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2017

The quantum Fokker-Planck equation of stochastic inflation

Collins, Hael, Holman, Richard, Vardanyan, Tereza

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We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory.

This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation.
This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory.
We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.

The quantum Fokker-Planck equation of stochastic inflation · Around

Built on

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I. Antoniadis, J. Iliopoulos, and T. N. Tomaras, “Quantum Instability of De Sitter Space,” Phys. Rev. Lett. 56
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A. A. Starobinsky and J. Yokoyama, “Equilibrium state of a selfinteracting scalar field in the De Sitter background,” Phys. Rev. D 50
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T. Prokopec, N. C. Tsamis, and R. P. Woodard, “Two Loop Scalar Bilinears for Inflationary SQED,” Class. Quant. Grav. 24
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T. Prokopec, N. C. Tsamis, and R. P. Woodard, “Stochastic Inflationary Scalar Electrodynamics,” Annals Phys. 323
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2008
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T. Prokopec, N. C. Tsamis, and R. P. Woodard, “Two loop stress-energy tensor for inflationary scalar electrodynamics,” Phys. Rev. D 78
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2008
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Then

C. P. Burgess, L. Leblond, R. Holman and S. Shandera, “Super-Hubble de Sitter Fluctuations and the Dynamical RG,” JCAP 1003
Original
2010
Later among the works it cites.
D. Seery,‘ ‘Infrared effects in inflationary correlation functions,” Class. Quant. Grav. 27
Original
2010
Later among the works it cites.
E. O. Kahya, V. K. Onemli, and R. P. Woodard, “The ζ \zeta - ζ \zeta Correlator is Time Dependent,” Phys. Lett. B 694
Original
2011
Later among the works it cites.
C. P. Burgess, R. Holman, G. Tasinato, and M. Williams, “EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical,” JHEP 1503
Original
2015
Later among the works it cites.
C. P. Burgess, R. Holman, and G. Tasinato, “Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation,” JHEP 1601

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2016

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