Cosmological reconstruction and stability in f(R, T) gravity

We study the cosmological reconstruction of f(R, T) gravity (where R and T denote the Ricci scalar and trace of the energy-momentum tensor) corresponding to the evolution background in FRW universe. It is shown that any cosmological evolution including Lambda cold dark matter, phantom or non-phantom eras and possible phase transition from decelerating to accelerating can be reproduced in this theory. We propose some specific forms of Lagrangian in the perspective of de Sitter and power law expansion history. Finally, we formulate the perturbed evolution equations and analyze the stability of some important solutions.