Attractor states and infrared scaling in de Sitter space

Journal Article · Fri Dec 15 04:00:00 EST 2000 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.62.124019· OSTI ID:40205233

Anderson, Paul R; Eaker, Wayne; Habib, Salman; Molina-Paris, Carmen; Mottola, Emil

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{sub 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{sup 2}+{xi}R>0, <T{sub 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}{>=}0 we show that the state independent asymptotic value of the energy-momentum tensor is proportional to the conserved geometrical tensor {sup (3)}H{sub 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, nonconformal fields. In the case m{sup 2}+{xi}R=0, but m and {xi} separately different from zero, <T{sub ab}> grows linearly with cosmic time at late times. For most values of m{sup 2} and {xi} in the tachyonic cases, m{sup 2}+{xi}R<0, <T{sub ab}> grows exponentially at late cosmic times for all physically admissible initial states.

• Sponsoring Organization: (US)
• OSTI ID: 40205233
• Journal Information: Physical Review D, Journal Name: Physical Review D Journal Issue: 12 Vol. 62; ISSN 0556-2821
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATTRACTORS
ENERGY-MOMENTUM TENSOR
EXPECTATION VALUE
SCALAR FIELDS