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= trip. 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.;An explicit computation of the noise kernel for the conformally invariant scalar field in a thermal state is shown in Minkowski and Schwarzschild spacetimes for non-null separations of the spacetime points. For Minkowski spacetime, this result is exact; for Schwarzschild, this is an approximate result valid at short distances. Additionally, an exact expression for the noise kernel for the conformal vacuum valid for an arbitrary separation of points is given for all conformally flat spacetimes. This expression is evaluated in the static de Sitter coordinates, and an analysis of the behavior in the region near the cosmological horizon is given. A comparison is made between the noise kernel in Schwarzschild spacetime and the noise kernel in static de Sitter spacetime in the near horizon region. Within the context of static de Sitter space, an investigation is made into the validity of the quasi-local expansion near the cosmological horizon.