Statistical nature of infrared dynamics on de Sitter background

Tokuda, Junsei; Tanaka, Takahiro

doi:10.1088/1475-7516/2018/02/014

Cited by 49 publications

(57 citation statements)

References 28 publications

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“…However, when self-interactions are important it is well-known that for light fields the perturbative expansion fails [27,28], requiring one to employ other techniques. The stochastic approach [29,30] provides a powerful tool for such computations and is in agreement with, and in fact often superior to, other approaches to quantum field theory in de Sitter space [31][32][33][34][35][36][37][38][39]. In particular we note the direct QFT approaches making use of the Schwinger-Dyson equations: in Ref.…”

Section: Introductionmentioning

confidence: 68%

Scalar correlation functions in de Sitter space from the stochastic spectral expansion

Markkanen

Rajantie

Stopyra

et al. 2019

J. Cosmol. Astropart. Phys.

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We consider light scalar fields during inflation and show how the stochastic spectral expansion method can be used to calculate two-point correlation functions of an arbitrary local function of the field in de Sitter space. In particular, we use this approach for a massive scalar field with quartic self-interactions to calculate the fluctuation spectrum of the density contrast and compare it to other approximations. We find that neither Gaussian nor linear approximations accurately reproduce the power spectrum, and in fact always overestimate it. For example, for a scalar field with only a quartic term in the potential, V = λφ 4 /4, we find a blue spectrum with spectral index n − 1 = 0.579 √ λ.

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Section: Introductionmentioning

confidence: 68%

Scalar correlation functions in de Sitter space from the stochastic spectral expansion

Markkanen

Rajantie

Stopyra

et al. 2019

J. Cosmol. Astropart. Phys.

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“…This approach is usually studied in the slow-roll regime, which is an attractor of the classical field dynamics, where the frictional force due to the expansion balances the force coming from the potential gradient. In this regime, excellent agreement between stochastic inflation and usual quantum field theoretic techniques has been found [14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 76%

Stochastic inflation beyond slow roll

Pattison¹,

Vennin²,

Assadullahi³

et al. 2019

J. Cosmol. Astropart. Phys.

125

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We study the stochastic formalism of inflation beyond the usual slow-roll approximation. We verify that the assumptions on which the stochastic formalism relies still hold even far from the slow-roll attractor. This includes demonstrating the validity of the separate universe approach to evolving long-wavelength scalar field perturbations beyond slow roll. We also explain that, in general, there is a gauge correction to the amplitude of the stochastic noise. This is because the amplitude is usually calculated in the spatially-flat gauge, while the number of e-folds is used as the time variable (hence one works in the uniform-N gauge) in the Langevin equations. We show that these corrections vanish in the slow-roll limit, but we also explain how to calculate them in general. We compute them in difference cases, including ultra-slow roll and the Starobinsky model that interpolates between slow roll and ultra-slow roll, and find the corrections to be negligible in practice. This confirms the validity of the stochastic formalism for studying quantum backreaction effects in the very early universe beyond slow roll. Keywords: physics of the early universe, inflationRecently, situations in which non-slow-roll stochastic effects are at play have been highlighted [24][25][26][27][28]. For instance, if the inflationary potential features a very flat section close to the end of inflation, large curvature perturbations could be produced that later collapse into primordial black holes. If such a flat portion exists, it may be associated with both large stochastic diffusion [29] and deviations from slow-roll, e.g. along the so-called ultra-slow-roll (or "friction dominated") regime [30,31], which in some cases can be stable [32]. This explains the need for implementing the stochastic inflation programme beyond slow roll, which is the aim of the present work.This paper is organised as follows. In Sec. 2, we quickly review the stochastic inflation formalism and identify the three main requirements for the validity of this approach: the quantum-to-classical transition of super-Hubble fluctuations, the validity of the separate universe approach, and the consistent implementation of gauge corrections. The two latter requirements are the non-trivial ones and we examine them in Secs. 3 and 4 respectively. Although recently questioned [33], we find the separate universe approach to hold beyond slow roll, and we explain how the gauge corrections to the amplitude of the stochastic noise (that vanish in the slow-roll regime if the number of e-folds is used as a time variable) can be derived in general. We then apply this program to three situations of interest: slow roll in Sec. 5, where we recover the usual results, ultra-slow roll in Sec. 6, and the Starobinsky model in Sec. 7, which interpolates between an ultra-slow-roll and a slow-roll phase. In all cases, we find the gauge corrections to be negligible, allowing for the usual stochastic formulation to be employed.

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“…As this work was in final preparation, a related work was released [23]. Their emphasis is different, adopting a wavefunctional/path integral approach to understanding stochastic inflation, building on [24][25][26]. In particular, they do not adopt a fully diagrammatic framework, and discussions of semiclassicality rely on statements made at fixed order in perturbation theory, rather than our all-orders approach.…”

Section: Jhep07(2020)119mentioning

confidence: 99%

De Sitter diagrammar and the resummation of time

Baumgart

Sundrum

2020

J. High Energ. Phys.

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Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy "landscape" on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a resummation may provide insight into De Sitter holography. We present here a novel diagrammatic analysis of these infrared divergences and their resummation. Basic graph theory observations and momentum power counting for the in-in propagators allow a simple and insightful determination of the leading-log contributions. One thus sees diagrammatically how the superhorizon sector consists of a semiclassical theory with quantum noise evolved by a first-order, interacting classical equation of motion. This rigorously leads to the "Stochastic Inflation" ansatz developed by Starobinsky to cure the scalar infrared pathology nonperturbatively. Our approach is a controlled approximation of the underlying quantum field theory and is systematically improvable.

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Statistical nature of infrared dynamics on de Sitter background

Cited by 49 publications

References 28 publications

Scalar correlation functions in de Sitter space from the stochastic spectral expansion

Scalar correlation functions in de Sitter space from the stochastic spectral expansion

Stochastic inflation beyond slow roll

De Sitter diagrammar and the resummation of time

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