Cosmological Model with Nonminimal Derivative Coupling of Scalar Fields in Five Dimensions

TL;DR

This paper explores a five-dimensional cosmological model with a scalar field nonminimally coupled to curvature, revealing solutions including de Sitter expansion and unstable static extra dimensions.

Contribution

It introduces a novel five-dimensional model with nonminimal derivative coupling of scalar fields and analyzes its solutions and stability properties.

Findings

Pure scalar field without NMDC yields stiff matter cosmology.

De Sitter solutions with linearly evolving scalar fields are found.

Static extradimensions are unstable and tend to shrink.

Abstract

We study a nonminimal derivative coupling (NMDC) of scalar field, where the scalar field is coupled to curvature tensor in the five dimensional universal extra dimension model. We apply the Einstein equation and find its solution. First, we consider a special case of pure free scalar field without NMDC and we find that for static extradimension, the solution is equivalent to the standard cosmology with stiff matter. For a general case of pure free scalar field with NMDC, we find that the de Sitter solution is the solution of our model. For this solution, the scalar field evolves linearly in time. In the limit of small Hubble parameter, the general case give us the same solution as in the pure free scalar field. Finally, we perform a dynamical analysis to determine the stability of our model. We find that the extradimension, if it exist, can not be static and always shrinks with the expansion of four dimensional spacetime.