Quantum diffusion during inflation and primordial black holes

By C. Pattison, V. Vennin, H. Assadullahi, D. Wands. 2017

210 citations recorded by the source corpus.

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-δ N 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.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/4ed2046593d6507c320ea0e0d793431cf11b4429

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Florian Kuhnel
2. B. Carr
3. Juan García-Bellido
4. A. Kehagias
5. J. Rubio
6. J. Ezquiaga
7. V. Vennin
8. A. Riotto

In Instrumentation

1. B. Carr
2. Florian Kuhnel
3. V. Vennin
4. Juan García-Bellido
5. A. Riotto
6. S. Patil
7. A. Starobinsky
8. F. Finelli

Citations in the corpus

• Primordial black holes from string inflation (2018, background): “It would therefore be important to perform a more careful analysis of stochastic effects since the perturbative expansion might not be fully justified [95].”
• Generating PBHs and small-scale GWs in two-field models of inflation (2020, background): “[24–26] for the effects of quantum diffusion in the PBH abundance.”
• Steepest growth of the power spectrum and primordial black holes (2018, methodology): “In the context of PBH formation, quantum diffusion during inflation has been discussed subject to the slow-roll approximation by [67] and during USR with conflicting conclusions about its importance in [47, 68–70].”
• Primordial Black Holes as Dark Matter: Recent Developments (2020, background): “[94] Chris Pattison, Vincent Vennin, Hooshyar Assadullahi, and David Wands, “Quantum diffusion during inflation and primordial black holes,” JCAP 1710, 046 (2017), arXiv:1707.”
• Primordial black holes from inflation and quantum diffusion (2018, background): “One might be reasonably suspicious that during the non-attractor phase the quantum diffusion becomes relevant [49].”
• Higgs Inflation (2018, background): “In this regime, even the classical treatment is compromised since stochastic effects can no longer be ignored [158–161].”