it requires gravity to work differently than we think it does 2) it causes the early universe to expand rather slowly which causes problems with big bang nucleosynthesis and CMB 3) it doesn't fit with the most recent supernova measurements.

There is a variant of the Milne model called Milne-Dirac in which antimatter repels matter. In one recent thread, I was sort of defending it as "probably wrong, but not totally crazy."

 

[Chronos]

Yes, twofish occasionally argues the less probable side of issues [he is old and enjoys stirring the pot now and then]. The odds favoring anti gravity from anti matter are not favorable. Gravity is almost surely mediated by an integer boson, and integer bosons appear to be indifferent to charge.

 

[johne1618]

Congratulations you've used reinvented the Milne model!

The co-moving perfect cosmological principle is also consistent with the Coasting Cosmology model with equation of state:

p = -\frac{\rho c^2}{3}

In any flat model without cosmological constant we have

\rho \propto \frac{1}{R_H^2}

In the CC model R_H is constant in comoving co-ordinates and therefore the energy density \rho is constant in co-moving co-ordinates.

This makes sense to me because if you factor out the expansion of space then you would expect the energy density to remain constant as energy is conserved locally.

 

[clamtrox]

This has actually been discussed quite a bit recently. Here's a paper you might find interesting: http://arxiv.org/abs/1109.5189

(and no, it's not correct :)