Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.084035· OSTI ID:21541501

Janssen, T M; Prokopec, T ^[1]

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1. Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, Postbus 80.195, 3508 TD Utrecht (Netherlands)

In this paper we consider a massless scalar field, with a possible coupling {xi} to the Ricci scalar in a D dimensional Friedmann-Lemaitre-Robertson-Walker space-time with a constant deceleration parameter q={epsilon}-1, {epsilon}=-H/H{sup 2}. Correlation functions for the Bunch-Davies vacuum of such a theory have long been known to be infrared divergent for a wide range of values of {epsilon}. We resolve these divergences by explicitly matching the space-time under consideration to a space-time without infrared divergencies. Such a procedure ensures that all correlation functions with respect to the vacuum in the space-time of interest are infrared finite. In this newly defined vacuum we construct the coincidence limit of the propagator and as an example calculate the expectation value of the stress-energy tensor. We find that this approach gives both in the ultraviolet and in the infrared satisfactory results. Moreover, we find that, unless the effective mass due to the coupling to the Ricci scalar {xi}R is negative, quantum contributions to the energy density always dilute away faster, or just as fast, as the background energy density. Therefore, quantum backreaction is insignificant at the one-loop order, unless {xi}R is negative. Finally we compare this approach with known results where the infrared is regulated by placing the Universe in a finite box. In an accelerating universe, the results are qualitatively the same, provided one identifies the size of the Universe with the physical Hubble radius at the time of the matching. In a decelerating universe, however, the two schemes give different late time behavior for the quantum stress-energy tensor. This happens because in this case the length scale at which one regulates the infrared becomes sub-Hubble at late times.

• OSTI ID: 21541501
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 8; Other Information: DOI: 10.1103/PhysRevD.83.084035; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCELERATION
COMPARATIVE EVALUATIONS
CORRELATION FUNCTIONS
COUPLING
EFFECTIVE MASS
ENERGY DENSITY
EXPECTATION VALUE
HUBBLE EFFECT
INFRARED DIVERGENCES
RICCI TENSOR
SCALAR FIELDS
SPACE-TIME
ULTRAVIOLET RADIATION
UNIVERSE
ELECTROMAGNETIC RADIATION
EVALUATION
FUNCTIONS
MASS
RADIATIONS
TENSORS