Thick branes with inner structure in mimetic f(R) gravity
Jing Chen, Wen-Di Guo, Yu-Xiao Liu
Abstract
Abstract In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in f ( R ) gravity. We obtain several typical thick brane solutions for $$f(R)=R+\alpha R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> . To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with $$df/dR>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>f</mml:mi> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi> <mml:mi>R</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> on the gravitational resonances is studied. As a brane splits into multi sub-branes, the effective potential of the tensor perturbation will have an abundant inner structure with multi-wells, and this will lead to new phenomena of the gravitational resonances.