Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime

Rajantie, Arttu

doi:10.1103/physrevd.106.123522

Cited by 6 publications

(4 citation statements)

References 66 publications

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“…We will choose the background inflationary potential to be of the plateau type so that H is roughly constant and we can therefore assume that the spectator field exists in an exact de Sitter background. While the noise term in (2.5) has been computed in the massless limit, it has been shown recently [15,16] how to modify the noise appropriately for more massive spectator fields. We will assume here that the field is sufficiently light such that (2.5) is a good approximation, in any case the procedure we outline in this chapter is easily adapted to incorporate different values of the noise.…”

Section: Jcap04(2023)046mentioning

confidence: 99%

“…The long-wavelength perturbations can be treated as effectively classical greatly simplifying the analysis. The initially short-wavelength quantum perturbations are stretched by the rapid inflationary expansion and can be consistently included as a classical random noise term on the dynamical equations which is a well established approximation for the behaviour of IR quantum fields in inflationary spacetimes [9][10][11][12][13][14] -see [15,16] however for how this picture breaks down for too massive test fields and see [17] for next-to-next-to leading order corrections to the standard stochastic framework. In this way it is clear that the stochastic framework can be imagined as an Effective Field Theory (EFT) of the long-wavelength sector.…”

Section: Introductionmentioning

confidence: 99%

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Computing first-passage times with the functional renormalisation group

Rigopoulos

Wilkins

2023

J. Cosmol. Astropart. Phys.

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We use Functional Renormalisation Group (FRG) techniques to analyse the behaviour of a spectator field, σ, during inflation that obeys an overdamped Langevin equation. We briefly review how a derivative expansion of the FRG can be used to obtain Effective Equations of Motion (EEOM) for the one- and two-point function and derive the EEOM for the three-point function. We show how to compute quantities like the amplitude of the power spectrum and the spectral tilt from the FRG. We do this explicitly for a potential with multiple barriers and show that in general many different potentials will give identical predictions for the spectral tilt suggesting that observations are agnostic to localised features in the potential. Finally we use the EEOM to compute first-passage time (FPT) quantities for the spectator field. The EEOM for the one- and two-point function are enough to accurately predict the average time taken 〈𝒩〉 to travel between two field values with a barrier in between and the variation in that time δ𝒩 2. It can also accurately resolve the full PDF for time taken ρ(𝒩), predicting the correct exponential tail. This suggests that an extension of this analysis to the inflaton can correctly capture the exponential tail that is expected in models producing Primordial Black Holes.

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Section: Jcap04(2023)046mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computing first-passage times with the functional renormalisation group

Rigopoulos

Wilkins

2023

J. Cosmol. Astropart. Phys.

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“…This is achieved by splitting the inflationary perturbations into short-and long-wavelength components where the long-wavelength perturbations can be treated as effectively classical. The initially short-wavelength quantum perturbations are stretched by the inflationary expansion and impact the dynamical equations by the inclusion of a classical random noise term which is a well established approximation for the infrared (IR) behaviour of quantum fields in inflationary spacetimes [39][40][41][42][43][44] -see [45,46] however for how to correct the standard picture for massive test fields and see [47] for next-to-next-to leading order corrections to the standard stochastic framework. Because the dynamics are now stochastic it means that the time taken (measured in e-folds) to reach ϕ e is also a stochastic quantity, denoted by N .…”

Section: Introductionmentioning

confidence: 99%

Spectators no more! How even unimportant fields can ruin your Primordial Black Hole model

Wilkins,

Cable

2024

J. Cosmol. Astropart. Phys.

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In this work we terminate inflation during a phase of Constant Roll by means of a waterfall field coupled to the inflaton and a spectator field. The presence of a spectator field means that inflation does not end at a single point, ϕ e, but instead has some uncertainty resulting in a stochastic end of inflation. We find that even modestly coupled spectator fields can drastically increase the abundance of Primordial Black Holes (PBHs) formed by many orders of magnitude. The power spectrum created by the inflaton can be as little as 10-4 during a phase of Ultra Slow-Roll and still form a cosmologically relevant number of PBHs. We conclude that the presence of spectator fields, which very generically will alter the end of inflation, is an effect that cannot be ignored in realistic models of PBH formation.

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“…Thus final correlation functions remain IR-finite. Since then, the stochastic formalism has been studied as a solution of the IR divergences in dS using various methods, see [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] for recent examples.…”

Section: Introductionmentioning

confidence: 99%

On the IR divergences in de Sitter space: loops, resummation and the semi-classical wavefunction

Céspedes,

Davis,

Wang

2024

J. High Energ. Phys.

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In this paper, we revisit the infrared (IR) divergences in de Sitter (dS) space using the wavefunction method, and explicitly explore how the resummation of higher-order loops leads to the stochastic formalism. In light of recent developments of the cosmological bootstrap, we track the behaviour of these nontrivial IR effects from perturbation theory to the non-perturbative regime. Specifically, we first examine the perturbative computation of wavefunction coefficients, and show that there is a clear distinction between classical components from tree-level diagrams and quantum ones from loop processes. Cosmological correlators at loop level receive contributions from tree-level wavefunction coefficients, which we dub classical loops. This distinction significantly simplifies the analysis of loop-level IR divergences, as we find the leading contributions always come from these classical loops. Then we compare with correlators from the perturbative stochastic computation, and find the results there are essentially the ones from classical loops, while quantum loops are only present as subleading corrections. This demonstrates that the leading IR effects are contained in the semi-classical wavefunction which is a resummation of all the tree-level diagrams. With this insight, we go beyond perturbation theory and present a new derivation of the stochastic formalism using the saddle-point approximation. We show that the Fokker-Planck equation follows as a consequence of two effects: the drift from the Schrödinger equation that describes the bulk time evolution, and the diffusion from the Polchinski’s equation which corresponds to the exact renormalization group flow of the coarse-grained theory on the boundary. Our analysis highlights the precise and simple link between the stochastic formalism and the semi-classical wavefunction.

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Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime

Cited by 6 publications

References 66 publications

Computing first-passage times with the functional renormalisation group

Computing first-passage times with the functional renormalisation group

Spectators no more! How even unimportant fields can ruin your Primordial Black Hole model

On the IR divergences in de Sitter space: loops, resummation and the semi-classical wavefunction

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