Full linear perturbations and localization of gravity on $f(R,T)$ brane

Abstract

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. We try to get the analytic background solutions and discuss the full linear perturbations, especially the scalar perturbations. We compare how the brane world model is modified with that of general relativity coupled to a canonical scalar field. It is found that some more interesting background solutions are allowed, and only the scalar perturbation mode is modified. There is no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.

v3: 8 pages, 2 figures, improved version with minor corrections, accepted by EPJC

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• First-order formalism for thick branes in $f(T,\mathcal{T})$ gravity
• Stable Palatini $f(\mathcal{R})$ braneworld
• Quasinormal modes and echoes of a double braneworld
• Linear Stability of $f(R,\varphi ,X)$ Thick Branes: Tensor Perturbations
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• Multi-kink brane in Gauss-Bonnet gravity and its stability
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• Fermion Localization and Degenerate Resonances on Brane Array
• Models of modified $F(R,T)$ and cuscuton braneworld
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• Graviscalar quasinormal modes and asymptotic tails of a thick brane
• Quantized Scalar Fields in Curved Spacetime Background of Thick Brane
• Constraints on generalized Eddington-inspired Born-Infeld branes
• Thick branes in the scalar-tensor representation of $f(R,T)$ gravity