One-loop corrections to scalar and tensor perturbations during inflation in stochastic gravity

Urakawa, Yuko; Maeda, Kei Ichi

doi:10.1103/physrevd.78.064004

Cited by 47 publications

(30 citation statements)

References 76 publications

(113 reference statements)

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“…A similar divergence has been reported for various fields [20,21,22,23]. The accumulated effect of the IR contributions has been explored also in the presence of the gravitational fluctuations [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. The IR contributions for multi scalar fields also have been studied [40,41,42].…”

Section: Motivations and Overviewsupporting

confidence: 58%

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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Section: Motivations and Overviewsupporting

confidence: 58%

Loops in inflationary correlation functions

Tanaka

Urakawa

2013

Class. Quantum Grav.

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“…One might speculate that the stochastic formalism is nonetheless correct, and it has been employed on this basis to estimate corrections to the inflationary power spectra [65]. Other plausible approximations were earlier invoked to arrive at somewhat different estimates [66,67,68].…”

Section: Discussionmentioning

confidence: 99%

Excitation of photons by inflationary gravitons

Wang

Woodard

2015

Phys. Rev. D

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We use a recent result for the graviton contribution to the one loop vacuum polarization to solve the effective field equations for dynamical photons on de Sitter background. Our results show that the electric field experiences a secular enhancement proportional to the number of inflationary e-foldings. We discuss the minimum this establishes for primordial inflation to seed cosmic magnetic fields.

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“…In the stochastic gravity approach some insights on the exact treatment of the inflaton scalar field perturbations have been discussed in [316,353,354]. The main features that would characterize an exact treatment of the inflaton perturbations are the following.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Gravity: Theory and Applications

Verdaguer

2008

Living Rev. Relativ.

156

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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One-loop corrections to scalar and tensor perturbations during inflation in stochastic gravity

Cited by 47 publications

References 76 publications

Loops in inflationary correlation functions

Loops in inflationary correlation functions

Excitation of photons by inflationary gravitons

Stochastic Gravity: Theory and Applications

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