Initial time singularities and admissible initial states for a system of coupled scalar fields

Abstract

We discuss the problem of initial states for a system of coupled scalar fields out of equilibrium in the one-loop approximation. The fields consist of classical background fields, taken constant in space, and quantum fluctuations. If the initial state is the adiabatic vacuum, i.e., the ground state of a Fock space of particle excitations that diagonalize the mass matrix, the energy-momentum tensor is infinite at t=0, its most singular part behaves as 1/t. When the system is coupled to gravity this presents a problem that we solve by a Bogoliubov transformation of the naive initial state. As a side result we also discuss the canonical formalism and the adiabatic particle number for such a system. Most of the formalism is presented for Minkowksi space. Embedding the system and its dynamics into a flat FRW universe is straightforward and we briefly address the essential modifications.

26 pages, no figures; typos corrected, added 6 paragraphs et the end of section 3, and 1 paragraph at the end of section 5

References in corpus (6)

• Short distance and initial state effects in inflation: stress tensor and decoherence
• Decoupling in an expanding universe: backreaction barely constrains short distance effects in the CMB
• Renormalization of initial conditions and the trans-Planckian problem of inflation
• The Fate of SUSY Flat Directions and their Role in Reheating
• Longevity of supersymmetric flat directions
• The renormalization of the energy-momentum tensor for an effective initial state

Cited by in corpus (1)

• Coupled scalar fields in a flat FRW universe: renormalisation