We investigate the Robertson-Walker cosmology with Lagrangian $R+\alpha_1\hbar R^2+\alpha_2\hbar R^{ \mu\nu}R_{ \mu\nu} +L_{ rad}$ where $L_{ rad}$ means classical source with traceless energy-momentum tensor. We weaken the self-consistence condition (L. Parker, J. Z. Simon, Phys. Rev. { D47}(1993),{ 1339}). Quantum corrections are expressed as contributions to the effective equation of state. We show that the empty space-time is stable within the class of radiation-filled expanding universes with no order reduction of the field equations.
Categories: astro-ph gr-qc
