2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/178550We investigate the Robertson-Walker cosmology with Lagrangian $R+α_1\hbar R^2+α_2\hbar R^{μν}R_{μν} +L_{rad}$ 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.to be published in Phys.Rev.D vol. 59, 6 pages with 2 figuresAstrophysicsGeneral Relativity and Quantum Cosmologytext