Gravitational resonances on f(R)-brane

Hao Yu,Yu-Xiao Liu,Bao-Min Gu,Yuan Zhong

doi:10.1140/epjc/s10052-016-4039-3

Abstract

In this paper, we investigate various $f(R)$-brane models and compare their gravitational resonance structures with the corresponding general relativity (GR)-branes. {Starting from some known GR-brane solutions}, we derive thick $f(R)$-brane solutions such that the metric, scalar field, and scalar potential coincide with those of the corresponding GR-branes. {We find that for branes generated by a single or several canonical scalar fields, there is no obvious distinction between the GR-branes and corresponding $f(R)$-branes in terms of gravitational resonance structure.} Then we discuss the branes generated by K-fields. In this case, there could exist huge differences between GR-branes and $f(R)$-branes.

Highlights

Since general relativity (GR) was established by Einstein in 1915, a wide range of new theories of gravity have been proposed in the past 100 years
In this paper we focus on the appearance of gravitational resonances in thick Randall and Sundrum (RS)-II type brane models, where the branes can be generated by, for example, a single canonical scalar field in an AdS5 space [30,31,32,33]
Our results show that for the brane generated by a canonical scalar field or two canonical scalar fields, there is no striking difference between f (R)-brane and GR-brane in terms of gravitational resonance

Summary

Introduction

Since general relativity (GR) was established by Einstein in 1915, a wide range of new theories of gravity have been proposed in the past 100 years. The equation of the gravitational mode is independent from the background scalar fields and only depends on the warp factor This is not always true in modified gravity theories. It is possible to find gravitational resonances in thick brane models in scalar-tensor gravity [50]. In our third f (R)-brane model, we find that even for the case with only one single noncanonical scalar field, gravitational resonances on f (R)-brane can be significantly different from the GR-brane. Where a2(y) = e2A(y) is the warp factor, and ημν is the induced metric on the brane For this background space-time, the scalar fields only depend on the extra dimension, i.e., φi = φi (y).

The general b

Conclusion and discussion