Thick brane in f(R) gravity with Palatini dynamics

D Bazeia,D Rubiera-Garcia,Gonzalo J Olmo,R Menezes,L Losano

doi:10.1140/epjc/s10052-015-3803-0

Abstract

This work deals with modified gravity in five dimensional spacetime. We study a thick Palatini $f(R)$ brane, that is, a braneworld scenario described by an anti-de Sitter warped geometry with a single extra dimension of infinite extent, sourced by real scalar field under the Palatini approach, where the metric and the connection are regarded as independent degrees of freedom. We consider a first-order framework which we use to provide exact solutions for the scalar field and warp factor. We also investigate a perturbative scenario such that the Palatini approach is implemented through a Lagrangian $f(R)=R+\epsilon R^n$, where the small parameter $\epsilon$ controls the deviation from the standard thick brane case.

Highlights

To reconcile the constraint of three spatial dimensions of the natural world with the introduction of extra dimensions, important scenarios have been proposed
This scenario assumes that the (3, 1) space-time that describes the natural world is embedded in an AdS5 warped geometry, with a single extra spatial dimension of infinite extent
Soon after the proposed thin braneworld scenario, it was modified with the presence of scalar fields, giving rise to a new, very interesting thick braneworld scenario, in which the warp factor is described by another function, which depends on the specific scalar field model one considers [9,10,11,12]

Summary

Introduction

To reconcile the constraint of three spatial dimensions of the natural world with the introduction of extra dimensions, important scenarios have been proposed. We note from Eq (5) that for f (R) = R, the new metric hμν coincides with gμν, and we get back to GR It is worth mentioning (i) the second-order character of the field equations (6) and (ii) the fact that in vacuum, Tμν = 0, they boil down to the equations of GR plus a cosmological constant term (depending on the explicit functional form of the f (R) Lagrangian chosen), which implies absence of new propagating degrees of freedom in the spectrum of the theory. (i) the conformal factor relating the metrics hμν and gμν is determined by the matter fields and does not require solving an independent dynamical equation, and (ii) the energy density of the matter fields can be seen as playing a role analogous to that of the density of point defects in a hypothetical space-time microstructure [29]. Since the scalar-tensor representation does not bring about any useful new insight or simplification in our analysis, in this work we prefer not to use it

Braneworld setup

Consistency of the model

First-order equations

Example

Perturbative approach

Comments and conclusions