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

Based on the observed increase of Ω0 as a function of cosmic scale, the Robertson–Walker metric and the Einstein equation are generalized so that Ω0, H0, and the age of the Universe, t0, 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 H0 increases as scale increases, qualitatively consistent with the recent observations. 95.30.-k,95.30.Sf,98.80.-k Typeset using REVTEX E-mail [email protected] E-mail [email protected] E-mail [email protected]