Cosmological solutions of the semiclassical Einstein-Dirac equations

Abstract

Exact solutions to the semiclassical backreaction equations with an unquantised Dirac field are found when the ratio of the renormalisation parameters beta and alpha is 9/4. For alpha (0 there is a one-parameter family of solutions which do not have particle horizons and a two-parameter family of solutions which oscillate at about the Planck frequency and, on average, behave asymptotically as a matter-dominated Friedmann solution. There is a two-parameter family with an asymptotically de Sitter stage, which is stable for any alpha )0 and beta )0.