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.
R. J. Hardwick, T. Markkanen and S. Nurmi, Renormalisation group improvement in the stochastic formalism , JCAP 09
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. Escrivà, C. Germani and R. K. Sheth, Universal threshold for primordial black hole formation , Phys. Rev. D 101
Original
1907
Earlier work this paper cites.
P. Carrilho, K. A. Malik and D. J. Mulryne, Dissecting the growth of the power spectrum for primordial black holes , Phys. Rev. D 100
Original
1907
Earlier work this paper cites.
T. Prokopec and G. Rigopoulos, Δ \Delta N and the stochastic conveyor belt of ultra slow-roll inflation , Phys. Rev. D 104
Original
1910
Earlier work this paper cites.
J. Grain and V. Vennin, Canonical transformations and squeezing formalism in cosmology , JCAP 02
Original
1910
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.
O. Özsoy and G. Tasinato, On the slope of the curvature power spectrum in non-attractor inflation , JCAP 04
Original
1912
Earlier work this paper cites.
B. J. Carr and S. W. Hawking, Black holes in the early Universe , Mon. Not. Roy. Astron. Soc. 168
1974
Earlier work this paper cites.
B. J. Carr, The Primordial black hole mass spectrum , Astrophys. J. 201
1975
Earlier work this paper cites.
G. F. Chapline, Cosmological effects of primordial black holes , Nature 253
1975
Earlier work this paper cites.
T. Kloek and H. K. van Dijk, Bayesian estimates of equation system parameters: An application of integration by monte carlo , Econometrica 46
1978
Earlier work this paper cites.
A. A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity , Phys. Lett. B 91
1980
Earlier work this paper cites.
D. Kazanas, Dynamics of the Universe and Spontaneous Symmetry Breaking , Astrophys. J. Lett. 241
1980
Earlier work this paper cites.
A. H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems , Phys. Rev. D 23
1981
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.
M. Morikawa, Dissipation and Fluctuation of Quantum Fields in Expanding Universes , Phys. Rev. D 42
1990
Earlier work this paper cites.
D. S. Salopek and J. R. Bond, Nonlinear evolution of long wavelength metric fluctuations in inflationary models , Phys. Rev. D 42
1990
Earlier work this paper cites.
L. P. Grishchuk and Y. V. Sidorov, Squeezed quantum states of relic gravitons and primordial density fluctuations , Phys. Rev. D 42
1990
Earlier work this paper cites.
D. S. Salopek and J. R. Bond, Stochastic inflation and nonlinear gravity , Phys. Rev. D 43
1991
Earlier work this paper cites.
S. Habib, Stochastic inflation: The Quantum phase space approach , Phys. Rev. D 46
1992
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.
M. Mijic, Stochastic dynamics of coarse grained quantum fields in the inflationary universe , Phys. Rev. D 49
1994
Earlier work this paper cites.
A. Albrecht, P. Ferreira, M. Joyce and T. Prokopec, Inflation and squeezed quantum states , Phys. Rev. D 50
1994
Earlier work this paper cites.
M. Bellini, H. Casini, R. Montemayor and P. Sisterna, Stochastic approach to inflation: Classicality conditions , Phys. Rev. D 54
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.
A. Matacz, Inflation and the fine tuning problem , Phys. Rev. D 56
1997
Earlier work this paper cites.
M. Sasaki and T. Tanaka, Superhorizon scale dynamics of multiscalar inflation , Prog. Theor. Phys. 99
1998
Earlier work this paper cites.
D. Wands, Duality invariance of cosmological perturbation spectra , Phys. Rev. D 60
1999
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.
B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, Constraints on primordial black holes , Rept. Prog. Phys. 84
Original
2002
Earlier work this paper cites.
M. Bounakis and G. Rigopoulos, Feynman Rules for Stochastic Inflationary Correlators , JCAP 05
Original
2002
Earlier work this paper cites.
R. P. Woodard, A Leading logarithm approximation for inflationary quantum field theory , Nucl. Phys. B Proc. Suppl. 148
2005
Earlier work this paper cites.

Similar

N. C. Tsamis and R. P. 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.
B. Carr and F. Kuhnel, Primordial Black Holes as Dark Matter: Recent Developments , Ann. Rev. Nucl. Part. Sci. 70
Original
2006
Cited alongside, same era.
J. Martin and M. Musso, On the reliability of the Langevin perturbative solution in stochastic inflation , Phys. Rev. D 73
2006
Cited alongside, same era.
J. Martin and M. Musso, Solving stochastic inflation for arbitrary potentials , Phys. Rev. D 73
2006
Cited alongside, same era.

Then

M. Raidal, V. Vaskonen and H. Veermäe, Gravitational Waves from Primordial Black Hole Mergers , JCAP 09
Original
2017
Later among the works it cites.
Y. Ali-Haïmoud, E. D. Kovetz and M. Kamionkowski, Merger rate of primordial black-hole binaries , Phys. Rev. D 96
Original
2017
Later among the works it cites.
I. Moss and G. Rigopoulos, Effective long wavelength scalar dynamics in de Sitter , JCAP 05
Original
2017
Later among the works it cites.
J. Grain and V. Vennin, Stochastic inflation in phase space: Is slow roll a stochastic attractor? , JCAP 05
Original
2017
Later among the works it cites.
H. Collins, R. Holman and T. Vardanyan, The quantum Fokker-Planck equation of stochastic inflation , JHEP 11

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2022

Numerical stochastic inflation constrained by frozen noise

Tomberg, Eemeli

Understand

Stochastic inflation can resolve strong inflationary perturbations, which seed primordial black holes.

I present a fast and accurate way to compute these perturbations in typical black hole producing single-field models, treating the short-wavelength Fourier modes beyond the de Sitter approximation.
The squeezing and freezing of the modes reduces the problem to one dimension, and the resulting new form of the stochastic equations, dubbed `constrained stochastic inflation,' can be solved efficiently with semi-analytical techniques and numerical importance sampling.
In an example case, the perturbation distribution is resolved in seconds deep into its non-Gaussian tail, a speed-up of factor $10^9$ compared to a previous study.

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.
R. J. Hardwick, T. Markkanen and S. Nurmi, Renormalisation group improvement in the stochastic formalism , JCAP 09
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. Escrivà, C. Germani and R. K. Sheth, Universal threshold for primordial black hole formation , Phys. Rev. D 101
Original
1907
Earlier work this paper cites.
P. Carrilho, K. A. Malik and D. J. Mulryne, Dissecting the growth of the power spectrum for primordial black holes , Phys. Rev. D 100
Original
1907
Earlier work this paper cites.
T. Prokopec and G. Rigopoulos, Δ \Delta N and the stochastic conveyor belt of ultra slow-roll inflation , Phys. Rev. D 104
Original
1910
Earlier work this paper cites.
J. Grain and V. Vennin, Canonical transformations and squeezing formalism in cosmology , JCAP 02
Original
1910
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.
O. Özsoy and G. Tasinato, On the slope of the curvature power spectrum in non-attractor inflation , JCAP 04
Original
1912
Earlier work this paper cites.
B. J. Carr and S. W. Hawking, Black holes in the early Universe , Mon. Not. Roy. Astron. Soc. 168
1974
Earlier work this paper cites.
B. J. Carr, The Primordial black hole mass spectrum , Astrophys. J. 201
1975
Earlier work this paper cites.
G. F. Chapline, Cosmological effects of primordial black holes , Nature 253
1975
Earlier work this paper cites.
T. Kloek and H. K. van Dijk, Bayesian estimates of equation system parameters: An application of integration by monte carlo , Econometrica 46
1978
Earlier work this paper cites.
A. A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity , Phys. Lett. B 91
1980
Earlier work this paper cites.
D. Kazanas, Dynamics of the Universe and Spontaneous Symmetry Breaking , Astrophys. J. Lett. 241
1980
Earlier work this paper cites.
A. H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems , Phys. Rev. D 23
1981
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.
M. Morikawa, Dissipation and Fluctuation of Quantum Fields in Expanding Universes , Phys. Rev. D 42
1990
Earlier work this paper cites.
D. S. Salopek and J. R. Bond, Nonlinear evolution of long wavelength metric fluctuations in inflationary models , Phys. Rev. D 42
1990
Earlier work this paper cites.
L. P. Grishchuk and Y. V. Sidorov, Squeezed quantum states of relic gravitons and primordial density fluctuations , Phys. Rev. D 42
1990
Earlier work this paper cites.
D. S. Salopek and J. R. Bond, Stochastic inflation and nonlinear gravity , Phys. Rev. D 43
1991
Earlier work this paper cites.
S. Habib, Stochastic inflation: The Quantum phase space approach , Phys. Rev. D 46
1992
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.
M. Mijic, Stochastic dynamics of coarse grained quantum fields in the inflationary universe , Phys. Rev. D 49
1994
Earlier work this paper cites.
A. Albrecht, P. Ferreira, M. Joyce and T. Prokopec, Inflation and squeezed quantum states , Phys. Rev. D 50
1994
Earlier work this paper cites.
M. Bellini, H. Casini, R. Montemayor and P. Sisterna, Stochastic approach to inflation: Classicality conditions , Phys. Rev. D 54
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.
A. Matacz, Inflation and the fine tuning problem , Phys. Rev. D 56
1997
Earlier work this paper cites.
M. Sasaki and T. Tanaka, Superhorizon scale dynamics of multiscalar inflation , Prog. Theor. Phys. 99
1998
Earlier work this paper cites.
D. Wands, Duality invariance of cosmological perturbation spectra , Phys. Rev. D 60
1999
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.
B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, Constraints on primordial black holes , Rept. Prog. Phys. 84
Original
2002
Earlier work this paper cites.
M. Bounakis and G. Rigopoulos, Feynman Rules for Stochastic Inflationary Correlators , JCAP 05
Original
2002
Earlier work this paper cites.
R. P. Woodard, A Leading logarithm approximation for inflationary quantum field theory , Nucl. Phys. B Proc. Suppl. 148
2005
Earlier work this paper cites.

Similar

N. C. Tsamis and R. P. 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.
B. Carr and F. Kuhnel, Primordial Black Holes as Dark Matter: Recent Developments , Ann. Rev. Nucl. Part. Sci. 70
Original
2006
Cited alongside, same era.
J. Martin and M. Musso, On the reliability of the Langevin perturbative solution in stochastic inflation , Phys. Rev. D 73
2006
Cited alongside, same era.
J. Martin and M. Musso, Solving stochastic inflation for arbitrary potentials , Phys. Rev. D 73
2006
Cited alongside, same era.