Einstein and Brans-Dicke frames in multidimensional cosmology

TL;DR

This paper explores multidimensional cosmological models with non-minimal couplings, emphasizing the Einstein frame as the physical frame, and demonstrates the reformulation of solutions like Kasner solutions within this framework.

Contribution

It provides a general method for transforming known solutions from the Brans-Dicke frame to the Einstein frame in multidimensional cosmology.

Findings

In the Einstein frame, no solutions exhibit external space inflation.

The paper offers a systematic approach for Einstein frame reformulation.

Explicit example with Kasner solutions illustrates the method.

Abstract

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold M= M_0 x M_1 ...x M_n are investigated under dimensional reduction to a D_0-dimensional effective non-minimally coupled sigma-model which generalizes the familiar Brans-Dicke model. It is argued that the Einstein frame should be considered as the physical one. The general prescription for the Einstein frame reformulation of known solutions in the Brans-Dicke frame is given. As an example, the reformulation is demonstrated explicitly for the generalized Kasner solutions where it is shown that in the Einstein frame there are no solutions with inflation of the external space.