Cosmologies from nonlinear multidimensional gravity with acceleration and slowly varying G

TL;DR

This paper develops multidimensional cosmological models with exponential expansion of both observable and extra dimensions, allowing for a slowly varying gravitational constant G, and predicts significant future changes in physical laws due to extra dimension growth.

Contribution

It introduces a class of multidimensional cosmological models with higher-order curvature terms that accommodate a slowly varying G within observational limits.

Findings

Both the observable scale factor and extra dimensions grow exponentially.

The effective gravitational constant G varies slowly within observational bounds.

Future growth of extra dimensions may drastically alter physical laws.

Abstract

We consider multidimensional gravity with a Lagrangian containing the Ricci tensor squared and the Kretschmann invariant. In a Kaluza-Klein approach with a single compact extra space of arbitrary dimension, with the aid of a slow-change approximation (as compared with the Planck scale), we build a class of spatially flat cosmological models in which both the observed scale factor $a(\tau)$ and the extra-dimensional one, $b(\tau)$, grow exponentially at large times, but $b(\tau)$ grows slowly enough to admit variations of the effective gravitational constant $G$ within observational limits. Such models predict a drastic change in the physical laws of our Universe in the remote future due to further growth of the extra dimensions.