EDIT: I corrected a typo below: I had forgotten to put my entire expression for a(t) to the power 1/3. It's corrected now(adsbygoogle = window.adsbygoogle || []).push({});

This may sound like a silly question but it's bugging me quite a bit.

Consider a cosmological model, let's say the simple case of no pressure, no cosmological constant, no curvature so that the solution is simply of the form

[tex] a(t) = (6 \pi G \rho_0 t^2 + C)^{1/3} [/tex]

where rho_0 is the density at the present epoch. Now, this specifies completely how the scale factor evolves with time up to the integration constant C. We may impose th einitial condition a(0) = 0 (Big Bang) which sets C=0.

Fine so far. But then we also impose that a_now is equal to one and this leads to an equation giving the age of the universe in terms of H_0. It's this step that baffles me. I am not sure what it means. This seems to correspond to a rescaling of the time axis so that a_now is equal to one. But then I don't know what this time means at all. We may use this equation to then show that in this universe the age of the universe is 2/(3 H_0).

The question is then: how is this time related to our physical time (that we measure on our watch? We measure a certain value of H_0 experimentally so we have an actual number for H_0. How can we see that this experimental value is actually consistent with this calculation that assigns a value of 2/(3H_0) to the age of the universe?

It's not clear to me at all. Putting it another way, what if I decided that the scale factor at the present epoch was 2 instead of 1? Wouldn't that lead to a different estimae of th eage of the universe or a different estimate of the density required to have a flat universe?

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# Meaning of setting the scale factor equal to 1 at present epoch

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