Cosmology in nonlinear multidimensional gravity and the Casimir effect

TL;DR

This paper explores cosmological models in multidimensional gravity with nonlinear curvature terms, demonstrating how Casimir energy can be balanced to produce realistic cosmological constants and inflationary behavior.

Contribution

It introduces models where Casimir energy is balanced by curvature nonlinearities, enabling realistic cosmological constants and inflation in multidimensional gravity.

Findings

Effective potential minima yield realistic cosmological constants.

Casimir energy is compensated by curvature nonlinear terms.

Models exhibit slow evolution of extra dimensions and power-law inflation.

Abstract

We study the possible cosmological models in Kaluza-Klein-type multidimensional gravity with a curvature-nonlinear Lagrangian and a spherical extra space, taking into account the Casimir energy. First, we find a minimum of the effective potential of extra dimensions, leading to a physically reasonable value of the effective cosmological constant in our 4D space-time. In this model, the huge Casimir energy density is compensated by a fine-tuned contribution of the curvature-nonlinear terms in the original action. Second, we present a viable model with slowly evolving extra dimensions and power-law inflation in our space-time. In both models, the results formulated in Einstein and Jordan frames are compared.