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Abstract: In this paper we shall discuss the backreaction of a massive quantum scalarfield on the curvature, the latter treated as a classical field. Furthermore,we shall deal with this problem in the realm of cosmological spacetimes byanalyzing the Einstein equations in a semiclassical fashion. More precisely, weshall show that, at least on small intervals of time, solutions for thisinteracting system exist. This result will be achieved providing an iterationscheme and showing that the series, obtained starting from the masslesssolution, converges in the appropriate Banach space. The quantum states withgood ultraviolet behavior Hadamard property, used in order to obtain thebackreaction, will be completely determined by their form on the initialsurface if chosen to be lightlike. Furthermore, on small intervals of time,they do not influence the behavior of the exact solution. On large intervals oftime the situation is more complicated but, if the spacetime is expanding, weshall show that the end-point of the evolution does not depend strongly on thequantum state, because, in this limit, the expectation values of the matterfields responsible for the backreaction do not depend on the particularhomogeneous Hadamard state at all. Finally, we shall comment on theinterpretation of the semiclassical Einstein equations for this kind ofproblems. Although the fluctuations of the expectation values of pointlikefields diverge, if the spacetime and the quantum state have a large spatialsymmetry and if we consider the smeared fields on regions of large spatialvolume, they tend to vanish. Assuming this point of view the semiclassicalEinstein equations become more reliable.



Author: Nicola Pinamonti

Source: https://arxiv.org/







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