Particle creation and entropy generation during a tunneling between spacetimes

This paper explores the evolution of a quantum matter field on a gravitational instanton, investigating in particular the fact that this evolution results oftentimes in an end state which is "nearly thermal." The key features leading to this systematic evolution are the facts (a) that evolution on an instanton entails a systematic suppression of any initial excitations and (b) that an initial vacuum evolves oftentimes to an end state which, albeit pure, is characterized by a nearly thermal expectation value for the number $N_k$ of particles in each mode $\mathbf{k}$, the temperature being determined by the duration (in imaginary time) of the instanton. Both these facts are a direct consequence of the nonunitary evolution implicit in an imaginary-time Tomonaga-Schwinger equation. The "nearly thermal" character of the end state may also be manifest by the expectation value of other functions $f\left(N_k\right)$, but significant discrepancies arise when considering mode-mode correlations or other properties of the field that probe the "phase information" complementary to the "number information," a fact interpreted within the context of work by Hu and Kandrup on information-theoretic measures of entropy for a quantum field. These results are established rigorously for the special case of homogeneous tunneling, using a straightforward analogue of techniques developed by Parker and by Zel'dovich and Starobinsky, and are motivated in more general settings, allowing in particular for topology-changing instantons, using the functional integral approach of, e.g., Lavrelashvili, Rubakov, and Tinyakov.