On cosmology in nonlinear multidimensional gravity with multiple factor spaces

TL;DR

This paper investigates how nonlinear multidimensional gravity with multiple extra spaces can produce a small effective cosmological constant, identifying parameter sets that stabilize extra dimensions and discussing observational implications in different conformal frames.

Contribution

It demonstrates the existence of parameter configurations in multidimensional Kaluza-Klein models that yield a stable, fine-tuned cosmological constant and explores the size of extra dimensions in different conformal frames.

Findings

Existence of parameter sets with minimized effective potential.

Size of extra dimensions depends on conformal frame.

Total dimension constrained to D ≤ 20 for invisibility.

Abstract

Within the scope of multidimensional Kaluza--Klein gravity with nonlinear curvature terms and two spherical extra spaces of dimensions $m$ and $n$, we study the properties of an effective action for the scale factors of the extra dimensions. Dimensional reduction leads to an effective 4D multiscalar-tensor theory. Based on qualitative estimates of the Casimir energy contribution on a physically reasonable length scale, we demonstrate the existence of such sets of initial parameters of the theory in the case $m=n$ that provide a minimum of the effective potential that yield a fine-tuned value of the effective 4D cosmological constant. The corresponding size of extra dimensions depends of which conformal frame is interpreted as the observational one: it is about three orders of magnitude larger than the standard Planck length if we adhere to the Einstein frame, but it is $n$-dependent in the Jordan frame, and its invisibility requirement restricts the total dimension to values $D = 4+2n \leq 20$.