Attractor states and infrared scaling in de Sitter space

Details Attractor states and infrared scaling in de Sitter space Attractor states and infrared scaling in de Sitter space

2000-05-23

arxiv.org/abs/gr-qc/0005102v1

Phys.Rev. D62 (2000) 124019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, 6 figures, 46 kB tar.gz file

Scientific paper

10.1103/PhysRevD.62.124019

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 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, 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, grows linearly with cosmic time at late times. For most values of m and xi in the tachyonic cases, m^2 + xi R < 0, grows exponentially at late cosmic times for all physically admissable initial states.

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