Nucleation rates in flat and curved space

Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we consider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of a false (or true) vacuum at zero temperature in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls, and monopoles during inflation. The instantons for these processes are spherical world sheets or world lines embedded in flat or de Sitter backgrounds. We find the contribution of such instantons to the semiclassical partition function, including the one loop corrections due to small fluctuations around the spherical world sheet. We suggest a prescription for obtaining, from the partition function, the distribution of objects nucleated during inflation. This can be seen as an extension of the usual formula, valid in flat space, according to which the nucleation rate is twice the imaginary part of the free energy. For the case of pair production, the results reproduce those that can be obtained using second quantization methods, confirming the validity of instanton techniques in de Sitter space. Throughout the paper, both the gravitational field and the antisymmetric tensor field are assumed external.

Pair production by and electric field in (1+1)-dimensional de Sitter space

We use the method of Bogolubov transformations to compute the rate of pair production by an electric field in (1+1)-dimensional de Sitter space. The results are in agreement with those obtained previously using the instanton methods. This is true even when the size of the instanton is comparable to the size of the de Sitter horizon.

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.

Classical anisotropies in models of open inflation

In the simplest model of open inflation there are two inflaton fields decoupled from each other. One of them, the tunneling field, produces a first stage of inflation which prepares the ground for the nucleation of a highly symmetric bubble. The other, a free field, drives a second period of slow-roll inflation inside the bubble. However, the second field also evolves during the first stage of inflation, which to some extent breaks the needed symmetry. We show that this generates large supercurvature anisotropies which, together with the results of Tanaka and Sasaki, rule out this class of simple models (unless, of course, Omega0 is sufficiently close to 1). The problem does not arise in modified models where the second field does not evolve in the first stage of inflation.

Open inflation and the singulary boundary

The singularity in the Hawking-Turok model of open inflation has some appealing properties, such as the fact that its action is integrable. Also, if one thinks of the singularity as the boundary of spacetime, then the Gibbons-Hawking term is nonvanishing and finite. Here, we consider a model where the gravitational and scalar fields are coupled to a dynamical membrane. The singular instanton can then be obtained as the limit of a family of no-boundary solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking term. Unrelated to this issue, we also point out that the singularity acts as a reflecting boundary for scalar perturbations and gravity waves. Therefore, the quantization of cosmological perturbations seems to be well posed in this background.

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.

Quantum black hole entropy and newton constant renormalization

ty that low-energy effective field theory could be sufficient to understand the microscopic degrees of freedom underlying black hole entropy. We propose a qualitative physical picture in which black hole entropy refers to a space of quasicoherent states of infalling matter, together with its gravitational field. We stress that this scenario might provide a low-energy explanation of both the black hole entropy and the information puzzle.