Research ArticleNo Access

Braneworld mimetic $f (R)$ gravity

Kourosh Nozari

http://orcid.org/0000-0003-4368-5823

Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran

Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P. O. Box 55134-441, Maragha, Iran

E-mail Address: knozari@umz.ac.ir

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and

Naser Sadeghnezhad

Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran

Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P. O. Box 55134-441, Maragha, Iran

E-mail Address: nsadegh@stu.umz.ac.ir

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https://doi.org/10.1142/S0219887819500427Cited by:8 (Source: Crossref)

Abstract

Following our recent work on braneworld mimetic gravity, in this paper, we study an extension of braneworld mimetic gravity to the case that the gravitational sector on the brane is modified in the spirit of $f (R)$ theories. We assume the physical 5D bulk metric in the Randall–Sundrum II braneworld scenario consists of a 5D scalar field (which mimics the dark sectors on the brane) and an auxiliary 5D metric. We find the 5D Einstein’s field equations and the 5D equation of motion of the bulk scalar field in this setup. By using the Gauss–Codazzi equations, we obtain the induced Einstein’s field equations on the brane. Finally, by adopting the FRW background, we find the Friedmann equation on the brane in this $f (R)$ mimetic braneworld setup.

Keywords:

AMSC: 83D05, 83E15, 83F05

PACS: 04.50.−h, 98.80.Cq, 95.36.

$+$ x, 95.35.

$+$ d

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