Constructions of f(R; G; T) gravity from some expansions of the Universe

Here we propose the extended modified gravity theory named f(R; G, T) gravity where R is the Ricci scalar, G is the Gauss{Bonnet invariant, and T is the trace of the stressenergy tensor.We derive the gravitational field equations in f(R; G, T) gravity by taking the least action principle. Next we construct the f(R; G, T) in terms of R, G and T in de Sitter as well as power-law expansion. We also construct f(R, G, T) if the expansion follows the finite-time future singularity (big rip singularity). We investigate the energy conditions in this modified theory of gravity and examine the validity of all energy conditions.