Nonlinear multidimensional cosmological models with form fields: stabilization of extra dimensions and the cosmological constant problem

TL;DR

This paper explores multidimensional gravity models with nonlinear curvature and form fields, demonstrating conditions for stabilizing extra dimensions and aligning the effective cosmological constant with observed dark energy limits.

Contribution

It provides new insights into stabilization mechanisms of extra dimensions in nonlinear multidimensional models with form fields, including parameter constraints and implications for the cosmological constant problem.

Findings

Extra dimensions can be stabilized for various signs of internal curvature and cosmological constants.

The effective four-dimensional cosmological constant can match observed dark energy density.

Parameter restrictions are derived from the connection between higher-dimensional and four-dimensional scales.

Abstract

We consider multidimensional gravitational models with a nonlinear scalar curvature term and form fields in the action functional. In our scenario it is assumed that the higher dimensional spacetime undergoes a spontaneous compactification to a warped product manifold. Particular attention is paid to models with quadratic scalar curvature terms and a Freund-Rubin-like ansatz for solitonic form fields. It is shown that for certain parameter ranges the extra dimensions are stabilized. In particular, stabilization is possible for any sign of the internal space curvature, the bulk cosmological constant and of the effective four-dimensional cosmological constant. Moreover, the effective cosmological constant can satisfy the observable limit on the dark energy density. Finally, we discuss the restrictions on the parameters of the considered nonlinear models and how they follow from the connection between the D-dimensional and the four-dimensional fundamental mass scales.