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Towards the theory of reheating after inflation

Lev Kofman

Andrei Linde

Alexei A. Starobinsky

  • Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822

  • Department of Physics, Stanford University, Stanford, California 94305-4060

  • Landau Institute for Theoretical Physics, Kosygina St. 2, Moscow 117334, Russia

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Phys. Rev. D 56, 3258 – Published 15 September, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.3258

Abstract

Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we briefly describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance, which we call preheating. It may occur in an expanding universe if the initial amplitude of oscillations of the inflaton field is large enough. We investigate a simple model of a massive inflaton field φ coupled to another scalar field χ with the interaction term g2φ2χ2. Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is quite different from parametric resonance in the case when the expansion of the universe is neglected. Quantum fields interacting with the oscillating inflaton field experience a series of kicks which, because of the rapid expansion of the universe, occur with phases uncorrelated to each other. Despite the stochastic nature of the process, it leads to exponential growth of fluctuations of the field χ. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and back reaction of produced particles, including the effects of rescattering. This investigation extends our previous study of reheating after inflation. We show that the contribution of the produced particles to the effective potential V(φ) is proportional not to φ2, as is usually the case, but to |φ|. The process of preheating can be divided into several distinct stages. In the first stage the back reaction of created particles is not important. In the second stage back reaction increases the frequency of oscillations of the inflaton field, which makes the process even more efficient than before. Then the effects related to scattering of χ particles on the oscillating inflaton field terminate the resonance. We calculate the number density of particles nχ produced during preheating and their quantum fluctuations 〈χ2〉 with all back reaction effects taken into account. This allows us to find the range of masses and coupling constants for which one can have efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.

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Physical Review D 50th Anniversary Milestones

This collection of seminal papers from PRD highlights research that remains central to developments today in particle physics, quantum field and string theory, gravitation, cosmology, and particle astrophysics.

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  44. In fact, the table in Sec. VI might suggest that the change of parameters by 10% can lead to exponentially large changes in the final results. This is indeed the case for the processes if g<3×10−4, where back reaction is not important. Meanwhile, for g≫3×10−4 back reaction makes the process terminate at a time which is somewhat less sensitive to the change of parameters. That is why it becomes possible to obtain analytical estimates despite the stochastic nature of the process.

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Phys. Rev. D 56, 3258– Published 15 September, 1997
  • Received 2 May 1997

© 1997 American Physical Society

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