Exact solutions of the Einstein equations including quantum effects and cosmological constant

Abstract

The solutions to the semiclassical backreaction equations are found for conformally invariant free quantum fields in partially flat homogeneous and isotropic spacetimes with cosmological constant and with no classical source, for certain relations between the regularisation parameters alpha , beta and the cosmological constant Lambda . These solutions satisfy the classical Einstein equations for an effective perfect fluid of uniform density and isotropic pressure and, its effective stress-energy tensor can violate the energy conditions. For 3 alpha >or= beta there is always a one-parameter family of solutions which undergoes a time-symmetric bounce and which contains no singularities. For 3 alpha >or= beta >0 there is a one-parameter family of solutions with an initial singularity but no particle horizons. The stability of the de Sitter solutions are investigated and one of them is stable even when Lambda <0 or alpha <0.