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Communications in Mathematical Physics

, Volume 334, Issue 1, pp 171–191 | Cite as

Global Existence of Solutions of the Semiclassical Einstein Equation for Cosmological Spacetimes

  • Nicola Pinamonti
  • Daniel Siemssen
Article

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 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 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 = 180π/G, both of which correspond to a divergence of the scalar curvature R, namely a spacetime singularity.

Keywords

Global Existence Adiabatic State Maximal Solution Energy Tensor Renormalization Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversitá di GenovaGenovaItaly

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