Rotating and expanding Bianchi type-IX model in f (R, T) theory of gravity

The spatially homogeneous shear-free, rotating and expanding Bianchi type-IX universe has been considered in the presence of perfect fluid in f (R, T) theory of gravity. The exact solution of the field equations has been obtained and the functional form of f (R, T) = R + 2f (T) gravity has been reconstructed. The existence of such a solution suggests that the general relativistic shear-free perfect fluid conjecture which claims that a shear-free perfect fluid cannot rotate and expand at the same time, is not valid in this modified theory