Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker spacetime in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a nonlocal term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near a zero scale factor (initial singularity), it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from ``nothing'' into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.

Black holes from nucleating strings

We evaluate the probability that a loop of string that has spontaneously nucleated during inflation will form a black hole upon collapse, after the end of inflation. We then use the observational bounds on the density of primordial black holes to put constraints on the parameters of the model. Combining these constraints with current upper limits on the expansion rate during inflation, we conclude that the density of black holes formed from nucleating strings is too low to be observed. Also, constraints on domain wall nucleation and monopole pair production during inflation are briefly discussed.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.

In defense of the "tunneling" wave function of the universe

The tunneling approach to the wave function of the Universe has been recently criticized by Bousso and Hawking who claim that it predicts a catastrophic instability of de Sitter space with respect to pair production of black holes. We show that this claim is unfounded. First, we argue that different horizon size regions in de Sitter space cannot be treated as independently created, as they contend. And second, the WKB tunneling wave function is not simply the inverse of the Hartle-Hawking one, except in very special cases. Applied to the related problem of pair production of massive particles, we argue that the tunneling wave function leads to a small constant production rate, and not to a catastrophe as the argument of Bousso and Hawking would suggest.

Heat kernels and thermodynamics in Rindler space

We point out that using the heat kernel on a cone to compute the first quantum correction to the entropy of Rindler space does not yield the correct temperature dependence. In order to obtain the physics at arbitrary temperature one must compute the heat kernel in a geometry with different topology (without a conical singularity). This is done in two ways, which are shown to agree with computations performed by other methods. Also, we discuss the ambiguities in the regularization procedure and their physical consequences.

Large N phases, gravitational instantons and the nuts and bolts of AdS holography

Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity (at least with a negative cosmological constant) can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay, and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taub-bolt spacetimes, and compare them to a (2+1)-dimensional conformal field theory (at large N) compactified on a squashed three-sphere and on the twisted plane.

Charged AdS black holes and catastrophic holography

We compute the properties of a class of charged black holes in antide Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der WaalsMaxwell liquid-gas system. In that case, the phases are controlled by the universal cusp and swallowtail shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.

Propagation in a thermal graviton background

It is well known that radiative corrections evaluated in nontrivial backgrounds lead to effective dispersion relations which are not Lorentz invariant. Since gravitational interactions increase with energy, gravity-induced radiative corrections could be relevant for the trans-Planckian problem. As a first step to explore this possibility, we compute the one-loop radiative corrections to the self-energy of a scalar particle propagating in a thermal bath of gravitons in Minkowski spacetime. We obtain terms which originate from the thermal bath and which indeed break the Lorentz invariance that possessed the propagator in the vacuum. Rather unexpectedly, however, the terms which break Lorentz invariance vanish in the high three-momentum limit. We also found that the imaginary part, which gives the rate of approach to thermal equilibrium, vanishes at one loop.

Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity

A spatially flat Robertson-Walker spacetime driven by a cosmological constant is nonconformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially isotropic perturbations of the metric and the quantum state. These results are independent of the free renormalization parameters.

Particle creation due to cosmological contraction of extra dimensions

Particle production in a cosmological spacetime with extra dimensions is discussed. A five-dimensional cosmological model with a three-dimensional space expanding isotropically like in a radiative Friedmann-Robertson-Walker model and an internal space contracting to a constant small size is considered. The parameters of the model are adjusted so that time variations in internal space are compatible with present limits on time variations of the fundamental constants. By requiring that the energy density of the particles produced be less than the critical density at the radiation era we set restrictions on two more parameters: namely, the initial time of application of the semiclassical approach and the relative sizes between the internal space and the horizon of the ordinary Universe at this time. Whereas the production of massless particles allows a large range of variation to these parameters, the production of massive particles sets severe constraints on them, since, if they are overproduced, their energy density might very soon dominate the Universe and make cosmological dimensional reduction by extradimensional contraction unlikely.

Semiclassical equations for weakly inhomogeneous cosmologies

The in-in effective action formalism is used to derive the semiclassical correction to Einsteins equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the back-reaction effect on the gravitational field of the string is discussed.

Particle creation in a colliding plane wave spacetime: Wave packet quantization

We use wave packet mode quantization to compute the creation of massless scalar quantum particles in a colliding plane wave spacetime. The background spacetime represents the collision of two gravitational shock waves followed by trailing gravitational radiation which focus into a Killing-Cauchy horizon. The use of wave packet modes simplifies the problem of mode propagation through the different spacetime regions which was previously studied with the use of monochromatic modes. It is found that the number of particles created in a given wave packet mode has a thermal spectrum with a temperature which is inversely proportional to the focusing time of the plane waves and which depends on the mode trajectory.