Built on

T. Markkanen, A. Rajantie, S. Stopyra and T. Tenkanen, Scalar correlation functions in de Sitter space from the stochastic spectral expansion , JCAP 08
Original
1904
Earlier work this paper cites.
Y. Tada and S. Yokoyama, Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes , Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
C. Pattison, V. Vennin, H. Assadullahi and D. Wands, Stochastic inflation beyond slow roll , JCAP 07
Original
1905
Earlier work this paper cites.
A. Moradinezhad Dizgah, G. Franciolini and A. Riotto, Primordial Black Holes from Broad Spectra: Abundance and Clustering , JCAP 11
Original
1906
Earlier work this paper cites.
J. M. Ezquiaga, J. García-Bellido and V. Vennin, The exponential tail of inflationary fluctuations: consequences for primordial black holes , JCAP 03
Original
1912
Earlier work this paper cites.
E. M. Lifshitz and I. M. Khalatnikov, About singularities of cosmological solutions of the gravitational equations. I , ZhETF 39
1960
Earlier work this paper cites.
A. A. Starobinsky, Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations , Phys. Lett. B 117
1982
Earlier work this paper cites.
A. A. Starobinsky, Isotropization of arbitrary cosmological expansion given an effective cosmological constant , JETP Lett. 37
1983
Earlier work this paper cites.
A. A. Starobinsky, Multicomponent de Sitter (Inflationary) Stages and the Generation of Perturbations , JETP Lett. 42
1985
Earlier work this paper cites.
V. F. Mukhanov, Gravitational Instability of the Universe Filled with a Scalar Field , JETP Lett. 41
1985
Earlier work this paper cites.
A. A. Starobinsky, Stochastic De Sitter (inflationary) stage in the early universe , Lect. Notes Phys. 246
1986
Earlier work this paper cites.
V. F. Mukhanov, Quantum Theory of Gauge Invariant Cosmological Perturbations , Sov. Phys. JETP 67
1988
Earlier work this paper cites.
Springer, 1989
H. Risken and H. Haken, The Fokker-Planck Equation: Methods of Solution and Applications Second Edition · 1989
Earlier work this paper cites.
A. A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the de Sitter background , Phys. Rev. D 50
1994
Earlier work this paper cites.
G. Comer, N. Deruelle, D. Langlois and J. Parry, Growth or decay of cosmological inhomogeneities as a function of their equation of state , Phys. Rev. D 49
1994
Earlier work this paper cites.
D. Polarski and A. A. Starobinsky, Semiclassicality and decoherence of cosmological perturbations , Class. Quant. Grav. 13
1996
Earlier work this paper cites.
M. Sasaki and E. D. Stewart, A General analytic formula for the spectral index of the density perturbations produced during inflation , Prog. Theor. Phys. 95
1996
Earlier work this paper cites.
J. Lesgourgues, D. Polarski and A. A. Starobinsky, Quantum to classical transition of cosmological perturbations for nonvacuum initial states , Nucl. Phys. B 497
1997
Earlier work this paper cites.
D. Wands, K. A. Malik, D. H. Lyth and A. R. Liddle, A New approach to the evolution of cosmological perturbations on large scales , Phys. Rev. D 62
2000
Earlier work this paper cites.
D. Green and R. A. Porto, Signals of a Quantum Universe , Phys. Rev. Lett. 124
Original
2001
Earlier work this paper cites.

Similar

I. Khalatnikov and A. Kamenshchik, Comment about quasiisotropic solution of Einstein equations near cosmological singularity , Class. Quant. Grav. 19
2002
Cited alongside, same era.
D. H. Lyth and D. Wands, Conserved cosmological perturbations , Phys. Rev. D 68
2003
Cited alongside, same era.
N. Tsamis and R. Woodard, Stochastic quantum gravitational inflation , Nucl. Phys. B 724
2005
Cited alongside, same era.
D. H. Lyth, K. A. Malik and M. Sasaki, A General proof of the conservation of the curvature perturbation , JCAP 05
2005
Cited alongside, same era.
D. Campo and R. Parentani, Inflationary spectra and violations of Bell inequalities , Phys. Rev. D 74
2006
Cited alongside, same era.

Then

S. Clesse and J. García-Bellido, Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies , Phys. Rev. D 92
Original
2015
Later among the works it cites.
J. Martin, C. Ringeval and V. Vennin, Observing Inflationary Reheating , Phys. Rev. Lett. 114
Original
2015
Later among the works it cites.
J. Martin and V. Vennin, Quantum Discord of Cosmic Inflation: Can we Show that CMB Anisotropies are of Quantum-Mechanical Origin? , Phys. Rev. D 93
Original
2016
Later among the works it cites.
J. Maldacena, A model with cosmological Bell inequalities , Fortsch. Phys. 64
Original
2016
Later among the works it cites.
C. Burgess, R. Holman and G. Tasinato, Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation , JHEP 01

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2020

Power spectrum in stochastic inflation

Ando, Kenta, Vennin, Vincent

Understand

We compute the power spectrum of curvature perturbations in stochastic inflation.

This combines the distribution of first crossing times through the end-of-inflation surface, which has been previously studied, with the distribution of the fields value at the time when a given scale crosses out the Hubble radius during inflation, which we show how to compute.
This allows the stochastic-$\delta N$ formalism to make concrete contact with observations.
As an application, we study how quantum diffusion at small scales (arising e.g.

Built on

T. Markkanen, A. Rajantie, S. Stopyra and T. Tenkanen, Scalar correlation functions in de Sitter space from the stochastic spectral expansion , JCAP 08
Original
1904
Earlier work this paper cites.
Y. Tada and S. Yokoyama, Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes , Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
C. Pattison, V. Vennin, H. Assadullahi and D. Wands, Stochastic inflation beyond slow roll , JCAP 07
Original
1905
Earlier work this paper cites.
A. Moradinezhad Dizgah, G. Franciolini and A. Riotto, Primordial Black Holes from Broad Spectra: Abundance and Clustering , JCAP 11
Original
1906
Earlier work this paper cites.
J. M. Ezquiaga, J. García-Bellido and V. Vennin, The exponential tail of inflationary fluctuations: consequences for primordial black holes , JCAP 03
Original
1912
Earlier work this paper cites.
E. M. Lifshitz and I. M. Khalatnikov, About singularities of cosmological solutions of the gravitational equations. I , ZhETF 39
1960
Earlier work this paper cites.
A. A. Starobinsky, Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations , Phys. Lett. B 117
1982
Earlier work this paper cites.
A. A. Starobinsky, Isotropization of arbitrary cosmological expansion given an effective cosmological constant , JETP Lett. 37
1983
Earlier work this paper cites.
A. A. Starobinsky, Multicomponent de Sitter (Inflationary) Stages and the Generation of Perturbations , JETP Lett. 42
1985
Earlier work this paper cites.
V. F. Mukhanov, Gravitational Instability of the Universe Filled with a Scalar Field , JETP Lett. 41
1985
Earlier work this paper cites.
A. A. Starobinsky, Stochastic De Sitter (inflationary) stage in the early universe , Lect. Notes Phys. 246
1986
Earlier work this paper cites.
V. F. Mukhanov, Quantum Theory of Gauge Invariant Cosmological Perturbations , Sov. Phys. JETP 67
1988
Earlier work this paper cites.
Springer, 1989
H. Risken and H. Haken, The Fokker-Planck Equation: Methods of Solution and Applications Second Edition · 1989
Earlier work this paper cites.
A. A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the de Sitter background , Phys. Rev. D 50
1994
Earlier work this paper cites.
G. Comer, N. Deruelle, D. Langlois and J. Parry, Growth or decay of cosmological inhomogeneities as a function of their equation of state , Phys. Rev. D 49
1994
Earlier work this paper cites.
D. Polarski and A. A. Starobinsky, Semiclassicality and decoherence of cosmological perturbations , Class. Quant. Grav. 13
1996
Earlier work this paper cites.
M. Sasaki and E. D. Stewart, A General analytic formula for the spectral index of the density perturbations produced during inflation , Prog. Theor. Phys. 95
1996
Earlier work this paper cites.
J. Lesgourgues, D. Polarski and A. A. Starobinsky, Quantum to classical transition of cosmological perturbations for nonvacuum initial states , Nucl. Phys. B 497
1997
Earlier work this paper cites.
D. Wands, K. A. Malik, D. H. Lyth and A. R. Liddle, A New approach to the evolution of cosmological perturbations on large scales , Phys. Rev. D 62
2000
Earlier work this paper cites.
D. Green and R. A. Porto, Signals of a Quantum Universe , Phys. Rev. Lett. 124
Original
2001
Earlier work this paper cites.

Similar

I. Khalatnikov and A. Kamenshchik, Comment about quasiisotropic solution of Einstein equations near cosmological singularity , Class. Quant. Grav. 19
2002
Cited alongside, same era.
D. H. Lyth and D. Wands, Conserved cosmological perturbations , Phys. Rev. D 68
2003
Cited alongside, same era.
N. Tsamis and R. Woodard, Stochastic quantum gravitational inflation , Nucl. Phys. B 724
2005
Cited alongside, same era.
D. H. Lyth, K. A. Malik and M. Sasaki, A General proof of the conservation of the curvature perturbation , JCAP 05
2005
Cited alongside, same era.
D. Campo and R. Parentani, Inflationary spectra and violations of Bell inequalities , Phys. Rev. D 74
2006
Cited alongside, same era.