Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation
HJE
Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm in ation
Mar Bastero-Gil 0 1 2 4 5
Arjun Berera 0 1 2 3 5
Rudnei O. Ramos 0 1 2 5
Jo~ao G. Rosa 0 1 2 5
0 20550-013 Rio de Janeiro, RJ , Brazil
1 Edinburgh , EH9 3FD , United Kingdom
2 Granada-18071 , Spain
3 School of Physics and Astronomy, University of Edinburgh
4 Departamento de F sica Teorica y del Cosmos, Universidad de Granada
5 Campus de Santiago , 3810-183 Aveiro , Portugal
We show that, in warm in ation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phasespace distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller e ective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm in ation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm in ation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states.
Cosmology of Theories beyond the SM; Thermal Field Theory
1 Introduction
2
3
4
5
Adiabatic baryogenesis during warm in ation
Generation of baryon isocurvature perturbations
Summary and future prospects
A Boltzmann equation for scattering processes
if strong dissipation is attained at the end of the slow-roll evolution regime (see, e.g.,
refs. [8{11]). The greatest appeal of warm in ation lies perhaps in the fact that thermal
in aton
uctuations are directly sourced by dissipative processes, changing the form of the
primordial spectrum of curvature perturbations and thus providing a unique observational
window into the particle physics behind in ation [11{18]. In addition, we have recently
shown that warm in ation can be consistently realized in a simple quantum
eld theory
framework requiring very few
elds, the Warm Little In aton scenario [19], where the
required atness of the in aton potential is not spoiled by thermal e ects (see also refs. [20{26]
for earlier alternative models), paving the way for developing a complete particle physics
description of in ation that can be fully tested with CMB and Large-Scale Structure (LSS)
observations and possibly have implications for collider and particle physics data.
Independently of the particle physics involved in sustaining a thermal bath during
ination, a generic feature of warm in ation is the slow evolution of both the temperature
and the Hubble parameter for the usually required 50{60 e-folds of expansion. Since both
scattering and particle decay rates typically depend on the former, this implies that the
ratio =H will generically evolve slowly during in ation. Consequently, as we explicitly show
in this work for the rst time, particle species in the warm in ationary plasma can maintain
distributions that are slowly evolving and out-of-equilibrium throughout in ation, whether
or not they are directly involved in the dissipative dynamics. This may have an important
impact not only on the in ationary dynamics and predictions themselves but also on the
present abundance of di erent components. As an example of application of this novel
observation, we show that this can lead to the production of a baryon asymmetry during
in ation, a possibility that can be tested in the near future with CMB and LSS observations.
This work is organized as follows. In section 2 we analyze the Boltzmann equation for a
particle species interacting with a thermal bath for an adiabatic evolution of the ratio
=H,
focusing explicitly on the case of decays and inverse decays for concreteness. We then show
that this leads to slowly varying out-of-equilibrium con gurations, obtaining the overall
particle number density and its phase space distribution. We brie y discuss how similar
results can be obtained for scattering processes. In section 3 we use these results to develop
a generic baryogenesis (or leptogenesis) mechanism during in ation. Then, in section 4,
we discuss how this generically leads to baryon isocurvature modes that give a small
contribution to the primordial curvature perturbation spectrum. In section 5 we summarize
our results and discuss their potential impact on other aspects of the in ationary and
post-in ationary history. An appendix is included where some technical details are given.
2
Adiabatic out-of-equilibrium dynamics
Let us consider a particle X interacting with a thermal bath at temperature T in an
expanding Universe.1 For concreteness, let u (...truncated)