Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times

This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress–energy tensor of a quantum field with classical gravity. Here, we consider a free, massless scalar field with general (not necessarily conformal) coupling to curvature. In a cosmological scenario with flat spatial sections for special choices of the initial conditions, we observe a separation of the dynamics of the quantum degrees of freedom from the dynamics of the scale factor, which extends a classical result by Starobinski (1980 Phys. Lett. B 91 99–102) to general coupling. For this new equation of fourth order governing the dynamics of the scale factor, we study numerical solutions. Typical solutions show a radiation-like Big Bang for the early Universe and de Sitter-like expansion for the late Universe. We discuss a specific solution to the cosmological horizon problem that can be produced by tuning parameters in the given equation. Although the model proposed here only contains massless matter, we give a preliminary comparison of the obtained cosmology with the ΛCDM standard model of cosmology and investigate parameter ranges in which the new models, to a certain extent, is capable of assimilating standard cosmology.