Astonishing Coincidence: Age of Universe in $\Lambda$CDM & Milne Cosmologies

[Garth]

Coincidence of Universe age in $\Lambda$CDM and Milne cosmologies

The age of the Universe in the \LambdaCDM cosmology with \Omega_{matter}=0.26 and \Omega_{\Lambda}=0.74 is the same as in the Milne cosmology which correspods to an almost empty universe. In both cases it is a reciprocal Hubble constant, 1/H_0, that for now preferred value H_0=71 km/s/Mpc is 13.7 billion years. The most curious coincidence is that at the present time, in the \LambdaCDM model the decelerated expansion is exactly compensated by the accelerated expansion, as if the Universe coast for 13.7 billion years.

I wonder why...

Just another example of the degeneracy* perhaps?

Garth

(*Now accepted for publication in Astrophysics and Space Science)

 

[gptejms]

Coincidence of Universe age in $\Lambda$CDM and Milne cosmologies

If \Omega_R is a very small number,then couldn't there be many combinations of \Omega_{matter} and \Omega_\Lambda that give the same result?

 

[hellfire]

If \Omega_R is a very small number,then couldn't there be many combinations of \Omega_{matter} and \Omega_\Lambda that give the same result?

Given the current value of the Hubble parameter H = 71, there are other models that give the same result. For example \Omega_m = 0.1, \Omega_{\Lambda} = 0.4. This is a degeneracy as any other. For example, mantaining \Omega_m = 0.3 you get the same age with \Omega_{\Lambda} = 0 and H = 60, which might not be a very unrealistic model (or at least it was not some years ago).

However, there is only one model that provides the same age for every value of H. This is the Milne model. I have not done any calculation but there must be some mathematical reason for this that should become clear when calculating the age as a function of H in the current model.

 

[Garth]

If \Omega_R is a very small number,then couldn't there be many combinations of \Omega_{matter} and \Omega_\Lambda that give the same result?

Yes, where \Omega_R is the curvature component, the deviation of the total density parameter from unity.

However, lensing of distant quasars is observed to place \Omega_{matter} in the 0.3 range and the standard WMAP concordance model puts it at 0.23 (DM) + 0.04 (baryon) with \Omega_{Dark Energy} = 0.76.

The point of this paper is to point out that the result of this complicated standard theory results in the same age as the very simplest models, the linearly expanding one. Coincidence??

EDIT: Crossed with hellfire!

Garth

 

[gptejms]

I think all this coincidence means is that the average effect of gravity over time is quite weak.