Uncertainty relations for cosmological particle creation and existence of large fluctuations in reheating

We derive an uncertainty relation for the energy density and pressure of a quantum scalar field in a time-dependent, homogeneous and isotropic, classical background, which implies the existence of large fluctuations comparable to their vacuum expectation values. A similar uncertainty relation is known to hold for the field square since the field can be viewed as a Gaussian random variable. We discuss possible implications of these results for the reheating process in scalar field driven inflationary models, where reheating is achieved by the decay of the coherently oscillating inflaton field. Specifically we argue that the evolution after backreaction can seriously be altered by the existence of these fluctuations. For example, in one model the coherence of the inflaton oscillations is found to be completely lost in a very short time after backreaction starts. Therefore we argue that entering a smooth phase in thermal equilibrium is questionable in such models and reheating might destroy the smoothness attained by inflation.Comment: 6 pages, essay written for the Gravity Research Foundation 2011 Awards for Essays on Gravitation, Received Honorable Mentio

On the Geometric Properties of AdS Instantons

According to the positive energy conjecture of Horowitz and Myers, there is a specific supergravity solution, AdS soliton, which has minimum energy among all asymptotically locally AdS solutions with the same boundary conditions. Related to the issue of semiclassical stability of AdS soliton in the context of pure gravity with a negative cosmological constant, physical boundary conditions are determined for an instanton solution which would be responsible for vacuum decay by barrier penetration. Certain geometric properties of instantons are studied, using Hermitian differential operators. On a $d$-dimensional instanton, it is shown that there are $d-2$ harmonic functions. A class of instanton solutions, obeying more restrictive boundary conditions, is proved to have $d-1$ Killing vectors which also commute. All but one of the Killing vectors are duals of harmonic one-forms, which are gradients of harmonic functions, and do not have any fixed points.Comment: 22 pages, Latex, short comments and a reference adde