2013/09/30 by Nicola Pinamonti, Daniel Siemssen · 1 citation
Physics and Astronomy · Mathematics · #math-ph #gr-qc #math.MP
paper · pdf · doi:10.1007/s00220-014-2099-5
published as Commun. Math. Phys. 334, 171-191 (2014) · 20 pages; corrected references
arxiv created 2015/03/07 · arxiv updated 2015/03/10
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 stress-energy tensor. Furthermore, it is possible to control this expectation value by means of a global estimate on regular cosmological spacetimes. The obtained estimates permit to write 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 becomes singular or the Hubble function reaches a critical value Hc = 180π/G, which both correspond to a divergence of the scalar curvature, namely a spacetime singularity.