A metric tensor in cosmology

The standard Friedmann-Robertson-Walker ( FRW ) cosmological model is modified by including a time dependent eccentricity term ε(t) in the metric tensor that describes the oblateness for an expanding hyperellipsoid. The oblateness dissipates when cosmic time is much greater than a characteristic time t_char, on the order of a fraction of the Hubble time, consequently the geometry of space-time reduces to that of a perfect hypersphere.

The metric tensor g_μv retains a diagonal matrix form, but the inclusion of the eccentricity term will generate off-diagonal terms G₀₁, and G₁₀ in the Einstein tensor g_μv If the stress-energy tensor is described by an imperfect relativistic fluid, then a time dependent thermal gradient will appear as a non-diagonal term. This term is a function of the eccentricity ε(t), and may account for thermal equilibrium during the initial stages of development for the universe. A numerical solution for the cosmic radius R(t) is presented.