We consider cosmological perturbations caused by modulated inflaton velocity. During inflation, the inflaton motion is damped and the velocity is determined by the parameters such as couplings or masses that may depend on light fields(moduli). The number of e-foldings is different in different patches if there are spatial fluctuations of such parameters. Based on this simple idea, we consider ``modulated inflation'' in which the curvature perturbation is generated by the fluctuation of the inflaton velocity. This talk is based on our recent papers.
Cosmological inflation gives a natural answer for a variety of cosmological questions, including the horizon problem, the flatness problem, and others. However, inflation yields new questions relating to the flatness of the inflaton potential. Recent studies of ``little'' fields, a special class of pseudo-Goldstone bosons, have shown it is possible to protect the mass of a field while still yielding order one interactions with other fields. In this paper, we will show that ``little inflatons'' are natural candidates for the slow roll field of hybrid inflation models. We consider both supersymm…
The evolution of the inflaton field fluctuations from gauge-invariant metric fluctuations is discused. In particular, the case of a symmetric $ϕ_c$-exponential potential is analyzed.
We have studied modulated inflation that generates curvature perturbation from light-field fluctuation. As discussed in previous works, even if the fluctuation of the inflaton itself does not generate the curvature perturbation at the horizon crossing, fluctuation of a light field may induce fluctuation for the end-line of inflation and this may lead to generation of cosmological perturbation ``at the end of the inflation''. Our scenario is different from those that are based on the fluctuations of the boundary of the inflaton trajectory, as clearly explained in this paper by using the $δN$ fo…
We consider models of inflation in supergravity with a shift symmetry. We focus on models with one moduli and one inflaton field. The presence of this symmetry guarantees the existence of a flat direction for the inflaton field. Mildly breaking the shift symmetry using a superpotential which depends not only on the moduli but also on the inflaton field allows one to lift the inflaton flat direction. Along the inflaton direction, the eta-problem is alleviated. Combining the KKLT mechanism for moduli stabilization and a shift symmetry breaking superpotential of the chaotic inflation type, we fin…
It has been shown that hybrid inflation may end with the formation of non-topological solitons of inflaton field. As a first step towards a fully realistic picture of the post-inflation era and reheating in supersymmetric hybrid inflation models, we study the classical scalar field equations of a supersymmetric hybrid inflation model using a semi-analytical ansatz for the spatial dependence of the fields. Using the minimal D-term inflation model as an example, the inflaton field is evolved using the full 1-loop effective potential from the slow-rolling era to the U(1)_{FI} symmetry-breaking ph…
We propose a new inflation model in which a gauge singlet inflaton turns into the Higgs condensate after inflation. The inflationary path is characterized by a moduli space of supersymmetric vacua spanned by the inflaton and Higgs field. The inflation energy scale is related to the soft supersymmetry breaking, and the Hubble parameter during inflation is smaller than the gravitino mass. The initial condition for the successful inflation is naturally realized by the pre-inflation in which the Higgs plays a role of the waterfall field.
We clarify classical inflaton models by considering them as effective field theories `a la Ginzburg-Landau. In this approach, the WMAP statement excluding the pure phi^4 potential implies the presence of an inflaton mass term at the scale m ~ 10^{13}GeV.Chaotic, new and hybrid inflation models are studied in an unified manner.In all cases the inflaton potential takes the form V(phi)=m^2 M_{Pl}^2 v(phi/M_{Pl}), where all coefficients in v(varphi) are of order one.If such potential corresponds to supersymmetry breaking, the susy scale is sqrt{m M_{Pl}}~10^{16}GeV which coincides with the GUT sca…
Most of the inflation models end up with non-vanishing vacuum expectation values of the inflaton fields ϕin the true vacuum, which induce, in general, nonvanishing auxiliary field G_ϕfor the inflaton potential in supergravity. We show that the presence of nonzero G_ϕgives rise to inflaton decay into a pair of the gravitinos and are thereby severely constrained by cosmology especially if the gravitino is unstable and its mass is in a range of O(100) GeV \sim O(10) TeV. For several inflation models, we explicitly calculate the values of G_ϕand find that most of them are excluded or on the verge …
We discuss inflation in models with large extra dimensions, driven by a bulk scalar field. The brane inflaton is then a single effective field, obtained from the bulk scalar field by scaling. The self interaction terms of the effective brane inflaton are then naturally suppressed. The picture is consistent with a fundamental string scale in the TeV range without the problem of a superlight inflaton. If hybrid inflation is considered, the right prediction for the density perturbations as observed by COBE can be obtained without any fine tunning. The bulk inflaton then decays preferentially into…
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, …
Reheating after inflation can occur through inflaton decay or efficient parametric resonant production of particles from the oscillation of the inflaton. If the particles produced interact with scalars that were light during inflation, then significant super-horizon density perturbations are generated during this era. These perturbations can be highly non-Gaussian.
Inflation ends with the formation of a Bose condensate of inflatons. We show that in hybrid inflation models this condensate is typically unstable with respect to spatial perturbations and can fragment to condensate lumps. The case of D-term inflation is considered as an example and it is shown that fragmentation occurs if λ> 0.2g, where λis the superpotential coupling and g is the U(1)_{FI} gauge coupling. Condensate fragmentation can result in an effective enhancement of inflaton annihilations over decays as the main mode of reheating. In the case of D-term inflation models in which the Stan…
We study the instability of a scalar field at the end of hybrid inflation, using both analytical techniques and numerical simulations. We improve previous studies by taking the inflaton field fully into account, and show that the range of unstable modes depends sensitively on the velocity of the inflaton field, and thereby on the Hubble rate, at the end of inflation. If topological defects are formed, their number density is determined by the shortest unstable wavelength. Finally, we show that the oscillations of the inflaton field amplify the inhomogeneities in the energy density, leading to …
We investigate the emergence of large, localized, pseudo-stable configurations (oscillons) from inflaton fragmentation at the end of inflation. We predict the number density of large oscillons, and the conditions necessary for their emergence in a class of inflationary models. Analytic estimates are provided for a 3+1 and 1+1-dimensional universe. We test our predictions with detailed numerical simulations in 1+1-dimensions. We see a zoo of oscillons emerging from the simulations, including the usual small amplitude "sech" oscillons as well as large "flat-topped" oscillons. The emergent oscill…
If the initial state of the inflaton field is taken to have a thermal distribution instead of the conventional zero particle vacuum state then the curvature power spectrum gets modified by a temperature dependent factor such that the fluctuation spectrum of the microwave background radiation is enhanced at larger angles. We compare this modified cosmic microwave background spectrum with Wilkinson microwave anisotropy probe data to obtain an upper bound on the temperature of the inflaton at the time our current horizon crossed the horizon during inflation. We further conclude that there must be…
The inflaton necessary to implement the mechanism of inflationary cosmology has natural candidates in quiver gauge theory. We discuss the dimensionless coefficients of quartic couplings and enumerate scalars which are singlet under the low-energy gauge group. The inflaton mass is generally predicted to be in the TeV region, close to 4 TeV for one specific unified model. A quartic inflaton potential, and a mutated hybrid inflation, are discussed. They can give adequate inflation and appropriate fluctuations but different spectral indices.
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…
A simple model is discussed to give rise to successful reheating in chaotic D-term inflation with a quadratic inflaton potential, introducing a trilinear coupling in the Kähler potential. Leptogenesis through the inflaton decay is also discussed in this model.
An inflationary brane model driven by a bulk inflaton with exponential potential is proposed. We find a family of exact solutions that describe power-law inflation on the brane. These solutions enable us to derive exact solutions for metric perturbations analytically. By calculating scalar and tensor perturbations, we obtain a spectrum of primordial fluctuations at the end of the inflation. The amplitudes of scalar and tensor perturbations are enhanced in the same way if the energy scale of the inflation is sufficiently higher than the tension of the brane. Then the relative amplitude of scala…
During cosmological inflation, it has been suggested that fields coupled to the inflaton can be excited by the slow-rolling inflaton into a quasi-stable non-vacuum state. Within this scenario of ``warm inflation'', this could allow for a smooth transition to a radiation dominated Universe without a separate reheating stage and a modification of the slow roll evolution, as the heat-bath backreacts on the inflaton through friction. In order to study this from first principles, we investigate the dynamics of a scalar field coupled to the inflaton and N light scalar boson fields, using the 2PI-1/N…
We construct a phenomenological model of electroweak-scale inflation that is in accordance with recent cosmic microwave background observations by WMAP, while setting the stage for a zero-temperature electroweak transition as assumed in recent models of baryogenesis. We find that the scalar spectral index especially poses tight constraints for low-scale inflation models. The inflaton-Higgs coupling leads to substantial mixing of the scalar degrees of freedom. Two types of scalar particles emerge with decay widths similar to that of the Standard Model Higgs particle.
We discuss the cosmological gravitino problem in inflation models in which the inflaton potential is constructed from Kähler potential rather than superpotential: a representative model is $\overline{\text{D}3}$-induced geometric inflation. A critical ingredient in this type of models is the coupling of the inflaton and Polonyi (supersymmetry-breaking) field in the Kähler potential, which is needed to build the inflaton potential. We point out the same coupling let the inflaton dominantly decay into a pair of inflatino and gravitino causing the gravitino problem. We propose some possible solut…
We argue that a non-thermal leptogenesis occurs spontaneously, without direct couplings of the inflaton with right-handed neutrinos, in a wide class of high-scale inflation models such as the chaotic and hybrid inflation. It is only a finite vacuum expectation value of the inflaton, or more precisely, a linear term in the Kahler potential, that is a prerequisite for the spontaneous non-thermal leptogenesis. To exemplify how it works, we show that a chaotic inflation model in supergravity naturally produces a right amount of baryon asymmetry via the spontaneous non-thermal leptogenesis. We also…
We propose a limited class of models, describing interacting chiral multiplets with a non-minimal coupling to a vector multiplet, in curved superspace of $N=1$ supergravity. Those models are suitable for the inflationary model building in supergravity with inflaton assigned to a massive vector multiplet and spontaneous SUSY breaking in Minkowski vacuum after inflation, for any values of the inflationary parameters $n_s$ and $r$, and any scale of SUSY breaking.
Dynamics of the inflaton is studied when it interacts with boson and fermion fields and in minimal supersymmetric models. This encompasses multifield inflation models, such as hybrid inflation, and typical reheating models. For much of the parameter space conducive to inflation, the inflaton is found to dissipate adequate radiation to have observational effects on density perturbations and in cases to significantly affect inflaton evolution. Thus, for many inflation models, believed to yield exclusively isentropic inflation, the parameter space now divides into regimes of isentropic and nonise…
It has been recently pointed out that the polarization BICEP2 results are consistent with the identification of an inflaton mass m \simeq 10^{13} GeV with the SUSY breaking scale in an MSSM with a fine-tuned SM Higgs. This identification leads to a Higgs mass m_h \simeq 126 GeV, consistent with LHC measurements. Here we propose that this naturally suggests to identify the inflaton with the heavy MSSM Higgs system. The fact that the extrapolated Higgs coupling lambda_{SM}\simeq 0 at scales below the Planck scale suggests the Higgs degrees of freedom could be associated to a Wilson line or D-bra…
We propose a scenario to flatten inflaton potential for a small-field slow-roll inflation from the origin. In the scenario, inflaton mass-square gets through a renormalization group running which depends on not only inflaton field but also an assisting field. Thanks to the assisting field participating in the running, initial condition for a slow-roll inflation can be set naturally, and inflaton potential can be flattened by the vacuum expectation value of the field. Applying this idea, we propose a scenario of inflation, dubbed here as \textit{assisted hilltop inflation}, which is free from t…
We propose a possibility that the inflaton potential is significantly modified after inflation due to heavy field dynamics. During inflation there may be a heavy scalar field stabilized at a value deviated from the low-energy minimum. As the heavy field moves to the low-energy minimum, the inflaton potential could be significantly modified. In extreme cases, the inflaton potential vanishes and the inflaton becomes almost massless at some time after inflation. Such transition of the inflaton potential has interesting implications for primordial density perturbations, reheating, creation of unwa…
We propose a model for early universe cosmology without the need for fundamental scalar fields. Cosmic acceleration and phenomenologically viable reheating of the universe results from a series of energy transitions, where during each transition vacuum energy is converted to thermal radiation. We show that this `cascading universe' can lead to successful generation of adiabatic density fluctuations and an observable gravity wave spectrum in some cases, where in the simplest case it reproduces a spectrum similar to slow-roll models of inflation. We also find the model provides a reasonable rehe…
We consider a 4+N dimensional Einstein gravity coupled to a non-linear sigma model. This theory admits a solution in which the N extra dimensions contract exponentially while the ordinary space expand exponentially. Physically, the non-linear sigma fields induce the dynamical compactification of the extra dimensions, which in turn drives inflation. No inflatons are required.
We study reheating in $α$-attractor models of inflation in which the inflaton couples to other scalars or fermions. We show that the parameter space contains viable regions in which the inflaton couplings to radiation can be determined from the properties of CMB temperature fluctuations, in particular the spectral index. This may be the only way to measure these fundamental microphysical parameters, which shaped the universe by setting the initial temperature of the hot big bang and contain important information about the embedding of a given model of inflation into a more fundamental theory o…
We study preheating in theories where the inflaton couples derivatively to scalar and gauge fields. Such couplings may dominate in natural models of inflation, in which the flatness of the inflaton potential is related to an approximate shift symmetry of the inflaton. We compare our results with previously studied models with non-derivative couplings. For sufficiently heavy scalar matter, parametric resonance is ineffective in reheating the universe, because the couplings of the inflaton to matter are very weak. If scalar matter fields are light, derivative couplings lead to a mild long-wavele…
We consider the extension of the Standard Model (SM) with a light inflaton where both unitarity problem in Higgs inflation and vacuum instability problem are resolved. The linear non-minimal coupling of the inflaton to gravity leads to a significant kinetic mixing between the inflaton and the graviton such that perturbative unitarity is restored up to Planck scale. We show the correlation between unitarity scale and inflationary observables in this model and discuss how the effective Higgs inflation appears.
We discuss inflaton decays and reheating in no-scale Starobinsky-like models of inflation, calculating the effective equation-of-state parameter, $w$, during the epoch of inflaton decay, the reheating temperature, $T_{\rm reh}$, and the number of inflationary e-folds, $N_*$, comparing analytical approximations with numerical calculations. We then illustrate these results with applications to models based on no-scale supergravity and motivated by generic string compactifications, including scenarios where the inflaton is identified as an untwisted-sector matter field with direct Yukawa coupling…
In this paper, we investigate the parameter space in the framework of hilltop supernatural inflation in which the inflaton field can play the role of Affleck-Dine field to produce successful baryogenesis. The suitable value of reheating temperature could coincide with the reheating temperature required to produce lightest supersymmetric particle dark matter. The baryon isocurvature perturbation is shown to be negligible. We consider $p=3$, $p=4$, and $p=6$ type III hilltop inflation and discuss how to connect the models to supersymmetric theories.
We propose a pseudo-Nambu-Goldstone inflation where twin waterfall fields coupled to the inflaton are responsible for the graceful exit from inflation by a waterfall transition. In this scenario, the $Z_2$ symmetry for the waterfall fields and the inflaton protects the inflaton potential against dangerous quantum corrections coming from the waterfall couplings. We show that there is a wide range of natural model parameters and initial conditions for a successful inflation and discuss the reheating process by the perturbative decay of the waterfall field with a $Z_2$ invariant Higgs portal. We …
We study preheating after hilltop inflation where the inflaton couples to another scalar field, e.g. a right-handed sneutrino, which provides a mechanism for generating the correct initial conditions for inflation and also a decay channel for the inflaton that allows for reheating and non-thermal leptogenesis. In the presence of such a coupling, we find that after the phases of tachyonic preheating and tachyonic oscillations, during which the inflaton field becomes inhomogeneous, there can be a subsequent preheating phase where the fluctuations of the other field get resonantly enhanced, from …
The inflaton condensate associated with a global symmetry can fragment into quasistable Q balls, provided the inflaton oscillations give rise to an effective equation of state with negative pressure. We study chaotic inflation with a running inflaton mass and show that, depending on the sign of the radiative mass correction, the process of fragmentation into inflatonic Q balls can actually take place even though no net charge exists. If the main decay channel of the Q ball is to fermions, the universe will be reheated slowly via surface evaporation.
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…
We study a recently proposed running kinetic inflation model in which the inflaton potential becomes flat due to rapid growth of the kinetic term at large inflaton field values. As concrete examples, we build a variety of chaotic inflation models in supergravity with e.g. quadratic, linear, and fractional-power potentials. The power of the potential generically increases after inflation, and the inflaton is often massless at the potential minimum in the supersymmetric limit, which leads to many interesting phenomena. First, the light inflaton mass greatly relaxes severe thermal and non-thermal…
Most successful models of inflation in supergravity have a shift symmetry for the inflaton and contain a stabilizer field coupled to the inflaton in a particular way. We argue that the natural interpretation of the stabilizer, from the viewpoint of the shift symmetry, is a three-form multiplet. Its coupling to the inflaton is uniquely determined by the shift symmetry and the invariance under three-form gauge transformations and has a natural string theory interpretation.
A simple model for chaotic inflation in supergravity is proposed. The model is N=1 supersymmetric massive U(1) gauge theory via the Stuckelberg superfield and gives rise to D-term inflation with a quadratic term of inflaton in the potential. The Fayet-Iliopoulos field plays a role of the inflaton.
Status of light inflaton: from inflation to laboratory
Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）；Indian Institute of Technology Hyderabad（印度理工学院海德拉巴分校）；Indian Institute of Science Education and Research, Thiruvananthapuram（印度科学教育与研究机构（特鲁凡得琅））；SRM University-AP（SRM大学安得拉邦校区）
We propose an extension of natural inflation, where the inflaton potential is a general periodic function. Specifically, we study elliptic inflation where the inflaton potential is given by Jacobi elliptic functions, Jacobi theta functions or the Dedekind eta function, which appear in gauge and Yukawa couplings in the string theories compactified on toroidal backgrounds. We show that in the first two cases the predicted values of the spectral index and the tensor-to-scalar ratio interpolate from natural inflation to exponential inflation such as $R^2$- and Higgs inflation and brane inflation, …
We discuss thermalization through perturbative inflaton decay at the end of inflation. We find that a thermal plasma should form well before all inflatons have decayed, unless all gauge symmetries are badly broken during that epoch. However, before they thermalize, the very energetic inflaton decay products can contribute to the production of massive stable particles, either through collisions with the thermal plasma, or through collisions with each other. If such reactions exist, the same massive particles can also be produced directly in inflaton decay, once higher--order processes are inclu…
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the e…
Current cosmological data favour inflationary models non-minimally coupled to gravity. In this work we study the implications of the metastability of the electroweak vacuum in this framework. We consider an inflaton field with a non-minimal coupling to Ricci curvature and a portal coupling between the Higgs field and the inflaton and find that the ratio of the two couplings is severely constrained from stability during inflation and reheating dynamics, with constraints becoming more severe for weaker non-minimal coupling as during inflation Higgs fluctuations are amplified by inflationary expa…
We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. Quantum field inflation (under conditions that are the quant…
Usual inflation is realized with a slow rolling scalar field minimally coupled to gravity. In contrast, we consider dynamics of a scalar with a flat effective potential, conformally coupled to gravity. Surprisingly, it contains an attractor inflationary solution with the rapidly rolling inflaton field. We discuss models with the conformal inflaton with a flat potential (including hybrid inflation). There is no generation of cosmological fluctuations from the conformally coupled inflaton. We consider realizations of modulated (inhomogeneous reheating) or curvaton cosmological fluctuations in th…
We realize and study a model of hybrid inflation in the context of softly broken supersymmetry. The inflaton is taken to be a flat direction in the superfield space and, due to unsuppressed couplings, its soft supersymmetry breaking mass runs with scale. Both gauge and Yukawa couplings are taken into account and different inflationary scenarios are investigated depending on the relative strenght of the couplings and the mass spectrum.
During hybrid inflation, the slowly-rolling inflaton field has a significant coupling to the trigger field which is responsible for most of the potential. Barring a fine-tuned accidental cancellation, this coupling induces a minimal one-loop contribution to the inflaton potential. The requirement that this contribution be not too large constrains a wide class of hybrid inflation models. Assuming that the inflaton perturbation generates structure in the Universe, the inflaton field and/or the trigger field after inflation have to be bigger than $10^9\GeV$. This and other results make hybrid inf…
We investigate inflation with a class of concave inflaton potentials of the form $\sim ϕ^n$ $(0<n<1)$ in the Randall-Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ($M_5$) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology.
It is a longstanding desire of cosmologists, and particle physicists as well, to connect inflation to low energy physics, culminating, for instance, in what is known as Higgs inflation. The condition for the standard Higgs boson playing the role of the inflaton, and driving successfully inflation, is that it couples nonminimally with gravity. Nevertheless, cosmological constraints impose that the nonminimal coupling be large. This causes the loss of perturbative unitarity in a scale of energy far below the Planck one. Our aim in this work is to point out that inflaton potential containing a pa…
We construct a chaotic inflation model in which the Higgs fields play the role of the inflaton in the standard model as well as in the singlet extension of the supersymmetric standard model. The key idea is to allow a non-canonical kinetic term for the Higgs field. The model is a realization of the recently proposed running kinetic inflation, in which the coefficient of the kinetic term grows as the inflaton field. The inflaton potential depends on the structure of the Higgs kinetic term. For instance, the inflaton potential is proportional to phi^2 and phi^{2/3} in the standard model and NMSS…
In this paper, we consider a chaotic inflation model where the role of inflaton is played by the Higgs triplet in type II seesaw mechanism for generating the small masses of left-handed neutrinos. Leptogenesis could happen after inflation. This model is constructed without introducing supersymmetry (SUSY).
The distance between BPS branes in string theory corresponds to a flat direction in the effective potential. Small deviations from supersymmetry may lead to a small uplifting of this flat direction and to brane inflation. However, this scenario can work only if the BPS properties of the branes and the corresponding flatness of the inflaton potential are preserved in the theories with the stable volume compactification. We present an ``inflaton trench'' mechanism that keeps the inflaton potential flat due to shift symmetry, which is related to near BPS symmetry in our model.
In order for the inflaton to decay into radiation at the end of inflation, it needs to couple to light matter fields. In this article we determine whether such couplings cause the inflaton to decay during inflation rather than after it. We calculate decay amplitudes during inflation, and determine to what extent such processes have an impact on the mean and variance of the inflaton, as well as on the expected energy density of its decay products. Although the exponential growth of the decay amplitudes with the number of e-folds appears to indicate the rapid decay of the inflaton, cancellations…
