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

TL;DR

This paper examines initial states in coupled scalar fields out of equilibrium, addressing singularities at t=0 and proposing a Bogoliubov transformation to obtain finite energy-momentum tensors, with implications for cosmological models.

Contribution

It introduces a method to regularize initial states of coupled scalar fields in out-of-equilibrium conditions, especially when coupled to gravity, by using a Bogoliubov transformation.

Findings

Adiabatic vacuum initial state leads to infinite energy-momentum tensor at t=0.

Bogoliubov transformation regularizes the initial state, removing singularities.

Formalism applicable to Minkowski space and adaptable to flat FRW universe.

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.