Inflationary stochastic anomalies

Pinol, Lucas; Renaux‐Petel, Sébastien; Tada, Yuichiro

doi:10.1088/1361-6382/ab097f

Cited by 27 publications

(41 citation statements)

References 68 publications

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“…Here we mention the previous study of the stochastic equation for the same model [9]. The previous study did not take into account the contribution from the second term in the lefthand side of (3.5).…”

Section: )mentioning

confidence: 99%

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Infrared resummation for derivative interactions in de Sitter space

Kitamoto

2019

Phys. Rev. D

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In de Sitter space, scale invariant fluctuations give rise to infrared logarithmic corrections to physical quantities, which eventually spoil perturbation theories. For models without derivative interactions, it has been known that the field equation reduces to a Langevin equation with white noise in the leading logarithm approximation. The stochastic equation allows us to evaluate the infrared effects nonperturbatively. We extend the resummation formula so that it is applicable to models with derivative interactions. We first consider the nonlinear sigma model and next consider a more general model which consists of a noncanonical kinetic term and a potential term. The stochastic equations derived from the infrared resummation in these models can be understood as generalizations of the standard one to curved target spaces.

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Section: )mentioning

confidence: 99%

“…As concrete examples, we consider the nonlinear sigma model and a more general model which consists of a noncanonical kinetic term and a potential term. Although there has been an attempt to derive stochastic equations in these models [9], the consistency with the resummation of the leading IR logarithms has not been verified completely.…”

Section: Introductionmentioning

confidence: 99%

Infrared resummation for derivative interactions in de Sitter space

Kitamoto

2019

Phys. Rev. D

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“…For other techniques, see Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29] The stochastic approach has become increasingly popular in recent years, likely due to its great efficacy, and in this vein we note the recent works [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Often the focus is on the local probability distribution of the field or on local expectation values, even though the correlation of fluctutations over space is arguably the more relevant object physically.…”

Section: Introductionmentioning

confidence: 99%

Scalar correlation functions for a double-well potential in de Sitter space

Markkanen

Rajantie

2020

J. Cosmol. Astropart. Phys.

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We use the spectral representation of the stochastic Starobinsky-Yokoyama approach to compute correlation functions in de Sitter space for a scalar field with a symmetric or asymmetric double-well potential. The terms in the spectral expansion are determined by the eigenvalues and eigenfunctions of the time-independent Fokker-Planck differential operator, and we solve them numerically. The long-distance asymptotic behaviour is given by the lowest state in the spectrum, but we demonstrate that the magnitude of the coeffients of different terms can be very different, and the correlator can be dominated by different terms at different distances. This can give rise to potentially observable cosmological signatures. In many cases the dominant states in the expansion do not correspond to small fluctuations around a minimum of the potential and are therefore not visible in perturbation theory. We discuss the physical interpretation these states, which can be present even when the potential has only one minimum.

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“…the noises are not multiplicative. There is no Itô versus Stratonovich ambiguity then [59,67], the h a describe the deterministic dynamics (2.10), i.e. h a = {π/H, −(3π + ∂ h V eff /H)}, and the generalised FP equation for the probability distribution in phase space W (h, π, N ) reads…”

Section: Stochastic Formalism In Phase Spacementioning

confidence: 99%

Higgs vacuum (in)stability during inflation. The dangerous relevance of de Sitter departure and Planck-suppressed operators

Fumagalli

Renaux‐Petel

Ronayne

2020

J. High Energ. Phys.

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The measured Standard Model parameters lie in a range such that the Higgs potential, once extrapolated up to high scales, develops a minimum of negative energy density. This has important cosmological implications. In particular, during inflation, quantum fluctuations could have pushed the Higgs field beyond its potential barrier, triggering the formation of anti-de Sitter regions, with fatal consequences for our universe. By requiring that this did not happen, one can in principle connect (and constrain) Standard Model parameters with the energy scale of inflation. In this context, we highlight the sensitivity of the fate of our vacuum to seemingly irrelevant physics. In particular, the departure of inflation from an exact de Sitter phase, as well as Planck-suppressed derivative operators, can, already and surprisingly, play a decisive role in (de)stabilizing the Higgs during inflation. Furthermore, in the stochastic dynamics, we quantify the impact of the amplitude of the noise differing from the one of a massless field, as well as of going beyond the slow-roll approximation by using a phase-space approach. On a general ground, our analysis shows that relating the period of inflation to precision particle physics requires a knowledge of these "irrelevant" effects.

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Inflationary stochastic anomalies

Abstract: 1 We concentrate on these two well known discretisations, but one can easily consider more general α-discretisatons [27], where 0 ≤ α ≤ 1, recovering Itô calculus for α = 0 and the Stratonovich

Cited by 27 publications

References 68 publications

Infrared resummation for derivative interactions in de Sitter space

Infrared resummation for derivative interactions in de Sitter space

Scalar correlation functions for a double-well potential in de Sitter space

Higgs vacuum (in)stability during inflation. The dangerous relevance of de Sitter departure and Planck-suppressed operators

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