Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times. (English) Zbl 1496.83002
Summary: 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 A. A. Starobinsky [Phys. Lett., B 91, No. 1, 99–102 (1980; Zbl 1371.83222)] 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 \(\Lambda\)CDM standard model of cosmology and investigate parameter ranges in which the new models, to a certain extent, is capable of assimilating standard cosmology.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 83F05 | Relativistic cosmology |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 70S05 | Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 58J47 | Propagation of singularities; initial value problems on manifolds |
| 65H05 | Numerical computation of solutions to single equations |
| 83E05 | Geometrodynamics and the holographic principle |
| 83C56 | Dark matter and dark energy |
Keywords:
semiclassical Einstein equation; cosmology; higher derivative gravity; asymptotic de Sitter solutionsCitations:
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