Cosmological solutions in multidimensional model with multiple exponential potential

TL;DR

This paper derives and analyzes cosmological solutions in a multidimensional scalar field model with exponential potentials, identifying conditions for different expansion behaviors and exploring quantum wave functions.

Contribution

It presents new exact classical solutions with power-law and exponential scale factors, and quantum solutions to the Wheeler-DeWitt equation in this context.

Findings

Power-law solutions occur only with linearly independent coupling vectors.

Exponential solutions occur with linearly dependent coupling vectors.

A subset of solutions exhibits accelerated expansion.

Abstract

A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions with power-law and exponential behaviour of scale factors are singled out. It is proved that power-law solutions may take place only when coupling vectors are linearly independent and exponential dependence occurs for linearly dependent set of coupling vectors. A subfamily of solutions with accelerated expansion is singled out. A generalized isotropization behaviours of certain classes of general solutions are found. In quantum case exact solutions to Wheeler-DeWitt equation are obtained and special "ground state" wave functions are considered.