Reconstructing f(R,T) gravity from holographic dark energy

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We consider cosmological scenarios based on f(R,T) theories of gravity (R is the Ricci scalar and T is the trace of the energy-momentum tensor) and numerically reconstruct the function f(R,T) which is able to reproduce the same expansion history generated, in the standard General Relativity theory, by dark matter and holographic dark energy. We consider two special f(R,T) models: in the first instance, we investigate the modification R + 2f(T), i.e. the usual Einstein-Hilbert term plus a f(T) correction. In the second instance, we consider a f(R)+λT theory, i.e. a T correction to the renown f(R) theory of gravity.