Cosmological perturbations from stochastic gravity

Roura, Albert; Verdaguer, Enric

doi:10.1103/physrevd.78.064010

Cited by 52 publications

(48 citation statements)

References 93 publications

(199 reference statements)

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“…Note that in contrast to the existing calculations of loop corrections to the spectrum of cosmological perturbations in inflationary models, where the self-interaction of the matter fields often plays an important role [56,57,58], the only interaction vertices associated with the free fields that we have considered here are those corresponding to their gravitational interaction. Moreover, we do not consider a non-vanishing homogeneous background configuration for the scalar fields (which would give also a tree-level contribution to the stress-tensor two-point function [59]) and the usual treatment for the correlations of the scalar-type metric perturbations [60,47,61,62] cannot be directly applied. On the other hand, the calculation for tensor metric perturbations should be equivalent (since the slow-roll geometry is usually approximated by de Sitter space in that case) but the existing results are either approximate [63] or restricted to the massless case [62].…”

Section: Discussionmentioning

confidence: 99%

Stress tensor fluctuations in de Sitter spacetime

Pérez-Nadal

Roura

Verdaguer

2010

J. Cosmol. Astropart. Phys.

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The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m 2 /H 2 . In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.

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Section: Discussionmentioning

confidence: 99%

Stress tensor fluctuations in de Sitter spacetime

Pérez-Nadal

Roura

Verdaguer

2010

J. Cosmol. Astropart. Phys.

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“…[126,129,130,131] and also Refs. [132,133,134].) This process is interpreted as the transition from the initial coherent superposition of many different worlds to the final statistical ensemble of them.…”

Section: The Quantum Decoherence and The Ir Problemmentioning

confidence: 99%

Loops in inflationary correlation functions

Tanaka

Urakawa

2013

Class. Quantum Grav.

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Abstract. We review the recent progress regarding the loop corrections to the correlation functions in the inflationary universe. A naive perturbation theory predicts that loop corrections generated during inflation suffer from various infrared (IR) pathologies. Introducing an IR cutoff by hand is neither satisfactory nor enough to fix the problem of secular growth, which may ruin the predictive power of inflation models if the inflation lasts sufficiently long. We discuss the origin of the IR divergences and explore the regularity conditions of loop corrections for the adiabatic perturbation, the iso-curvature perturbation, and the tensor perturbation, in turn. These three kinds of perturbations have qualitative differences, but in discussing the IR regularity there is a feature common to all cases, which is the importance of the proper identification of observable quantities. Genuinely observable quantities should respect the gauge invariance from the view point of a local observer. Interestingly, we find that the requirement of the IR regularity restricts the allowed quantum states.

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“…One can conceivably assume that it will also break down when the fluctuations of the stress-energy operator are large [111,237]. Calculations of the fluctuations of the energy density for Minkowski, Casimir and hot flat spaces as well as Einstein and de Sitter universes are available [86,198,237,258,259,282,302,303,304,305,313,316]. It is less clear, however, how to quantify what a large fluctuation is, and different criteria have been proposed [10,11,113,115,198,237,303,384,385].…”

Section: The Importance Of Quantum Fluctuationsmentioning

confidence: 99%

Stochastic Gravity: Theory and Applications

Verdaguer

2008

Living Rev. Relativ.

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153

184

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Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein-Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out directions for further developments and applications.

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Cosmological perturbations from stochastic gravity

Cited by 52 publications

References 93 publications

Stress tensor fluctuations in de Sitter spacetime

Stress tensor fluctuations in de Sitter spacetime

Loops in inflationary correlation functions

Stochastic Gravity: Theory and Applications

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