Effective cosmological equations of induced f(R) gravity

TL;DR

This paper develops effective cosmological equations for a brane universe with an induced f(R) gravity term, incorporating matter and bulk effects, and explores their applications to models like Starobinsky and DGP cosmology.

Contribution

It derives exact covariant equations for brane cosmology with induced f(R) gravity, including matter and bulk effects, extending previous models.

Findings

Formulation of generalized dark radiation in brane cosmology

Derivation of effective four-dimensional equations at low energies

Application to Starobinsky and DGP cosmological models

Abstract

We expand the study of generalized brane cosmologies by allowing for an $f(\tilde{\cal R})$ gravity term on the brane, with $\tilde{\cal R}$ the curvature scalar derived from the induced metric. We also include arbitrary matter components on the brane and in the five-dimensional bulk. At low energies, the effect of the bulk on the brane evolution can be described through a mirage component, termed generalized dark radiation, in the effective four-dimensional field equations. Using the covariant formalism, we derive the exact form of these equations. We also derive an effective conservation equation involving the brane matter and the generalized dark radiation. At low energies the coupled brane-bulk system has a purely four-dimensional description. The applications of the formalism include generalizations of the Starobinsky model and the Dvali-Gabadadze-Porrati cosmology.