- #1

mbond

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The scale factor: ##\displaystyle\frac{a(t)}{a_0}=(\frac{\Omega_{m0}}{\Omega_{\Lambda0}})^{^{^{1/3}}}\sinh^{^{2/3}}(\frac{t}{t_{\Lambda}})## with ##t_\Lambda=\displaystyle\frac{2}{\sqrt{3\Lambda c^2}}##, ##\Omega_x## the densities, and ##\Lambda## the cosmological constant.

The density of matter: ##\Omega_m(a)=\displaystyle\frac{\Omega_{m0}}{\Omega_{m0}+\Omega_{rad0}(a/a_0)^{-1}+\Omega_{\Lambda0}(a/a_0)^3}##

The particle horizon: ##d_p(t)=a(t)\displaystyle\int_{0}^{t}\frac{cdt^\prime}{a(t^\prime)}##

The event horizon: ##d_E(t)=a(t)\displaystyle\int_{t}^{\infty}\frac{cdt^\prime}{a(t^\prime)}##

These horizons are shown in the figure:

The two horizons cross at t=4.01 Gyr.

Let be ##h(t)## the smallest of the two horizons: ##h(t)=\min(d_p(t),d_E(t))##. The number of visible galaxies is then: ##V(t)\sim \Omega_m(a(t))h(t)^3## and this is shown on the figure below:

The number of visible galaxies was maximum at 4.1 Gyr when the two horizons cross. Today it has decreased by a factor of 16, and at t=37.2 Gyr, it will have diminished by another factor of 16.

Is my calculation correct?