Quantum diffusion during inflation and primordial black holes

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 ch...

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Bibliographic Details
Published in:Journal of cosmology and astroparticle physics 2017-10, Vol.2017 (10), p.46-46
Main Authors: Pattison, Chris, Vennin, Vincent, Assadullahi, Hooshyar, Wands, David
Format: Article
Language:English
Subjects:
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
BLACK HOLES
COMPUTERIZED SIMULATION
CORRECTIONS
DENSITY
DIFFERENTIAL EQUATIONS
DIFFUSION
DISTURBANCES
EXPANSION
INFLATIONARY UNIVERSE
MASS
PERTURBATION THEORY
PROBABILITY
PROBABILITY DENSITY FUNCTIONS
STOCHASTIC PROCESSES
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Summary: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.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2017/10/046