Numerically modeling stochastic inflation in slow-roll and beyond

De, Aritra; Mahbub, Rafid

doi:10.1103/physrevd.102.123509

Title: Numerically modeling stochastic inflation in slow-roll and beyond

Abstract

In this work, we present a complete numerical treatment of inflationary dynamics under the influence of stochastic corrections from sub-Hubble modes. We discuss how to exactly model the stochastic noise terms arising from the sub-Hubble quantum modes that give rise to the coarse-grained inflaton dynamics in the form of stochastic differential equations. The stochastic differential equations are solved event by event on a discrete time grid. We then compute the power spectrum of curvature perturbations that can be compared with the power spectrum computed in the traditional fashion using the Mukhanov-Sasaki equation by canonically quantizing the inflaton fluctuations. Our numerical procedure helps us to easily extend the formalism to ultra slow-roll inflation and study the possibility of primordial black hole formation.

Authors:

^[1];

^[1]

Univ. of Minnesota, Minneapolis, MN (United States)

Publication Date:: Tue Dec 01 00:00:00 EST 2020

Research Org.:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1849955

Grant/Contract Number:: FG02-87ER40328

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Volume: 102; Journal Issue: 12; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; Evolution of the universe; Inflation

Citation Formats


                    De, Aritra, and Mahbub, Rafid. Numerically modeling stochastic inflation in slow-roll and beyond.  United States: N. p., 2020. 
Web.  doi:10.1103/physrevd.102.123509.

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                    De, Aritra, & Mahbub, Rafid. Numerically modeling stochastic inflation in slow-roll and beyond.  United States.  https://doi.org/10.1103/physrevd.102.123509

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                    De, Aritra, and Mahbub, Rafid. Tue .  
"Numerically modeling stochastic inflation in slow-roll and beyond".  United States.  https://doi.org/10.1103/physrevd.102.123509.  https://www.osti.gov/servlets/purl/1849955.

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@article{osti_1849955,

  title        = {Numerically modeling stochastic inflation in slow-roll and beyond},

  author       = {De, Aritra and Mahbub, Rafid},

  abstractNote = {In this work, we present a complete numerical treatment of inflationary dynamics under the influence of stochastic corrections from sub-Hubble modes. We discuss how to exactly model the stochastic noise terms arising from the sub-Hubble quantum modes that give rise to the coarse-grained inflaton dynamics in the form of stochastic differential equations. The stochastic differential equations are solved event by event on a discrete time grid. We then compute the power spectrum of curvature perturbations that can be compared with the power spectrum computed in the traditional fashion using the Mukhanov-Sasaki equation by canonically quantizing the inflaton fluctuations. Our numerical procedure helps us to easily extend the formalism to ultra slow-roll inflation and study the possibility of primordial black hole formation.},

  doi          = {10.1103/physrevd.102.123509},

  journal      = {Physical Review. D.},

  number       = 12,

  volume       = 102,

  place        = {United States},

  year         = {Tue Dec 01 00:00:00 EST 2020},

  month        = {Tue Dec 01 00:00:00 EST 2020}

}

Copy to clipboard

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Similar Records

Title: Numerically modeling stochastic inflation in slow-roll and beyond

Abstract

Citation Formats

Nonminimal coupling of the scalar field and inflation journal, June 1996

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General inflaton potentials in supergravity journal, February 2011

Correlation functions in stochastic inflation journal, September 2015

Equilibrium state of a self-interacting scalar field in the de Sitter background journal, November 1994

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The Jackknife Estimate of Variance journal, May 1981

Numerical solutions of stochastic differential equations – implementation and stability issues journal, December 2000

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Spontaneous creation of almost scale-free density perturbations in an inflationary universe journal, August 1983

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Inflationary universe: A possible solution to the horizon and flatness problems journal, January 1981

Primordial black holes from α-attractors journal, January 2019

Emergence of classicality for primordial fluctuations: Concepts and analogies journal, March 1998

Non-perturbative approach for curvature perturbations in stochastic δ N formalism journal, October 2014

Stochastic inflation beyond slow roll journal, July 2019

Quantum diffusion beyond slow-roll: implications for primordial black-hole production journal, August 2018

A new algorithm for calculating the curvature perturbations in stochastic inflation journal, December 2013

Primordial black holes and uncertainties in the choice of the window function journal, May 2018

Primordial black hole production in Critical Higgs Inflation journal, January 2018

Stochastic inflation in phase space: is slow roll a stochastic attractor? journal, May 2017

An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations journal, January 2001

Planck 2018 results: X. Constraints on inflation journal, September 2020

Stochastic quantum gravitational inflation journal, September 2005

Quantum Squeezing and Late Time Classical Behavior of Massive Fields in Expanding Robertson–Walker Universe journal, August 1997

Backreaction and stochastic effects in single field inflation journal, March 2015

A Hitch-hiker’s Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics journal, March 2017

A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems journal, February 1982

Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations journal, November 1982

Primordial Cosmology conference, September 2018

Impact of nonlinear overdensity statistics on primordial black hole abundance journal, July 2020

Quantum-to-classical transition of cosmological perturbations for non-vacuum initial states journal, July 1997

Perturbations in stochastic inflation journal, July 2006

Fluctuations in the New Inflationary Universe journal, October 1982

Natural Chaotic Inflation in Supergravity journal, October 2000

A general proof of the conservation of the curvature perturbation journal, May 2005

Primordial black holes from string inflation journal, June 2018

Calculating fluctuations and self-correlations numerically for causal charge diffusion in relativistic heavy-ion collisions journal, August 2020

Primordial black holes from single field models of inflation journal, December 2017

A new type of isotropic cosmological models without singularity journal, March 1980

Ultra slow-roll inflation demystified journal, December 2017

Effective noise in a stochastic description of inflation journal, March 2000

Inflation in supergravity with a single chiral superfield journal, September 2014

The Jackknife, the Bootstrap and Other Resampling Plans book, January 1982

Stochastic inflation and the lower multipoles in the cosmic microwave background anisotropies journal, August 2004

Primordial black hole abundance from random Gaussian curvature perturbations and a local density threshold journal, December 2018

Physical Foundations of Cosmology book, September 2012

Generation of fluctuations during inflation: Comparison of stochastic and field-theoretic approaches journal, February 2009

Quantum Field Theory in De Sitter Space: Renormalization by Point-Splitting journal, March 1978

Nonminimal coupling of the scalar field and inflation
journal, June 1996

On inflation with non-minimal coupling
journal, November 2010

General inflaton potentials in supergravity
journal, February 2011

Correlation functions in stochastic inflation
journal, September 2015

Equilibrium state of a self-interacting scalar field in the de Sitter background
journal, November 1994

Eternally existing self-reproducing chaotic inflanationary universe
journal, August 1986

Primordial black holes from polynomial potentials in single field inflation
journal, April 2018

Theory of cosmological perturbations
journal, June 1992

The Jackknife Estimate of Variance
journal, May 1981

Numerical solutions of stochastic differential equations – implementation and stability issues
journal, December 2000

The primordial black hole formation criterion re-examined: Parametrisation, timing and the choice of window function
journal, November 2019

Spontaneous creation of almost scale-free density perturbations in an inflationary universe
journal, August 1983

Chaotic inflation
journal, September 1983

Inflationary universe: A possible solution to the horizon and flatness problems
journal, January 1981

Primordial black holes from α-attractors
journal, January 2019

Emergence of classicality for primordial fluctuations: Concepts and analogies
journal, March 1998

Non-perturbative approach for curvature perturbations in stochastic δ N formalism
journal, October 2014

Stochastic inflation beyond slow roll
journal, July 2019

Quantum diffusion beyond slow-roll: implications for primordial black-hole production
journal, August 2018

A new algorithm for calculating the curvature perturbations in stochastic inflation
journal, December 2013

Primordial black holes and uncertainties in the choice of the window function
journal, May 2018

Primordial black hole production in Critical Higgs Inflation
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Stochastic inflation in phase space: is slow roll a stochastic attractor?
journal, May 2017

An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
journal, January 2001

Planck 2018 results: X. Constraints on inflation
journal, September 2020

Stochastic quantum gravitational inflation
journal, September 2005

Quantum Squeezing and Late Time Classical Behavior of Massive Fields in Expanding Robertson–Walker Universe
journal, August 1997

Backreaction and stochastic effects in single field inflation
journal, March 2015

A Hitch-hiker’s Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics
journal, March 2017

A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems
journal, February 1982

Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations
journal, November 1982

Primordial Cosmology
conference, September 2018

Impact of nonlinear overdensity statistics on primordial black hole abundance
journal, July 2020

Quantum-to-classical transition of cosmological perturbations for non-vacuum initial states
journal, July 1997

Perturbations in stochastic inflation
journal, July 2006

Fluctuations in the New Inflationary Universe
journal, October 1982

Natural Chaotic Inflation in Supergravity
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A general proof of the conservation of the curvature perturbation
journal, May 2005

Primordial black holes from string inflation
journal, June 2018

Calculating fluctuations and self-correlations numerically for causal charge diffusion in relativistic heavy-ion collisions
journal, August 2020

Primordial black holes from single field models of inflation
journal, December 2017

A new type of isotropic cosmological models without singularity
journal, March 1980

Ultra slow-roll inflation demystified
journal, December 2017

Effective noise in a stochastic description of inflation
journal, March 2000

Inflation in supergravity with a single chiral superfield
journal, September 2014

The Jackknife, the Bootstrap and Other Resampling Plans
book, January 1982

Stochastic inflation and the lower multipoles in the cosmic microwave background anisotropies
journal, August 2004

Primordial black hole abundance from random Gaussian curvature perturbations and a local density threshold
journal, December 2018

Physical Foundations of Cosmology
book, September 2012

Generation of fluctuations during inflation: Comparison of stochastic and field-theoretic approaches
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Quantum Field Theory in De Sitter Space: Renormalization by Point-Splitting
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