Vacuum fluctuation of conformally coupled scalar field in FLRW space-times

Abstract

The regularized vacuum fluctuation related to a conformally coupled massless scalar field defined on a space-time with dynamical horizon is computed with respect a radially moving observer in a generic flat FLRW space-time. Two simple measurement prescriptions are given in order to remove the ambiguity associated with the short distance singularity of the correlation function. In some cases, it turns out that one is dealing with a "quantum thermometer", recovering a proposal due to Buchholz et al. in order to determine local temperature in the framework of quantum field theory. In general, by arranging the detector so that it does not register for inertial motion in flat space, the regularized quantum fluctuation may be used as a probe of space-time geometry and, in particular, may provide informations on the Hubble parameter. As an aside, it is not possible in general to fully decouple the effect of the detector's motion from the universe expansion, a fact that could be interpreted as a kind of Machian effect which can be traced back to the worldwide nature of the vacuum.

Vacuum Fluctuations as Quantum Probes in FRWL space-times

“…What about the use of fluctuation as thermometers in presence of gravity? Static black holes and FRWL space-times in cosmology are example of Spherically Symmetric Space-times (SSS), and both may have an unified descriptions [6]. With regard to this, first let us briefly review the Kodama-Hayward formalism.…”

Electroweak vacuum instability and renormalized Higgs field vacuum fluctuations in the inflationary universe

“…This is equal to the thermal fluctuations δφ 2 ren = T 2 /12 with the Gibbons-Hawking temperature T = H/2π experienced by a point observer inside the de Sitter horizon (see, e.g. Ref [66,67]…”