Quantum Effects of Scalar Fields in Black Hole and Cosmological Spacetimes
Using a background field calculation, an analysis is presented of the effects of free quantum scalar fields upon the geometry of a cosmological spacetime containing a big rip singularity. The spacetime investigated is that of a spatially flat FRW metric in which the scale factor increases as a power-law with a divergence at some future time $t=t_{\text{rip}}$. Results of analytical and numerical computations of the expectation value of the stress tensor for massive and massless minimally and conformally coupled quantized scalar fields are presented. It is shown that, for physically realistic spacetimes, and for reasonable choices of the state of the quantum field, there is no evidence that quantum effects become important prior to the point where the scalar curvature reaches the Planck scale.
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