- #1

JuanCasado

- 45

- 1

The radius of the observable universe grows with time at the speed of light. R refers to the Hubble radius or particle horizon. The Hubble sphere can be defined as the sphere of center 0 (observer) and radius the distance that light can travel within the characteristic expansion time, that is the Hubble time : τ=1/H(t).

So R=c τ.

A more detailed definition can be found at:

http://en.wikipedia.org/wiki/Particle_horizon

I am not referring with R to the radius of a physical entity, i. e. the scale distance, but to a theoretical construction, which coincides with the radius of the observable universe, since light coming from beyond has not had enough time to reach us nowadays.

According to SCM, in a flat universe the density equals the critical density, which is proportional to H squared (from the Friedman equation).

We have H ~ 1/ τ = c/c τ = c/R, so that ρ ~ 1/R

^{2}, meaning that the universe density decreases as R squared grows. Then the mass within the observable Universe M ~ R and should increase with time.

On the other hand, an accelerating Universe should have a decreasing mass within its observable portion since the radius of the observable Universe grows only linearly time, and some accelerated material should pass through this boundary.

How can we reconcile both statements?