Constraints on the primordial curvature perturbation from primordial black holes

Zaballa, Ignacio; Green, Anne M.; Malik, Karim A.; Sasaki, Misao

doi:10.1088/1475-7516/2007/03/010

Cited by 49 publications

(54 citation statements)

References 33 publications

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“…(2.14), the characteristic function χ N can be rewritten as 18) that is to say, the characteristic function is the Fourier transform of the PDF of curvature perturbations. Therefore, the PDF is the inverse Fourier transform of the characteristic function, i.e.…”

Section: The Characteristic Function Approachmentioning

confidence: 99%

Quantum diffusion during inflation and primordial black holes

Pattison

Vennin

Assadullahi

et al. 2017

J. Cosmol. Astropart. Phys.

167

259

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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 Characteristic Function Approachmentioning

confidence: 99%

Quantum diffusion during inflation and primordial black holes

Pattison

Vennin

Assadullahi

et al. 2017

J. Cosmol. Astropart. Phys.

167

259

View full text Add to dashboard Cite

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“…On subhorizon scales, k > ∼ H e , Ψ oscillates with decaying amplitude once the radiation dominated epoch begins. The relevant quantity to estimate the abundance of subhorizon PBHs formed at the end of inflation is the first maximum of the oscillations, Ψ M (k) [4,5]. Ψ M (k) increases with k, until the comoving scale approaches k ∼ H e /δ.…”

Section: The Transition Into Radiation Dominationmentioning

confidence: 99%

Boosted perturbations at the end of inflation

Zaballa

Sasaki²

2010

J. Cosmol. Astropart. Phys.

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We study the effect on the primordial cosmological perturbations of a sharp transition from inflationary to a radiation and matter dominated epoch respectively. We assume that the perturbations are generated by the vacuum fluctuations of a scalar field slowly rolling down its potential, and that the transition into the subsequent epoch takes place much faster than a Hubble time. The behaviour of the superhorizon perturbations corresponding to cosmological scales in this case is well known. However, it is not clear how perturbations on scales of and smaller than the Hubble horizon scale at the end of inflation may evolve through such a transition. We derive the evolution equation for the gravitational potential Ψ, which allows us to study the evolution of the perturbations on all scales under these circumstances. We show that for a certain range of scales inside the horizon at the end of inflation, the amplitude of the perturbations are enhanced relative to the superhorizon scales. This enhancement may lead to the overproduction of Primordial Black Holes (PBHs), and therefore constrain the dynamics of the transitions that take place at the end of inflation.

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“…This has been widely used in previous calculations of the one parametric probability of PBH formation [3,5,6,8,53,54]. When the probability depends on a single amplitude parameter, this method reduces to the integration of the corresponding PDF over the relevant perturbation amplitudes.…”

Section: Two Parametric Probability Of Pbh Formationmentioning

confidence: 99%

“…The PBH contribution to the energy density increases with time during the radiation-dominated epoch. For this reason, the PBHs formed considerably before the end of radiation domination are the most relevant to cosmology [5][6][7][8][9][10]. We will focus our study on these kind of PBHs and assume that the background matter at the time of PBH formation is radiationdominated.…”

Section: Introductionmentioning

confidence: 99%

Probability of primordial black hole formation and its dependence on the radial profile of initial configurations

Hidalgo

Polnarev

2009

Phys. Rev. D

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In this paper we derive the probability of the radial profiles of spherically symmetric inhomogeneities in order to provide an improved estimation of the number density of primordial black holes (PBHs). We demonstrate that the probability of PBH formation depends sensitively on the radial profile of the initial configuration. We do this by characterising this profile with two parameters chosen heuristically: the amplitude of the inhomogeneity and the second radial derivative, both evaluated at the centre of the configuration. We calculate the joint probability of initial cosmological inhomogeneities as a function of these two parameters and then find a correspondence between these parameters and those used in numerical computations of PBH formation. Finally, we extend our heuristic study to evaluate the probability of PBH formation taking into account for the first time the radial profile of curvature inhomogeneities.

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Constraints on the primordial curvature perturbation from primordial black holes

Cited by 49 publications

References 33 publications

Quantum diffusion during inflation and primordial black holes

Quantum diffusion during inflation and primordial black holes

Boosted perturbations at the end of inflation

Probability of primordial black hole formation and its dependence on the radial profile of initial configurations

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