https://doi.org/10.1140/epjc/s10052-021-09504-y
Regular Article - Theoretical Physics
Thick branes with inner structure in mimetic f(R) gravity
1
Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, 730000, Lanzhou, Gansu, China
2
Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, 730000, Lanzhou, People’s Republic of China
3
Joint Research Center for Physics, Lanzhou University and Qinghai Normal University, 730000, Lanzhou, People’s Republic of China
4
Joint Research Center for Physics, Lanzhou University and Qinghai Normal University, 810000, Xining, People’s Republic of China
5
Centro de Astrofísica e Gravitação-CENTRA, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal
Received:
28
May
2021
Accepted:
28
July
2021
Published online:
7
August
2021
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 
. To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with 
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 
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.
© The Author(s) 2021
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