Vacuum $ f(R)$ thick brane solution with a Gaussian warp function

TL;DR

This paper presents an exact five-dimensional $f(R)$ gravity solution with a Gaussian warp function, analyzing gravitational fluctuations and cosmological implications consistent with the Starobinsky model, including a transition from radiation to dark energy dominance.

Contribution

It introduces a novel exact $f(R)$ thick brane solution with a Gaussian warp function and studies its gravitational and cosmological properties.

Findings

Supports the Starobinsky $f(R)$ model with a flat FLRW background

Matter behaves like radiation initially, then transitions to dark energy dominance

Demonstrates stability of gravitational fluctuations in the model

Abstract

This work deals with $f(R)$ modified gravity in five dimensional space-time. The Gaussian thick brane is shown to be an exact solution in the frame work of $f(R)$ gravity in five dimensions with a bulk cosmological constant. Response of the brane to gravitational fluctuations and concordance with the Starobinsky model is addressed. It is shown that the matter which supports the Starobinsky $f(R)$ solution with the background geometry being flat FLRW with a Gaussian warp function, behaves like a radiation dominated era of universe, gradually changing to a dark energy dominated era.