2021/01/31 by Chris Pattison, Vincent Vennin, David Wands +1 · 1 citation
Physics and Astronomy · #Complement (music) #Cosmology and Gravitation Theories #Exponential function #Formalism (music) #High-Energy Particle Collisions Research #Inflation (cosmology) #Inflaton #Non-Gaussianity #Probability density function #Probability distribution #Pulsars and Gravitational Waves Research #Quantum #Slow roll #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1088/1475-7516/2021/04/080
published as JCAP 04 (2021) 080 · 35 pages without appendices (total 43 pages), 9 figures, matches the version published in JCAP
openalex created_date 2021/01/18 · openalex publication_date 2021/04/01 · arxiv created 2021/04/30 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/06
Abstract We consider the effect of quantum diffusion on the dynamics of the inflaton during a period of ultra-slow-roll inflation. We extend the stochastic-δ𝒩 formalism to the ultra-slow-roll regime and show how this system can be solved analytically in both the classical-drift and quantum-diffusion dominated limits. By deriving the characteristic function, we are able to construct the full probability distribution function for the primordial density field. In the diffusion-dominated limit, we recover an exponential tail for the probability distribution, as found previously in slow-roll inflation. To complement these analytical techniques, we present numerical results found both by very large numbers of simulations of the Langevin equations, and through a new, more efficient approach based on iterative Volterra integrals. We illustrate these techniques with two examples of potentials that exhibit an ultra-slow-roll phase leading to the possible production of primordial black holes.