AdS and stabilized extra dimensions in multidimensional gravitational models with nonlinear scalar curvature terms 1/R and R^4

TL;DR

This paper investigates multidimensional gravity models with nonlinear scalar curvature terms 1/R and R^4, analyzing the stability of extra dimensions and their implications for cosmic acceleration and inflation.

Contribution

It provides a detailed stability analysis of extra dimensions in models with 1/R and R^4 curvature nonlinearities, revealing conditions for stabilization and their cosmological consequences.

Findings

Stabilized extra dimensions in 1/R models are AdS, not supporting late-time acceleration.

In R^4 models, stability depends on total dimension D, with a single stable sector for D>8.

Multiple stability sectors exist in R^4 models, with some prone to collapse and others smoothly connected to stable regions.

Abstract

We study multidimensional gravitational models with scalar curvature nonlinearities of the type 1/R and R^4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with warped product structure. Special attention is paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the 1/R model that configurations with stabilized extra dimensions do not provide a late-time acceleration (they are AdS), whereas the solution branch which allows for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R^4 model, we obtain that the stability region in parameter space depends on the total dimension D=dim(M) of the higher dimensional spacetime M. For D>8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D<8 an additional (metastable) sector exists which is separated from the conformal singularity by a potential barrier of finite height and width so that systems in this sector are prone to collapse into the conformal singularity. This second sector is not smoothly connected with the first (absolutely stable) one. Several limiting cases and the possibility for inflation are discussed for the R^4 model.