Tensor-multi-scalar theories from multidimensional cosmology

TL;DR

This paper explores how multidimensional cosmological models can be reduced to tensor-multi-scalar theories, revealing their structure as a flat sigma-model and examining special cases like 2-dimensional manifolds leading to dilaton gravity.

Contribution

It demonstrates the dimensional reduction of inhomogeneous multidimensional models to tensor-multi-scalar theories and analyzes the special case of 2-dimensional manifolds in detail.

Findings

Models reduce to flat sigma-models in Einstein frame

Special case of 2D manifold leads to dilaton gravity

Different representations of the action are explored for the 2D case

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 tensor-multi-scalar theories. In the Einstein conformal frame, these theories take the shape of a flat sigma-model. For the singular case where M_0 is 2-dimensional, the dimensional reduction to dilaton gravity is preformed with different distinguished representations of the action.