I am trying to derive expression 19 in this article. First of all I have made setup for field equations and other tensors. Though it seems okay, I am getting slightly different expression from paper. For example, the expression for tensor P_abcd and energy momentum tensor does not match entirely. And in end, I think did some mistake and could not get the expression after solving. Can any one fix this issue? Am i defining all the tensors and scalars correctly? One can see here more details on the setup.

Thank You in advance.