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

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.

14 pages, 6 figures

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Cited by in corpus (3)

• Thick branes with inner structure in mimetic $f(R)$ gravity
• Spontaneous branes formation
• Formation and evolution of a 2-brane structure in multidimensional $f(R)$ gravity