Stochastic growth of quantum fluctuations during slow-roll inflation

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.064020· OSTI ID:21421162

Finelli, F ^[1]; Marozzi, G ^[2]; Starobinsky, A A ^[3]; Vacca, G P; Venturi, G ^[4]

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1. INAF/IASF Bologna, Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna, via Gobetti 101, I-40129 Bologna (Italy)
2. GRECO-Institut d'Astrophysique de Paris, UMR7095, CNRS, Universite Pierre and Marie Curie, 98 bis boulevard Arago, 75014 Paris (France)
3. Landau Institute for Theoretical Physics, Moscow, 119334 (Russian Federation)
4. Dipartimento di Fisica, Universita degli Studi di Bologna, via Irnerio, 46, I-40126 Bologna (Italy)

We compute the growth of the mean square of quantum fluctuations of test fields with small effective mass during a slowly changing, nearly de Sitter stage which takes place in different inflationary models. We consider a minimally coupled scalar with a small mass, a modulus with an effective mass {proportional_to}H{sup 2} (with H the Hubble parameter), and a massless nonminimally coupled scalar in the test field approximation and compare the growth of their relative mean square with the one of gauge-invariant inflaton fluctuations. We find that in most of the single field inflationary models the mean square gauge-invariant inflaton fluctuation grows faster than any test field with a non-negative effective mass. Hybrid inflationary models can be an exception: the mean square of a test field can dominate over the gauge-invariant inflaton fluctuation one on suitably chosen parameters. We also compute the stochastic growth of quantum fluctuations of a second field, relaxing the assumption of its zero homogeneous value, in a generic inflationary model; as a main result, we obtain that the equation of motion of a gauge-invariant variable associated, order by order, with a generic quantum scalar fluctuation during inflation can be obtained only if we use the number of e-folds as the time variable in the corresponding Langevin and Fokker-Planck equations for the stochastic approach. We employ this approach to derive some bounds for the case of a model with two massive fields.

• OSTI ID: 21421162
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevD.82.064020; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
DE SITTER SPACE
EFFECTIVE MASS
EQUATIONS OF MOTION
FLUCTUATIONS
FOKKER-PLANCK EQUATION
GAUGE INVARIANCE
HUBBLE EFFECT
INFLATIONARY UNIVERSE
LANGEVIN EQUATION
STOCHASTIC PROCESSES
CALCULATION METHODS
COSMOLOGICAL MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
INVARIANCE PRINCIPLES
MASS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
SPACE
VARIATIONS