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Based on the 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, to, 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 becomes scale-dependent.

The apparent cosmological conict between the age of the Universe, predicted in the standard Friedman cosmology by using the recent measurement of the larger Hubble constant from a direct calibration of the distance to the Virgo galaxy cluster, and the ages of the oldest stars and globular clusters is resolved by i n v oking the scale dependence of cosmological quantities, including the age of the Universe. The distance dependence or the running of cosmological quantities is motivated by the asymptotically-free higher-derivative quantum gravity. The running can also be derived by \properly" modifying the Friedman equations. This property can also provide partial explanation of the apparent disagreement b e t w een the two recent measurements of the Hubble constant using NGC 4571 at 15 Mpc and NGC 5253 at 4 Mpc.

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