Cosmological solutions from induced matter model applied to 5D $$f(R,T)$$ f ( R , T ) gravity and the shrinking of the extra coordinate

In this work, I present exact cosmological solutions from Wesson’s induced matter model applied to a general 5D metric in $$f(R,T)$$ theory of gravity. The non-conservation of the energy-momentum tensor, predicted by $$f(R,T)$$ theory, allows the derivation of a relation that describes the time evolution of the extra coordinate, revealing its compactification. It is shown that such a compactification could induce the effects of an accelerated expansion in the observable universe.