The dimensional reduction in a multi-dimensional cosmology

Abstract

Einstein's field equation are solved for the case of the eleven-dimensional vacuum spacetime which is the product R*Bianchi V*T7, where T7 is a seven-dimensional torus. Among all possible solutions the authors identify those in which the macroscopic space expands and the microscopic space contracts to a finite size. The solutions with this property are 'typical' within the considered class. They implement the idea of a purely dynamical dimensional reduction.