Global Existence of Solutions of the Semiclassical Einstein Equation for Cosmological Spacetimes
Abstract
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get a state for the quantum field which gives finite expectation values for the stressenergy tensor. Furthermore, it is possible to control this expectation value by means of a global estimate on regular cosmological spacetimes. The obtained estimates permit writing a theorem about the existence and uniqueness of the local solutions encompassing both the spacetime metric and the matter field simultaneously. Finally, we show that one can always extend local solutions up to a point where the scale factor a becomes singular or the Hubble function H reaches a critical value H _{ c } = 180 π/G, both of which correspond to a divergence of the scalar curvature R, namely a spacetime singularity.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 February 2015
 DOI:
 10.1007/s0022001420995
 arXiv:
 arXiv:1309.6303
 Bibcode:
 2015CMaPh.334..171P
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 20 pages