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

Abstract

The age of the Universe in the $\Lambda$CDM 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 $\Lambda$CDM model the decelerated expansion is exactly compensated by the accelerated expansion, as if the Universe coast for 13.7 billion years.