Gravitational resonances on $f(R)$-brane

TL;DR

This paper compares gravitational resonance structures of $f(R)$-brane models with those of general relativity branes, finding similarities in scalar field-generated branes but notable differences in K-field-generated branes.

Contribution

It derives $f(R)$-brane solutions from known GR-branes and analyzes their resonance structures, highlighting differences in K-field-generated branes.

Findings

No significant difference in resonance structure for scalar field branes.

Potential large differences in resonance structure for K-field branes.

Provides a method to derive $f(R)$-branes from GR-brane solutions.

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.