Curvature perturbation spectra from waterfall transition, black hole
  constraints and non-Gaussianity

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Abstract

We carried out numerical calculations of a contribution of the waterfall field to the primordial curvature perturbation (on uniform density hypersurfaces) \(\zeta\), which is produced during waterfall transition in hybrid inflation scenario. The calculation is performed for a broad interval of values of the model parameters. We show that there is a strong growth of amplitudes of the curvature perturbation spectrum in the limit when the bare mass-squared of the waterfall field becomes comparable with the square of Hubble parameter. We show that in this limit the primordial black hole constraints on the curvature perturbations must be taken into account. It is shown that, in the same limit, peak values of the curvature perturbation spectra are far beyond horizon, and the spectra are strongly non-Gaussian.

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Most cited references 31

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Particle production during out-of-equilibrium phase transitions

Jennie Traschen, Robert Brandenberger (1990)

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Reheating after Inflation

Lev Kofman, Alexei Starobinsky, Andrei Linde (1994)

The theory of reheating of the Universe after inflation is developed. The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages. Immediately after inflation the field \(\phi\) begins rapidly rolling towards the minimum of its effective potential. Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term \(\Gamma\dot\phi\) in the equation of motion of the field \(\phi\). Reheating becomes efficient only at the next stage, when the field \(\phi\) rapidly oscillates near the minimum of its effective potential. We have found that typically in the beginning of this stage the classical inflaton field \(\phi\) very rapidly (explosively) decays into \(\phi\)-particles or into other bosons due to broad parametric resonance. This stage cannot be described by the standard elementary approach to reheating based on perturbation theory. The bosons produced at this stage, as well as some part of the classical field \(\phi\) which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized. The last stages of decay can be described in terms of perturbation theory. Complete reheating is possible only in those theories where a single massive \(\phi\)-particle can decay into other particles. This imposes strong constraints on the structure of inflationary models. On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.

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Towards the Theory of Reheating After Inflation

Alexei Starobinsky, Andrei Linde, Lev Kofman (1997)

Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance called 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 coupled to another scalar field X. Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is different from the 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 occur with phases uncorrelated to each other. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and backreaction of produced particles, including the effects of rescattering. The process of preheating can be divided into several distinct stages. At the first stage the backreaction of created particles is not important. At the second stage backreaction 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 X-particles terminate the resonance. We calculate the density of X-particles and their quantum fluctuations with all backreaction effects taken into account. This allows us to find the range of masses and coupling constants for which one has efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.