Triviality of λϕ4 theory in 3+1-dimensional spatially flat Robertson-Walker space in Gaussian approximation

We investigate λϕ⁴ theory within the Gaussian approximation in spatially flat Robertson-Walker space in 3+1 dimensions. After having performed an adiabatic expansion for one of the ansatz functions we find that the renormalization of the energy-momentum tensor provides two additional constraints which have to be satisfied by bare couplings. These conditions force the theory to be trivial after renormalization.