There are at least three cosmic backgrounds of primordial gravitational waves coming from inflation: those produced during inflation and associated with the stretching of quantum modes; those produced at the violent stage of preheating after inflation; and those associated with the self-ordering of Goldstone modes if inflation ends via a global symmetry breaking scenario, like in hybrid inflation. Each background has its own characteristic spectrum with specific features. We describe in detail the origin of extra peaks in the PGW background from preheating in the case in which inflation ends with the formation of cosmic strings due to an Abelian Higgs model after hybrid inflation. We then discuss the prospects for detecting each gravitational wave background, and distinguishing between them with a very sensitive probe, the local B-mode of the cosmic microwave background polarization.
We study the two-phase scenario following inflation, where the initial step is preheating, accompanied by a step of perturbative reheating at which inflaton field decays transferring all of its energy to create relativistic particles, the interaction of these particles will evolve towards a state of thermal equilibrium with a temperature Tre called the reheating temperature. It is observed that the scenario of reheating normally predicts the maximum reheating temperature that corresponds to an almost instantaneous transition from inflation to the radiation domination era. This will naturally l…
The production of GWs during preheating in the Starobinsky model with a nonminimally coupled auxiliary scalar field is studied through the lattice simulation in this paper. We find that the GW spectrum $Ω_{\rm gw}$ grows fast with the increase of the absolute value of coupling parameter $ξ$. This is because the resonant bands become broad with the increase of $|ξ|$. When $ξ<0$, $Ω_{\rm gw}$ begins to grow once the inflation ends and grows faster than the case of $ξ>0$. $Ω_{\rm gw}$ reaches the maximum at $ξ=-20$ ($ξ=42$ for the case $ξ>0$) and then decreases with slight oscillation. Furthermor…
In this paper I review the theory and numerical simulations of non-linear dynamics of preheating, a stage of dynamical instability at the end of inflation during which homogeneous inflaton explosively decays and deposits its energy into excitation of other matter fields. I focus on preheating in chaotic inflation models, which proceeds via broad parametric resonance. I describe a simple method to evaluate Floquet exponents, calculating stability diagrams of Mathieu and Lame equations describing development of instability in $m^2ϕ^2$ and $λϕ^4$ preheating models. I discuss basic numerical metho…
The epochs of reheating and preheating are studied in a simple extension of the Starobinsky inflationary model, which consists of an $R^2$--correction to the Einstein--Hilbert action and an additional scalar field. We find that if the $R^2$--correction at the end of inflation is dynamically important, it affects the expansion rate and as a consequence the reheating and preheating processes. While we find that the reheating temperature and duration of reheating are only slightly affected, the effect has to be taken into account when comparing the theory to data. In the case of preheating, the g…
We study the details of preheating in Palatini Higgs inflation. We show, that contrary to what happens in the metric formulation of the model, the Universe does not reheat through the creation of gauge bosons only, but also through the tachyonic production of Higgs excitations. The latest entropy production channel turns out to be very efficient and leads to an almost instantaneous onset of radiation domination after the end of inflation. As compared to the metric case, this reduces the number of e-folds needed to solve the usual hot big bang problems while leading to a smaller spectral index …
When the inflaton couples to photons and amplifies electric fields, charged particles produced via the Schwinger effect can dominate the universe after inflation, which is dubbed as the Schwinger preheating. Using the hydrodynamic approach for the Boltzmann equation, we numerically study two cases, the Starobinsky inflation model with the kinetic coupling and the anisotropic inflation model. The Schwinger preheating is not observed in the latter model but occurs for a sufficiently large inflaton-photon coupling in the first model. We analytically address its condition and derive a general attr…
In this paper we review the production of primordial black holes (PBHs) during preheating after a chaotic inflationary model. All relevant equations of motion are solved numerically in a modified version of HLattice, and we then calculate the mass variance to determine structure formation during preheating. It is found that production of PBHs can be a generic result of the model, even though the results seem to be sensitive to the values of the smoothing scale. We consider a constraint for overproduction of PBHs that could uncover some stress between inflation-preheating models and observation…
We study preheating in the Palatini formalism with a quadratic inflaton potential and an added $αR^2$ term. In such models, the oscillating inflaton field repeatedly returns to the plateau of the Einstein frame potential, on which the tachyonic instability fragments the inflaton condensate within less than an e-fold. We find that tachyonic preheating takes place when $α\gtrsim 10^{13}$ and that the energy density of the fragmented field grows with the rate $Γ/H \approx 0.011 \times α^{0.31}$. The model extends the family of plateau models with similar preheating behaviour. Although it contains…
We study inflation and preheating in F(R) supergravity characterized by two mass scales of a scalar degree of freedom (scalaron): M (associated with the inflationary era) and m (associated with the preheating era). The allowed values of the masses M and m are derived from the amplitude of the CMB temperature anisotropies. We show that our model is consistent with the joint observational constraints of WMAP and other measurements in the regime where a sufficient amount of inflation (with the number of e-foldings larger than 50) is realized. In the low-energy regime relevant to preheating, we de…
Process of preheating for supersymmetric hybrid model of inflation is generally analyzed in two different ways known as parametric resonance and tachyonic preheating. In a common frame-work, we study both the processes from the decay or growth of homogeneous inflaton field and inhomogeneous waterfall field. We find that these two processes in SUSY hybrid F-term inflation are not parameter independent; rather one process will be more preferable than the other depending on the values of parameters and Fourier mode of the waterfall field. Parameters of the inflationary potential are constrained f…
Plateau inflation is an experimentally consistent framework in which the scale of inflation can be kept relatively low. Close to the edge of the plateau, scalar perturbations are subject to a strong tachyonic instability. Tachyonic preheating is realized when, after inflation, the oscillating inflaton repeatedly re-enters the plateau. We develop the analytic theory of this process and expand the linear approach by including backreaction between the coherent background and growing perturbations. For a family of plateau models, the analytic predictions are confronted with numerical estimates. Ou…
We examine effects of the Generalized Uncertainty Principle, predicted by various theories of quantum gravity to replace the Heisenberg's uncertainty principle near the Planck scale, on post inflation preheating in cosmology, and show that it can predict either an increase or a decrease in parametric resonance and a corresponding change in particle production. Possible implications are considered.
Stochastic gravitational wave backgrounds (SGWBs) receive increasing attention and provide a new possibility to directly probe the early Universe. In the preheating process at the end of inflation, parametric resonance can generate large energy density perturbations and efficiently produce gravitational waves (GWs) which carry unique information about inflation. Since the peak frequency of such GWs is approximately proportional to the inflationary energy scale, $Λ_{\mathrm{inf}}$, GWs from preheating are expected to be observed by interferometer GW detectors in low-scale inflationary models. W…
Current measurements of the Higgs boson mass and top Yukawa coupling suggest that the effective Higgs potential develops an instability below the Planck scale. If the energy scale of inflation is as high as the GUT scale, inflationary quantum fluctuations of the Higgs field can easily destabilize the standard electroweak vacuum and produce a lot of AdS domains. This destabilization during inflation can be avoided if a relatively large nonminimal Higgs-gravity or inflaton-Higgs coupling is introduced. Such couplings generate a large effective mass term for the Higgs, which can raise the effecti…
We take an analytic approach towards the framework of parametric resonance and apply it on preheating and locked inflation. A two-scalar toy model is analytically solved for the λϕ^2χ^2 coupling for the homogenous modes. The effects of dynamic universe background and backreaction are taken into account. We show the average effect of parametric resonance to be that χ's amplitude doubles for each cycle of ϕ. Our framework partly solves the preheating scenario, showing two distinct stages of preheating and making the parameters of preheating analytically calculable. It is demonstrated for slowrol…
We use classical lattice simulations in 3+1 dimensions to study the interplay between the resonant production of particles during preheating and the subsequent decay of these into a set of secondary species. We choose to work in a simplified version of Higgs inflation in which the Higgs field non-minimally coupled to gravity plays the role of the inflaton. Our numerical results extend the analytical estimates in the literature beyond the linear regime and shed some light on the limitations of the analytical techniques. The inclusion of fast and inefficient decays postpones the onset of paramet…
We study particle production at the preheating era in inflation models with nonminimal coupling $ξϕ^2R$ and quartic potential $λϕ^4/4$ for several cases: real scalar inflaton, complex scalar inflaton and Abelian Higgs inflaton. We point out that the preheating proceeds much more violently than previously thought. If the inflaton is a complex scalar, the phase degree of freedom is violently produced at the first stage of preheating. If the inflaton is a Higgs field, the longitudinal gauge boson production is similarly violent. This is caused by a spike-like feature in the time dependence of the…
We study the onset of the reheating epoch at the end of axion-driven inflation where the axion is coupled to an Abelian, $U(1)$, gauge field via a Chern-Simons interaction term. We focus primarily on $m^2ϕ^2$ inflation and explore the possibility that preheating can occur for a range of coupling values consistent with recent observations and bounds on the overproduction of primordial black holes. We find that for a wide range of parameters preheating is efficient. In certain cases the inflaton is seen to transfer all its energy to the gauge fields within a few oscillations. In most cases, we f…
We investigate how the production of gravitational waves (GWs) is affected by the GW velocity $(c_T)$ during preheating after inflation. For instance, we simulate the production of GWs after $λϕ^4$ chaotic inflation, and find that GW spectrum is enhanced for $c_T<1$, but distorted (suppressed at low frequency, but enhanced at high frequency) for $c_T>1$.
We study the preheating of gauge fields in a simple axion monodromy model and compute the induced entropy perturbations and their effect on the curvature fluctuations. We find that the correction to the spectrum of curvature perturbations has a blue spectrum with index $n_s = 5/2$. Hence, these induced modes are harmless for the observed structure of the universe. Since the spectrum is blue, there is the danger of overproduction of primordial black holes. However, we show that the observational constraints are easily satisfied.
We consider gravitational wave (GW) production during preheating in hybrid inflation models where an axion-like waterfall field couples to Abelian gauge fields. Based on a linear analysis, we find that the GW signal from such models can be within the reach of a variety of foreseeable GW experiments such as LISA, AEDGE, ET and CE, and is close to that of LIGO A+, both in terms of frequency range and signal strength. Furthermore, the resultant GW signal is helically polarized and thus may distinguish itself from other sources of stochastic GW background. Finally, such models can produce primordi…
We study the production of primordial circular ("V-mode") polarization in axion inflation coupled to fermions and gauge fields, with special attention paid to (p)reheating. We construct the power spectrum of $V$, and find a blue-tilted spectrum with index $n_V=4$. This is independent of the dominant decay channel of the inflaton (direct fermion vs. direct photon production)
A new class of non-Gaussian curvature fluctuations ζ_{pr} (\bx) \equiv δN(χ_i) arises from the post-inflation preheating behaviour of a non-inflaton field χ_i. Its billiard-like chaotic dynamics imprints regular log-spaced narrow spikes in the number of preheating e-folds N(χ_i). We perform highly accurate lattice simulations of SUSY-inspired quartic inflaton and coupling potentials in a separate-universe approximation to compute N(χ_i) as a function of the (nearly homogeneous) initial condition χ_i. The super-horizon modes of χ_i(\bx) result in positive spiky excursions in ζ_{pr} and hence ne…
After the end of inflation, the inflaton field oscillates around a local minimum of its potential and decays into ordinary matter. These oscillations trigger a resonant instability for cosmological perturbations with wavelengths that exit the Hubble radius close to the end of inflation. In this paper, we study the formation of Primordial Black Holes (PBHs) at these enhanced scales. We find that the production mechanism can be so efficient that PBHs subsequently dominate the content of the universe and reheating proceeds from their evaporation. Observational constraints on the PBH abundance als…
Here we consider the possibility of preheating the Universe via the parametric amplification of a massless, U(1) abelian gauge field. We assume that the gauge field is coupled to the inflaton via a conformal factor with one free parameter. We present the results of high-resolution three-dimensional simulations of this model and show this mechanism efficiently preheats the Universe to a radiation-dominated final state.
We investigate the feasibility of explosive particle production via parametric resonance or tachyonic preheating in multi-field inflationary models by means of lattice simulations. We observe a strong suppression of resonances in the presence of four-leg interactions between the inflaton fields and a scalar matter field, leading to insufficient preheating when more than two inflatons couple to the same matter field. This suppression is caused by a dephasing of the inflatons that increases the effective mass of the matter field. Including three-leg interactions leads to tachyonic preheating, wh…
We present the evolution of the full set of Einstein equations during preheating after inflation. We study a generic supersymmetric model of hybrid inflation, integrating fields and metric fluctuations in a 3-dimensional lattice. We take initial conditions consistent with Eintein's constraint equations. The induced preheating of the metric fluctuations is not large enough to backreact onto the fields, but preheating of the scalar modes does affect the evolution of vector and tensor modes. In particular, they do enhance the induced stochastic background of gravitational waves during preheating,…
We calculate the mass distribution of Primordial Black Holes (PBHs) produced during metric preheating. After inflation, the oscillations of the inflaton at the bottom of its potential source a parametric resonant instability for small-scale scalar perturbations, that may collapse into black holes. After reviewing in a pedagogical way different techniques that have been developed in the literature to compute mass distributions of PBHs, we focus on the excursion-set approach. We derive a Volterra integral equation that is free of a singularity sometimes encountered, and apply it to the case of m…
We discuss the impact of the preheating stage in radiative corrections due to interaction of the inflaton to fermions to $ϕ^4$ inflation with non-minimal coupling in Palatini formulation. In Palatini inflation with large non-minimal coupling the field is allow to return to the plateau region during the reheating stage, so the average equation of state per oscillations is closer to $-1$ than to $1/3$. The incursion in the plateau leads, however, to a highly efficient tachyonic instability able to reheat the Universe in less than one e-fold. By taking into account prescription II discussed in th…
Intermittent type of primordial non-Gaussian fluctuations from modulated preheating can produce an overabundance of $\sim 10^8M_\odot$ mini-haloes at high redshift $z\gtrsim 20$. This may have a significant impact on the formation of high-redshift supermassive black holes.
At the end of inflation, the inflaton oscillates at the bottom of its potential and these oscillations trigger a parametric instability for scalar fluctuations with wavelength $λ$ comprised in the instability band $(3H m)^{-1/2} <λ< H^{-1}$, where $H$ is the Hubble parameter and $m$ the curvature of the potential at its minimum. This "metric preheating" instability, which proceeds in the narrow resonance regime, leads to various interesting phenomena such as early structure formation, production of gravitational waves and formation of primordial black holes. In this work we study its fate in t…
It has been argued that the mixed Higgs-$R^2$ model acts as the UV extension of the Higgs inflation, pushing up its cut-off scale in the vacuum close up to the Planck scale. In this letter, we study the inflaton oscillation stage after inflation, focusing on the effective mass of the phase direction of the Higgs field, which can cause a violent preheating process. We find that the "spikes" in the effective mass of the phase direction observed in the Higgs inflation still appear in the mixed Higgs-$R^2$ model. While the spikes appear above the cut-off scale in the Higgs-only case, they appear b…
We study (p)reheating in alpha-attractor T-models of inflation, taking into account both scalar fields present in these models: the inflaton and the spectator. The two-field model has a negative field-space curvature which, at the end of inflation, may lead to geometrical destabilization of the spectator for small values of alpha<~10^(-3). We perform the instability (Floquet) analysis of the linear dynamics and a fully non-linear lattice computations with our numerical code, which we specifically designed for a class of two-field models with non-canonical kinetic terms. We find that the pertur…
After cosmic inflation and before the transition to radiation domination, the cosmic energy density may have been dominated during an extended period by an oscillating massive scalar condensate. We show that during this period, sub-Hubble scale perturbations are subject to a metric preheating instability in the narrow resonance regime. We analyze in detail both, quadratic and quartic potentials. The instability leads to the growth of density perturbations which in many cases become non-linear already before the beginning of a radiation dominated Universe. This is particularly the case when req…
Whereas preheating after chaotic and hybrid inflation models has been abundantly studied in the literature, preheating in small field inflation models, where the curvature of the inflaton potential is negative during inflation, remains less explored. In these models, a tachyonic instability at the end of inflation leads to a succession of exponentially large increases and \emph{decreases} of the inflaton fluctuations as the inflaton condensate oscillates around the minimum of its potential. The net effect is a competition between low-momentum modes which grow and decrease significantly, and mo…
We analyze and compare the multi-field dynamics during inflation and preheating in symmetric and asymmetric models of $α$-attractors, characterized by a hyperbolic field-space manifold. We show that the generalized (asymmetric) E- and (symmetric) T-models exhibit identical two-field dynamics during inflation for a wide range of initial conditions. The resulting motion can be decomposed in two approximately single-field segments connected by a sharp turn in field-space. The details of preheating can nevertheless be different. For the T-model one main mass-scale dominates the evolution of fluctu…
Axion monodromy is a generic phenomenon in string compactifications. We investigate the production of gravitational-wave background from axion monodromy inflation during preheating. By performing lattice simulations using pseudo-spectral methods, we find that significant single-peak stochastic gravitational-wave backgrounds are generated during preheating for asymptotic linear $|ϕ|$ and $ϕ^{2/3}$ potentials in axion monodromy inflation and cuspy potentials. This may allow us to explore string compactifications through gravitational waves.
We study (p)reheating in modular (closed string) inflationary scenarios, with a special emphasis on Kahler moduli/Roulette models. It is usually assumed that reheating in such models occurs through perturbative decays. However, we find that there are very strong non-perturbative preheating decay channels related to the particular shape of the inflaton potential (which is highly nonlinear and has a very steep minimum). Preheating after modular inflation, proceeding through a combination of tachyonic instability and broad-band parametric resonance, is perhaps the most violent example of preheati…
Primordial black holes through preheating instabilities in $α$-attractor models
Universidade da Beira Interior（贝拉内陆大学）；Centro de Matemática e Aplicações da Universidade da Beira Interior（贝拉内陆大学数学与应用中心）；Jagiellonian University（雅盖隆大学）；University of Utah（犹他大学）；Institute of Science Tokyo（东京科学大学）；University of Portsmouth（朴茨茅斯大学）
We study particle production and unitarity violation caused by a curved target space right after inflation. We use the inflaton field value instead of cosmic time as the time variable, and derive a semiclassical formula for the spectrum of produced particles. We then derive a simple condition for unitarity violation during preheating, which we confirm by our semiclassical method and numerical solution. This condition depends not only on the target space curvature but also on the height of the inflaton potential at the end of inflation. This condition tells us, for instance, that unitarity is v…
The dynamics of both the preinflationary and the preheating epochs for a model consisting of a Higgs inflaton plus an additional auxiliary field are studied in full General Relativity. The minimally coupled auxiliary field allows for parametric-type resonances that successfully transfer energy from the inflaton condensate to particle excitations in both fields. Depending on the interaction strengths of the fields, the broad resonance periods lead to structure formation consisting of large under/over-densities, and possibly the formation of compact objects. Moreover, when confronting the same m…
We investigate the anisotropies in the gravitational wave (GW) background produced at preheating after inflation. Using lattice field theory simulations of a massless preheating model, we show that the GW amplitude depends sensitively on the value of the decay product field chi coupled to the inflaton phi, with the only requisite that chi is light during inflation. We find a strong anisotropy in the amplitude of the GW background on large angular scales, the details of which strongly depend on the reheating dynamics. We expect similar conclusions for a wide class of inflationary models with li…
We study how the universe reheats following an era of chaotic Dirac-Born-Infeld inflation, and compare the rate of particle production with that in models based on canonical kinetic terms. Particle production occurs through non-perturbative resonances whose structure is modified by the nonlinearities of the Dirac-Born-Infeld action. We investigate these modifications and show that the reheating process may be efficient. We estimate the initial temperature of the subsequent hot, radiation-dominated phase.
We discuss preheating after multi-field inflation in the presence of several preheat matter fields that become light in the vicinity of (but not at) the inflatons' VEV, at distinct extra-species-points (ESP); this setup is motivated by inflationary models that include particle production during inflation, e.g.trapped inflation, grazing ESP encounters or modulated trapping, among others. While de-phasing of inflatons tends to suppress parametric resonance, we find two new effects leading to efficient preheating: particle production during the first in-fall (efficient if many preheat matter fiel…
By assuming the kinetic coupling $f^{2}(ϕ)FF$ of the effective inflaton field $ϕ$ with the electromagnetic field, we explore magnetogenesis during the inflation and preheating stages in the Starobinsky model. We consider the case of the exponential coupling function $f(ϕ)=\exp(αϕ/M_{p})$ and show that for $α\sim 12-15$ it is possible to generate the large scale magnetic fields with strength $\gtrsim 10^{-15}$ Gauss at the present epoch. The spectrum of generated magnetic fields is blue with the spectral index $n=1+s$, $s>0$. We have found that for the relevant values of the coupling parameter,…
We study the evolution of the Universe at early stages, we discuss also preheating in the framework of hybrid braneworld inflation by setting conditions on the coupling constants $λ$ and $g$\ for effective production of $χ$-particles. Considering the phase between the time observable CMB scales crossed the horizon and the present time, we write reheating and preheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in terms of the scalar spectral index $n_{s}$, and prove that, unlike the reheating case, the preheating duration does not depend on the values of the equation of state $ω^{\ast }$. We…
