Bimetric general relativity and cosmology

Abstract

A modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensorg μv describing the space-time geometry and gravitation, there exists also a background metric tensor γ μv The latter describes the space-time of the universe if no matter were present and is taken to correspond to a space-time of constant curvature with positive spatial curvature (k=1). Field equations are obtained, and these agree with the Einstein equations for systems that are small compared to the size of the universe, such as the solar system. Energy considerations lead to a generalized form of the De Donder condition. One can set up simple isotropic closed models of the universe which first contract and then expand without going through a singular state. It is suggested that the maximum density of the universe was of the order ofc 5 ħ −1 G −2∼1093 g/cm3. The expansion from such a high-density state is similar to that from the singular state (“big bang”) of the general relativity models. In the case of the dust-filled model one can fit the parameters to present cosmological data. Using the radiation-filled model to describe the early history of the universe, one can account for the cosmic abundance of helium and other light elements in the same way as in ordinary general relativity.