Energy-Momentum Tensor of Particles Created in an Expanding Universe

TL;DR

This paper develops a framework for calculating the energy-momentum tensor of quantum scalar fields in an expanding universe, analyzing particle creation and backreaction effects with a focus on de Sitter spacetime.

Contribution

It introduces an adiabatic basis for renormalizing <T_ab> and provides a numerical scheme for evolving arbitrary initial states in cosmological models.

Findings

Renormalized <T_ab> is conserved and physically transparent.

Late-time behavior of massless fields approaches de Sitter invariant state.

Backreaction effects are significant when m^2+xi R=0, with energy density growing linearly over time.

Abstract

We present a general formulation of the time-dependent initial value problem for a quantum scalar field of arbitrary mass and curvature coupling in a FRW cosmological model. We introduce an adiabatic number basis which has the virtue that the divergent parts of the quantum expectation value of the energy-momentum tensor <T_ab> are isolated in the vacuum piece of <T_ab>, and may be removed using adiabatic subtraction. The resulting renormalized <T_ab> is conserved, independent of the cutoff, and has a physically transparent, quasiclassical form in terms of the average number of created adiabatic `particles'. By analyzing the evolution of the adiabatic particle number in de Sitter spacetime we exhibit the time structure of the particle creation process, which can be understood in terms of the time at which different momentum scales enter the horizon. A numerical scheme to compute <T_ab> as a function of time with arbitrary adiabatic initial states (not necessarily de Sitter invariant) is described. For minimally coupled, massless fields, at late times the renormalized <T_ab> goes asymptotically to the de Sitter invariant state previously found by Allen and Folacci, and not to the zero mass limit of the Bunch-Davies vacuum. If the mass m and the curvature coupling xi differ from zero, but satisfy m^2+xi R=0, the energy density and pressure of the scalar field grow linearly in cosmic time demonstrating that, at least in this case, backreaction effects become significant and cannot be neglected in de Sitter spacetime.