From a theoretical point of view, there is a strong motivation to consider an MeV-scale reheating temperature induced by long-lived massive particles with masses around the weak scale, decaying only through gravitational interaction. In this study, we investigate lower limits on the reheating temperature imposed by big-bang nucleosynthesis assuming both radiative and hadronic decays of such massive particles. For the first time, effects of neutrino self-interactions and oscillations are taken into account in the neutrino thermalization calculations. By requiring consistency between theoretical and observational values of light element abundances, we find that the reheating temperature should conservatively be $T_{\rm RH} \gtrsim 1.8$ MeV in the case of the 100% radiative decay, and $T_{\rm RH} \gtrsim$ 4-5 MeV in the case of the 100% hadronic decays for particle masses in the range of 10 GeV to 100 TeV.
If reheating of the Universe takes place via Planck-suppressed decay, it seems that the thermalization of produced particles might be delayed, since they have large energy/small number densities and number violating large angle scatterings which decrease the momentum of particles by large amount are inefficient correspondingly. In this paper, we study the thermalization of such "under occupied" decay products in detail, following recent developments in understanding the thermalization of non-abelian plasma. Contrary to the above naive expectation, it is shown that in most cases thermalization …
We revisit the non-thermal dark matter (DM) production during the thermalization and reheating era after inflation. The decay of inflaton produces high-energy particles that are thermalized to complete the reheating of the Universe. Before the thermalization is completed, DM can be produced from a collision between the high-energy particles and/or the ambient plasma. We calculate the DM abundance produced from these processes for the case where the cross section of the DM production is proportional to the $n$-th power of the center of mass energy. We find that the collision between the high-en…
We study how the oscillations of the neutrinos affect their thermalization process during the reheating period with temperature O(1) MeV in the early universe. We follow the evolution of the neutrino density matrices and investigate how the predictions of big bang nucleosynthesis vary with the reheating temperature. For the reheating temperature of several MeV, we find that including the oscillations makes different predictions, especially for $^4$He abundance. Also, the effects on the lower bound of the reheating temperature from cosmological observations are discussed.
We consider the conditions for the decay products of perturbative inflaton decay to thermalize. The importance of considering the full spectrum of inflaton decay products in the thermalization process is emphasized. It is shown that the delay between the end of inflaton decay and thermalization allows the thermal gravitino upper bound on the reheating temperature to be raised from 10^{8} GeV to as much as 10^{12} GeV in realistic inflation models. Requiring that thermalization occurs before nucleosynthesis imposes an upper bound on the inflaton mass as a function of the reheating temperature, …
We consider a simple model for the Universe reheating, which consists of a single self--interacting scalar field in Minkowskian space--time. Making use of the existence of an additional small parameter proportional to the amplitude of the initial spatially homogeneous field oscillations, we show that the behavior of the field can be found reliably. We describe the evolution of the system from the homogeneous oscillations to the moment when thermalization is completed. We compare our results with the Hartree--Fock approximation and argue that some properties found for this model may be the comm…
We present a detailed examination of thermalization after inflation for perturbative inflaton decay. Different interactions among particles in the plasma of inflaton decay products are considered and it will be shown that 2 -> 2 scatterings and particle decay are the important ones. We show that thermalization occurs after decays dominate scatterings, and that depending on the typical mass scale of inflaton decay products, different situations may arise. In particular, thermalization may be delayed until late times, in which case the bounds from thermal gravitino production on supersymmetric m…
Assuming gauge/gravity correspondence we study reheating of the Universe using its holographic dual. Inflaton decay and thermalisation of the decay products correspond to collapse of a spherical shell and formation of a blackhole in the dual anti-de Sitter (AdS) spacetime. The reheating temperature is computed as the Hawking temperature of the developed blackhole probed by a dynamical boundary, and is determined by the inflaton energy density and the AdS radius, with corrections from the dynamics of the shell collapse. For given initial energy density of the inflaton field the holographic mode…
We investigate the thermalization process of the Universe after inflation to determine the evolution of the effective temperature. The time scale of thermalization is found to be so long that it delays the evolution of the effective temperature, and the resulting maximal temperature of the Universe can be significantly lower than the one obtained in the literature. Our results clarify the finite density corrections to the effective potential of a scalar field and also processes of heavy particle production. In particular, we find that the maximum temperature of the Universe may be at most elec…
In the framework of MSSM inflation, matter and gravitino production are here investigated through the decay of the fields which are coupled to the udd inflaton, a gauge invariant combination of squarks. After the end of inflation, the flat direction oscillates about the minimum of its potential, losing at each oscillation about 56% of its energy into bursts of gauge/gaugino and scalar quanta when crossing the origin. These particles then acquire a large inflaton VEV-induced mass and decay perturbatively into the MSSM quanta and gravitinos, transferring the inflaton energy very efficiently via …
We consider the case of a scalar field, the inflaton, coupled to both lighter scalars and fermions, and the study the relaxation of the inflaton via particle production in both the linear and non-linear regimes. This has an immediate application to the reheating problem in inflationary universe models. The linear regime analysis offers a rationale for the standard approach to the reheating problem, but we make a distinction between relaxation and thermalization. We find that particle production when the inflaton starts in the {\it non-linear} region is typically a far more efficient way of tra…
The behaviour of oscillating scalar spectator fields after inflation depends on the thermal background produced by inflaton decay. Resonant decay of the spectator is often blocked by large induced thermal masses. We account for the finite decay width of the inflaton and the protracted build-up of the thermal bath to determine the early evolution of a homogeneous spectator field, σ, coupled to the Higgs Boson, Φ, through the term g^2 σ^2 Φ^2, the only renormalisable coupling of a new scalar to the Standard Model. We find that for very large higgs-spectator coupling g > 10^{-3}, the resonance is…
Heavy-ion colliders have revealed the process of "fast thermalization". This experimental breakthrough has led to new theoretical tools to study the thermalization process at both weak and strong coupling. We apply this to the reheating epoch of inflationary cosmology, and the formation of a cosmological quark gluon plasma (QGP). We compute the thermalization time of the QGP at reheating, and find it is determined by the energy scale of inflation and the shear viscosity to entropy ratio $η/s$; or equivalently, the tensor-to-scalar ratio and the strong coupling constant at the epoch of thermali…
The inflaton must convert its energy into radiation after inflation, which, in a conventional scenario, is caused by the perturbative inflaton decay. This reheating process would be much more complicated in some cases: the decay products obtain masses from an oscillating inflaton and thermal environment, and hence the conventional reheating scenario can be modified. We study in detail processes of particle production from the inflaton, their subsequent thermalization and evolution of inflaton/plasma system by taking dissipation of the inflaton in a hot plasma into account. It is shown that the…
The late-time entropy production by the massive particle decay induces the various cosmological effects in the early epoch and modify the standard scenario. We investigate the thermalization process of the neutrinos after the entropy production by solving the Boltzmann equations numerically. We find that if the large entropy are produced at t $\sim$ 1 sec, the neutrinos are not thermalized very well and do not have the perfect Fermi-Dirac distribution. Then the freeze-out value of the neutron to proton ratio is altered considerably and the produced light elements, especially He4, are drastical…
We analyze in detail the perturbative decay of the inflaton oscillating about a generic form of its potential $V(ϕ) = ϕ^k$, taking into account the effects of non-instantaneous reheating. We show that evolution of the temperature as a function of the cosmological scale factor depends on the spin statistics of the final state decay products when $k > 2$. We also include the inflaton-induced mass of the final states leading to either kinematic suppression or enhancement if the final states are fermionic or bosonic respectively. We compute the maximum temperature reached after inflation, the subs…
We study the damping of an oscillating scalar field in a Friedmann-Robertson-Walker spacetime by perturbative processes, taking into account the finite density effects that interactions with the plasma of decay products have on the damping rate. The scalar field may be identified with the inflaton, in which case this process leads to the reheating of the universe after inflation. It can also resemble a modulus that dominates the energy density of the universe at later times. We find that the finite density corrections to the damping rate can have a drastic effect on the thermal history and con…
We study, analytically and with lattice simulations, the decay of coherent field oscillations and the subsequent thermalization of the resulting stochastic classical wave-field. The problem of reheating of the Universe after inflation constitutes our prime motivation and application of the results. We identify three different stages of these processes. During the initial stage of ``parametric resonance'', only a small fraction of the initial inflaton energy is transferred to fluctuations in the physically relevant case of sufficiently large couplings. A major fraction is transfered in the prom…
Reheating is an important part of inflationary cosmology. It describes the production of Standard Matter particles after the phase of accelerated expansion. We give a review of the reheating process, focusing on an in-depth discussion of the preheating stage which is characterized by exponential particle production due to a parametric resonance or tachyonic instability. We give a brief overview of the thermalization process after preheating and end with a survey of some applications to supersymmetric theories and to other issues in cosmology such as baryogenesis, dark matter and metric preheat…
The thermal and expansion history of the Universe before big bang nucleosynthesis is unknown. We investigate the evolution of cosmological perturbations through the transition from an early matter era to radiation domination. We treat reheating as the perturbative decay of an oscillating scalar field into relativistic plasma and cold dark matter. After reheating, we find that subhorizon perturbations in the decay-produced dark matter density are significantly enhanced, while subhorizon radiation perturbations are instead suppressed. If dark matter originates in the radiation bath after reheati…
We calculate the dissipation rate of a coherently oscillating scalar field in a thermal environment using nonequilibrium quantum field theory and apply it to the reheating stage after cosmic inflation. It is shown that the rate is nonvanishing even when particles coupled to the oscillating inflaton field have a larger thermal mass than it, and therefore the cosmic temperature can be much higher than inflaton's mass even in the absence of preheating. Its cosmological implications are also discussed.
In a class of (pseudoscalar) inflation, inflationary phase is followed by a kination phase, where the Universe is dominated by the kinetic energy of the inflaton that runs away in a vanishing scalar potential. In this class of postinflationary evolution of the Universe, reheating of the Universe cannot be achieved by the inflaton particle decay, which requires its coherent oscillation in a quadratic potential. In this study, we explore the U(1) gauge field production through the Chern-Simons coupling between the pseudoscalar inflaton and the gauge field during the kination era and examine the …
We study thermalization of the early Universe when the inflaton can decay into the Standard Model (SM) quarks and gluons, using QCD arguments. We describe the possible formation of the thermal plasma of soft gluons and quarks well before the completion of reheating. Relevant interaction rates of leading order processes and the corresponding thermalization time scale is presented. We discuss hadronization while thermalizing the decay products of the inflaton, when the reheat temperature of the Universe is below the QCD phase transition but above the temperature of the Big Bang nucleosynthesis.
We revisit gravitino production following inflation. As a first step, we review the standard calculation of gravitino production in the thermal plasma formed at the end of post-inflationary reheating when the inflaton has completely decayed. Next we consider gravitino production prior to the completion of reheating, assuming that the inflaton decay products thermalize instantaneously while they are still dilute. We then argue that instantaneous thermalization is in general a good approximation, and also show that the contribution of non-thermal gravitino production via the collisions of inflat…
We study the role of the Standard Model Higgs condensate, formed during cosmological inflation, in the epoch of reheating that follows. We focus on the scenario where the inflaton decays slowly and perturbatively, so that there is a long period between the end of inflation and the beginning of radiation domination. The Higgs condensate decays non-perturbatively during this period, and we show that it heats the primordial plasma to much higher temperatures than would result from the slowly-decaying inflaton alone. We discuss the effect of this hot plasma on the thermalization of the inflaton's …
The purely gravitational dark matter (PGDM) which interacts with the standard model particles only by gravitational interaction has recently been discussed. Due to its feeble interaction, PGDM may be produced mainly by the gravitational particle creation, which plays an important role in the reheating after kinetically driven inflation and some potential-driven inflation without subsequent inflaton oscillating phase. Therefore, we consider the possibility of the gravitational reheating model which can also explain the present PGDM density at the same time. We consider a model where two massive…
The reheating stage in post-inflationary cosmologies is reanalyzed. New techniques from non-equilibrium quantum field theory allow a consistent derivation of the equation of motion including the non-linearity of the dynamics. These offer a rationale for the elementary theory of reheating based on single particle decay which is seen to be valid only in the linear regime of coherent oscillations of the scalar field. A new non-perturbative mechanism of induced amplification of quantum fluctuations is introduced and studied in detail, both analytically and numerically. This is a non-linear mechani…
Gravitational ultra-relativistic freeze-out during general reheating
Université Paris-Saclay（巴黎萨克雷大学）；CNRS/IN2P3, IJCLab（法国国家科学研究中心/欧洲核子研究委员会粒子物理研究所，IJCLab）；William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学院威廉·I·芬理论物理研究所）；Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所理论物理部）；China Center of Advanced Science and Technology（中国高等科学技术中心）
The reheating process for the inflationary scenario is investigated phenomenologically. The decay of the oscillating massive inflaton field into light bosons is modeled after an out of equilibrium mixture of interacting fluids within the framework of irreversible thermodynamics. Self-consistent, analytic results for the evolution of the main macroscopic magnitudes like temperature and particle number densities are obtained. The models for linear and quadratic decay rates are investigated in the quasiperfect regime. The linear model is shown to reheat very slowly while the quadratic one is show…
Oscillating scalar fields are useful to model a variety of matter components in the universe. One or more scalar fields participate in the reheating process after inflation, while at much lower energies scalar fields are robust dark matter candidates. Pertaining structure formation in these models, it is well known that inhomogeneities of the Klein-Gordon field are unstable above the characteristic De Broglie wavelength. In this paper we show that such instability implies the existence of a threshold amplitude for the collapse of primordial fluctuations. We use this threshold to correctly pred…
We study in detail (p)reheating after multi-field inflation models with a particular focus on N-flation. We consider a variety of different couplings between the inflatons and the matter sector, including both quartic and trilinear interactions with a light scalar field. We show that the presence of multiple oscillating inflatons makes parametric resonance inefficient in the case of the quartic interactions. Moreover, perturbative processes do not permit a complete decay of the inflaton for this coupling. In order to recover the hot big bang, we must instead consider trilinear couplings. In th…
We study the problem of scalar particle production after inflation by a rapidly oscillating inflaton field. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first order Born approximation often underestimate the particle production. In the case of the quartic in…
We calculate the baryon asymmetry created by the decay of a pseudo Nambu-Goldstone boson whose interactions violate baryon number conservation. Our results are in disagreement with previous results in the original spontaneous baryogenesis models for the asymmetry produced by the decay of an oscillating scalar field with B number violating derivative couplings; we find that the net baryon number density is proportional to $þ_i^3$, where $þ_i$ is the amplitude of the PNGB-field in natural inflation at the onset of reheating. We also discuss our disagreement with the interpretation of $\dotθ$ as …
Field amplification and particle production due to parametric resonance are highly nontrivial predictions of quantum fields that couple to an oscillating source during inflation and reheating. Understanding this two effects is crucial for the connection between the resonance phenomenon and precise observational data. In this paper, we give a general and analytic analysis of parametric resonance of relevant field modes evolving during inflation and reheating by using the uniform asymptotic approximation. This analysis can provide a clear and quantitative explanation for the field amplification …
It is assumed that during inflation, all energy was contained in a slow-rolling inflaton field $ϕ$. The particles constituting the Universe are created due to interactions with the field $ϕ$ coherently oscillating after inflation. The leading channel of the particle production would be the non-perturbative regime of parametric resonance, preheating. Some of the recent developments in the theory of preheating are briefly reviewed. As a prototype we use the model ${λ\over 4}ϕ^4 + {m^2 \over 2}ϕ^2+ {g^2\over 2}ϕ^2χ^2$ in an expanding universe. In different domains of parameters the character of p…
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 ma…
We study the impact of thermalization and number-changing processes in the dark sector on the yield of gravitationally produced dark matter (DM). We take into account the DM production through the $s$-channel exchange of a massless graviton both from the scattering of inflatons during the reheating era, and from the Standard Model bath via the UV freeze-in mechanism. By considering the DM to be a scalar, a fermion, and a vector boson we show, in a model-independent way, that DM self-interaction gives rise to a larger viable parameter space by allowing lower reheating temperature to be compatib…
In inflationary cosmology, the particles constituting the Universe are created after inflation in the process of reheating due to the interaction with the oscillating inflaton field. We briefly review the basics of the slow reheating, and the stage of fast preheating, when the particles are created explosively in the regime of parametric resonance. The non-perturbative, out-of-equilibrium character of the parametric resonance changes many features of reheating. For these proceedings, we will highlight a few aspects of preheating: the structural dependence of the parametric resonance on the inf…
Relaxation process of a coherent scalar field oscillation in the thermal bath is investigated using nonequilibrium quantum field theory. The Langevin-type equation of motion is obtained which has a memory term and both additive and multiplicative noise terms. The dissipation rate of the oscillating scalar field is calculated for various interactions such as Yukawa coupling, three-body scalar interaction, and biquadratic interaction. When the background temperature is larger than the oscillation frequency, the dissipation rate arising from the interactions with fermions is suppressed due to the…
During the last ten years a detailed investigation of preheating was performed for chaotic inflation and for hybrid inflation. However, nonperturbative effects during reheating in the new inflation scenario remained practically unexplored. We do a full analysis of preheating in new inflation, using a combination of analytical and numerical methods. We find that the decay of the homogeneous component of the inflaton field and the resulting process of spontaneous symmetry breaking in the simplest models of new inflation usually occurs almost instantly: for the new inflation on the GUT scale it t…
We present a detailed and systematic analysis of the nonperturbative, nonequilibrium dynamics of a quantum field in the reheating phase of inflatonary cosmology, including full back reactions of the quantum field on the curved spacetime, as well as the fluctuations on the mean field. We use the O(N) field theory with unbroken symmetry in a spatially flat FRW universe to study the dynamics of the inflaton in the post-inflaton, preheating stage. Oscillations of the inflaton's zero mode induce parametric amplification of quantum fluctuations, resulting in a rapid transfer of energy to the inhomog…
We discuss baryogenesis in scenarios where the Universe is reheated to temperatures $\lesssim 100\,$GeV by the decay of long-lived massive particles into energetic SM particles. Before its thermalization, the center-of-mass energy in collisions between such a particle and a particle from the ambient plasma can be higher than the typical sphaleron mass, even if the temperature of the plasma itself is much lower. Optimistic estimates for the high energy enhancement of the sphaleron cross section suggest that successful baryogenesis is possible for reheating temperatures as low as $0.1\text{-}1\,…
Motivated by Refs \cite{am1,am2}, we analyze how the inflaton decay reheats the Universe within supersymmetry. In a non-supersymmetric case the inflaton usually decays via preheating unless its couplings to other fields are very small. Naively one would expect that supersymmetry enhances bosonic preheating as it introduces new scalars such as squarks and sleptons. On the contrary, we point out that preheating is unlikely within supersymmetry. The reason is that flat directions in the scalar potential, classified by gauge invariant combinations of slepton and squark fields, are generically disp…
We demonstrate that B-ball decay in the MSSM can naturally solve the puzzle of why the densities of baryons and dark matter in the Universe are similar. This requires that the B-balls survive thermalization and decay below the freeze-out temperature of the neutralino LSP, typically 1-10GeV. It is shown that this can happen if the baryon asymmetry originates from a squark condensate along the d=6 u^{c}d^{c}d^{c} D-flat direction of the MSSM scalar potential. For this to work the reheating temperature after inflation must be no greater than 10^3-10^5 GeV.
We propose a simple mechanism of light dark matter (DM) production from the decay of the oscillating inflaton condensation. If the reheating temperature after inflation is higher than the inflaton mass, which is of the same order of the momentum of the DM at the time of the production, the DM momentum can be suppressed compared to the temperature of the thermal plasma if the interaction of the DM is weak enough. Consequently, the DM can be cold enough to avoid the observational constraints on the warm DM, like the Lyman-$α$ bound even if the DM mass is small. We study the bosonic and fermionic…
The dynamics at the end of inflation can generate an asymmetry between particles and anti-particles of the inflaton field. This asymmetry can be transferred to baryons via decays, generating a baryon asymmetry in our Universe. We explore this idea in detail for a complex inflaton governed by an observationally consistent -"flatter than quadratic"- potential with a weakly broken global U(1) symmetry. We find that most of the inflaton asymmetry is locked in non-topological soliton like configurations (oscillons) produced copiously at the end of inflation. These solitons eventually decay into bar…
