Correlation functions in stochastic inflation

Vennin, Vincent; Starobinsky, Alexei A.

doi:10.1140/epjc/s10052-015-3643-y

Cited by 193 publications

(305 citation statements)

References 128 publications

(235 reference statements)

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“…When stochastic inflation is employed to describe such a family of universes and to calculate the amount of expansion realised in them, this gives rise to the stochastic-δN formalism [51][52][53][54][55][56][57]. This approach is sketched in Fig.…”

Section: The Stochastic-δn Formalismmentioning

confidence: 99%

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Quantum diffusion during inflation and primordial black holes

Pattison

Vennin

Assadullahi

et al. 2017

J. Cosmol. Astropart. Phys.

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Abstract. We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δN formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ∼ 1 e-fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

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Section: The Stochastic-δn Formalismmentioning

confidence: 99%

“…For the power spectrum P ζ for instance, since the coarse-grained δN cg receives an integrated contribution of all modes exiting the Hubble radius during inflation, δN 2 cg = k end k * P ζ dk/k, one has [52,54] …”

Section: The Stochastic-δn Formalismmentioning

confidence: 99%

Quantum diffusion during inflation and primordial black holes

Pattison

Vennin

Assadullahi

et al. 2017

J. Cosmol. Astropart. Phys.

Self Cite

161

259

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“…These objections are based on the statement that distributions of initial conditions violate a widely accepted naturalness assumption that all forms of inflaton energy (kinetic, gradient, and potential) should initially have the same Planckian scale magnitude [19][20][21]. Three known sources of these distributions-pure no-boundary [1,2] and "tunneling" [3] quantum states of the universe and the Fokker-Planck equation for coarse-grained cosmological evolution [22][23][24][25]-in their turn suffer from intrinsic difficulties associated with a missing clear canonical quantization ground, insufficient amount of generated inflation, anthropic (observer dependence) problems [26][27][28], the rather contrived multiverse measure problem [29], etc.…”

Section: Introductionmentioning

confidence: 99%

Origin of inflation in CFT driven cosmology: $$R^2$$ R 2 -gravity and non-minimally coupled inflaton models

Barvinsky¹,

Kamenshchik²,

Nesterov³

2015

Eur. Phys. J. C

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We present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology S 1 × S 3 , which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial S 3 -section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in R 2 gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters and η < 0 and their relation ∼ η 2 characteristic of these two models. We present the mechanism of formation of hill-like inflaton potentials, which is based on logarithmic loop corrections to the asymptotically shift-invariant tree-level potentials of these models in the Einstein frame. We also discuss the role of R 2 -gravity as an indispensable finite renormalization tool in the CFT driven cosmology, which guarantees the nondynamical (ghost free) nature of its scale factor and special properties of its cosmological garland-type instantons. Finally, as a solution to the problem of hierarchy between the Planckian scale and the inflation scale we discuss the concept of a hidden sector of conformal higher spin fields. a

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“…This can be performed using first passage time analysis [41,42]. Starting from an initial point φ in i in field space, the set of functions f n (φ i ) ≡ N n (φ in i = φ i ) are shown to satisfy the set of (deterministic) partial differential equations [28,29] …”

Section: Introductionmentioning

confidence: 99%

“…The standard results can be recovered as the sub-Planckian limit v ≪ 1 of the above formula using saddle-point approximations. For the power spectrum, for instance, one obtains [28] …”

Section: Introductionmentioning

confidence: 99%

Critical Number of Fields in Stochastic Inflation

et al. 2017

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Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary e-folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic δN formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes non-vanishing when more than two fields are driving inflation. The mean number of e-folds can be infinite, depending on the number of fields; for plateau potentials, this occurs even with one field. In such cases, correlation functions of curvature perturbations are infinite. They can, however, be regularised if a reflecting (or absorbing) wall is added at large energy or field value. The results are found to be independent of the exact location of the wall and this procedure is, therefore, well-defined for a wide range of cutoffs, above or below the Planck scale. Finally, we show that, contrary to single-field setups, multi-field models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations. IntroductionIn the inflationary paradigm [1-6], cosmological inhomogeneities result from the parametric amplification of the vacuum quantum fluctuations of the gravitational and matter fields during an early accelerated expansion [7][8][9][10][11][12]. The transition from quantum fluctuations to classical but stochastic density perturbations [13][14][15][16][17][18] plays an important role in this scenario. In particular, it implies that the open quantum system comprising the superHubble degrees of freedom can be described with a classical stochastic theory, the stochastic inflation formalism [10,[19][20][21][22][23][24][25][26][27]. This consists of an effective description of the long-wavelength parts of the quantum fields, which are "coarse grained" at a fixed physical scale, larger than the Hubble radius during the whole inflationary era. In this framework, the short-wavelength quantum fluctuations act as a classical noise on the dynamics of the super-Hubble scales, and at leading order in slow roll, the coarse-grained fields φ i follow Langevin equations

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Correlation functions in stochastic inflation

Cited by 193 publications

References 128 publications

Quantum diffusion during inflation and primordial black holes

Quantum diffusion during inflation and primordial black holes

Origin of inflation in CFT driven cosmology: $$R^2$$ R 2 -gravity and non-minimally coupled inflaton models

Critical Number of Fields in Stochastic Inflation

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