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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 ofthe energy-momentum tensor. We try to get the analytic background solutions anddiscuss the full linear perturbations, especially the scalar perturbations. Wecompare how the brane world model is modified with that of general relativitycoupled to a canonical scalar field. It is found that some more interestingbackground solutions are allowed, and only the scalar perturbation mode ismodified. There is no tachyon state exists in this model and only the masslesstensor mode can be localized on the brane, which recovers the effectivefour-dimensional gravity. These conclusions hold provided that two constraintson the original formalism of the action are satisfied.

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