A New Scale-Dependent Cosmology with the Generalized Robertson--Walker Metric and Einstein Equation

Abstract

Based on the observed increase of $\Omega _0$ as a function of cosmic scale, the Robertson--Walker metric and the Einstein equation are generalized so that $ \Omega_0$, $H_0$, and the age of the Universe, $t_0$, all become functions of cosmic scales at which we observe them. The calculated local (within our galaxy) age of the Universe is about 18 Gyr, consistent with the ages of the oldest stars and globular clusters in our galaxy, while the ages at distant scales are shorter than the local age, solving the age puzzle. It is also shown that $H_0$ increases as scale increases, qualitatively consistent with the recent observations.