D-DIMENSIONAL TORUS AS COMPACT MANIFOLD AND KALUZA-KLEIN COSMOLOGICAL MODEL

Singularity-free solutions of higher-dimensional Einstein field equations are obtained in the background of M4 X T(D) manifold (M4 is a usual four-dimensional Friedmann-Robertson-Walker model and T(D) is a D-dimensional torus). Moreover, through dimensional reduction and one-loop quantum correction to scalar field, time-dependent cosmological constant LAMBDA, effective gravitational constant G(eff), and a fine-structure constant e/4-pi are derived in the effective four-dimensional theory using solutions of Einstein's equations. It is found that at late times LAMBDA congruent-to 0.