Order reduction in semiclassical cosmology

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.Comment: to be published in Phys.Rev.D vol. 59, 6 pages with 2 figure

Canonical gauge-invariant variables for scalar perturbations in synchronous coordinates

Under an appropriate change of the perturbation variable Lifshitz-Khalatnikov propagation equations for the scalar perturbation reduce to d'Alembert equation. The change of variables is based on the Darboux transform.Comment: LaTeX, 9 page

Asymptonic states of Friedman universe and the energy conditions using the phase variable method

The evolution of Friedman models with arbitrary pressure p = p($\varepsilon$, H) in the phase plane: Hubble function-energy density a is presented. The conclusions are: critical points of the phase plane and their stability depend on energy conditions but not on the actual form of pressure; models with constant viscosity violate the condition e + p $\geq$ 0; the weak and the strong energy conditions are preserved if the viscosity coefficient is proportional to $\varepsilon^{1/2}$