D-dimensional torus as compact manifold and Kaluza–Klein cosmological model

Abstract

Singularity-free solutions of higher-dimensional Einstein field equations are obtained in the background of M4×TD manifold (M4 is a usual four-dimensional Friedmann– Robertson–Walker model and TD is a D-dimensional torus). Moreover, through dimensional reduction and one-loop quantum correction to scalar field, time-dependent cosmological constant Λ, effective gravitational constant Geff, and a fine-structure constant e/4π are derived in the effective four-dimensional theory using solutions of Einstein’s equations. It is found that at late times Λ≂0.