Attractor states and infrared scaling in de Sitter space

TL;DR

This paper investigates the late-time behavior of the energy-momentum tensor for scalar fields in de Sitter space, revealing attractor states and their dependence on mass and curvature coupling, with implications for quantum field theory in curved spacetime.

Contribution

It proves the existence of fixed point attractor states for the energy-momentum tensor in de Sitter space for a wide class of initial states, generalizing the understanding of infrared behavior and trace anomalies.

Findings

<T_{ab}> approaches de Sitter invariant values at late times.

The asymptotic value of <T_{ab}> is proportional to the geometrical tensor H_{ab} for massless, non-conformal fields.

In tachyonic cases, <T_{ab}> grows exponentially at late times.

Abstract

The renormalized expectation value of the energy-momentum tensor for a scalar field with any mass m and curvature coupling xi is studied for an arbitrary homogeneous and isotropic physical initial state in de Sitter spacetime. We prove quite generally that <T_{ab}> has a fixed point attractor behavior at late times, which depends only on m and xi, for any fourth order adiabatic state that is infrared finite. Specifically, when m^2 + xi R > 0, <T_{ab}> approaches the Bunch-Davies de Sitter invariant value at late times, independently of the initial state. When m = xi = 0, it approaches instead the de Sitter invariant Allen-Folacci value. When m = 0 and xi \ge 0 we show that this state independent asymptotic value of the energy-momentum tensor is proportional to the conserved geometrical tensor (3)H_{ab}, which is related to the behavior of the quantum effective action of the scalar field under global Weyl rescaling. This relationship serves to generalize the definition of the trace anomaly in the infrared for massless, non-conformal fields. In the case m^2 + xi R = 0, but m and xi separately different from zero, <T_{ab}> grows linearly with cosmic time at late times. For most values of m and xi in the tachyonic cases, m^2 + xi R < 0, <T_{ab}> grows exponentially at late cosmic times for all physically admissable initial states.