Inflaton Mass Research Articles

Ultra-high frequency gravitational waves from scattering, Bremsstrahlung and decay during reheating

We investigate ultra-high frequency gravitational waves (GWs) from gravitons generated during inflationary reheating. Specifically, we study inflaton scattering with its decay product, where the couplings involved in this 2 → 2 scattering are the same as those in the 1 → 3 graviton Bremsstrahlung process. We compute the graviton production rate via such 2 → 2 scattering. Additionally, we compare the resulting GW spectrum with that from Bremsstrahlung as well as that from pure 2 → 2 inflaton scatterings. For completeness, the GW spectrum from graviton pair production through one-loop induced 1 → 2 inflaton decay is also analyzed. With a systematic comparison among the four sources of GWs, we find that 2 → 2 inflaton scattering with its decay product can dominate over Bremsstrahlung if the reheating temperature is larger than the inflaton mass. Pure inflaton 2 → 2 scattering is typically subdominant compared to Bremsstrahlung except in the high-frequency tail. The contribution from one-loop induced 1 → 2 inflaton decay is shown to be suppressed compared to Bremsstrahlung and pure inflaton 2 → 2 scattering.

Inflaton production of scalar dark matter through fluctuations and scattering

We study the effects on particle production of a Planck-suppressed coupling between the inflaton and a scalar dark matter candidate, χ. In the absence of this coupling the dominant source for the relic density of χ is the long wavelength modes produced from the scalar field fluctuations during inflation. In this case, there are strong constraints on the mass of the scalar and the reheating temperature after inflation from the present-day relic density of χ (assuming χ is stable). When a coupling σϕ2χ2 is introduced, with σ=σ˜mϕ2/MP2∼10−10σ˜, where mϕ is the inflaton mass, the allowed parameter space begins to open up considerably even for σ˜ as small as ≳10−7. For σ˜≳916, particle production is dominated by the scattering of the inflaton condensate, either through single graviton exchange or the contact interaction between ϕ and χ. In this regime, the range of allowed masses and reheating temperatures is maximal. For 0.004<σ˜<50, constraints from isocurvature fluctuations are satisfied, and the production from parametric resonance can be neglected. Published by the American Physical Society 2024

Gravitational production of heavy particles during and after inflation

We investigate the gravitational production of a scalar field χ with a mass exceeding the Hubble scale during inflation mχ ≳ HI, employing both analytical and numerical approaches. We demonstrate that the steepest descent method effectively captures the epochs and yields of gravitational production in a compact and simple analytical framework. These analytical results align with the numerical solutions of the field equation. Our study covers three spacetime backgrounds: de Sitter, power-law inflation, and the Starobinsky inflation model. Within these models, we identify two distinct phases of particle production: during and after inflation. During inflation, we derive an accurate analytic expression for the particle production rate, accounting for a varying Hubble rate. After inflation, the additional burst of particle production depends on the inflaton mass around its minimum. When this mass is smaller than the Hubble scale during inflation, HI, there is no significant extra production. However, if the inflaton mass is larger, post-inflation production becomes the dominant contribution. Furthermore, we explore the implications of gravitationally produced heavy fields for dark matter abundance, assuming their cosmological stability.

Resonant reheating

We investigate a novel reheating scenario proceeding through s-channel inflaton annihilation, mediated by a massive scalar. If the inflaton ϕ oscillates around the minimum of a monomial potential ∝ ϕ n, we reveal the emergence of resonance phenomena originating from the dynamic evolution of the inflaton mass for n>2. Consequently, a resonance appears in both the radiation and the temperature evolution during the reheating process. By solving the coupled Boltzmann equations, we present solutions for radiation and temperature. We find non-trivial temperature characteristics during reheating, depending on the value of n and the masses of the inflaton and mediator. Some phenomenological aspects of the model are explored. As a concrete example, we show that the same mediator participates in the genesis of dark matter, modifying the standard freeze-in dynamics. In addition, we demonstrate that the resonant reheating scenario could be tested by next-generation low- and high-frequency gravitational wave detectors.

Traversing a kinetic pole during inflation: primordial black holes and gravitational waves

We consider an inflationary kinetic function with an integrable polethat is traversed during inflation.This scenario leads to enhanced spectra of primordial scalar inhomogeneities with detectable signals:formation of primordial black holes(that could explain Dark Matter) andscalar-induced gravitational waves (that couldreproduce the recent Pulsar Timing Array observation, or predict signals in future detectors such as LISA or ET).Spectral signatures depend on whether the inflaton mass dimensionat the pole is above or below 2.Values mildly below 2 allow a big power spectrum enhancement with a mild tuning.Finally, we discuss the possibility that a kinetic pole can arise as anomalousdimension of the inflaton due to quantum effects of Planckian particles that becomelight at some specific inflaton field value.

A unified model of particle physics and cosmology: Origin of inflation, baryogenesis, neutrino mass, CDM and dark energy

I propose a unified model of particle physic and cosmology based on both a new extension of the standard particle model and the fundamental principle of the standard cosmology. Beyond the standard model, I introduce several species of dark fields with the dark symmetry of [Formula: see text], the inflation field, cold dark matter (CDM) and dark energy (DE) are of course included among them. The model can coherently and completely describe the origin and evolution of the universe from the primordial inflation to the reheating, to the baryogenesis, to the current CDM and DE, and also the neutrino mass generation mechanism. For the energy evolution of each phase, I give its dynamical system of equations, and solve them by some special techniques. The numerical results can clearly show how each evolution is successfully implemented, furthermore, the model demonstrates that the DE genesis is purely from the CDM condensation, which is essentially a reverse process of the primordial slow-roll inflation, there is not the so-called “cosmological constant energy”. By use of fewer input parameters, the model not only exactly reproduces the measured inflationary data and the current energy density budget, but also finely predicts such important values as the tensor-to-scalar ratio [Formula: see text], the inflaton mass [Formula: see text][Formula: see text]GeV, the reheating temperature [Formula: see text][Formula: see text]GeV, the CDM mass [Formula: see text][Formula: see text]GeV, [Formula: see text] and [Formula: see text], in particular, the model smoothly clarifies and eliminates the “Hubble tension”. In short, the unified model newly establishes the deeper and closer relations between particle physics and cosmology, therefore we expect the ongoing and future experiments to test the model.

Gravitational waves from inflaton decay and bremsstrahlung

The concept of early Universe inflation resolves several problems of hot Big Bang theory and quantitatively explains the origin of the inhomogeneities in the present Universe. However, it is not possible to arrange inflation in a scalar field model with renormalizable potential, such that it would not contradict the recent Planck data. For this reason, inflaton must have also higher derivative couplings suppressed at least by the Planck scale. We show that these couplings may be relevant during reheating and lead to non-negligible production of gravitons. We consider the possibility that the unitarity breaking scale for the model of inflation is lower than the Planck scale and compute production of gravitons during reheating, due to the inflaton decay to two gravitons and graviton bremsstrahlung process. The spectrum of produced gravitons is crucially dependent on reheating temperature and inflaton mass. We find that for low reheating temperature decay to gravitons lead to significant amount of dark radiation. Confronting this result with CMB constraints, we find reheating dependent bounds on the unitarity breaking scale. We also compare the obtained gravitational wave signals with the projected limits of future high frequency gravitational wave experiments.

Parameter space of leptogenesis in polynomial inflation

Polynomial inflation is a very simple and well motivated scenario. A potential with a concave “almost” saddle point at field value ϕ = ϕ 0 fits well the cosmic microwave background (CMB) data and makes testable predictions for the running of the spectral index and the tensor to scalar ratio. In this work we analyze leptogenesis in the polynomial inflation framework. We delineate the allowed parameter space giving rise to the correct baryon asymmetry as well as being consistent with data on neutrino oscillations. To that end we consider two different reheating scenarios. (i) If the inflaton decays into two bosons, the reheating temperature can be as high as T rh ∼ 1014 GeV without spoiling the flatness of the potential, allowing vanilla N 1 thermal leptogenesis to work if T rh > M 1 where N 1 is the lightest right-handed neutrino and M 1 its mass. Moreover, if the dominant decay of the inflaton is into Higgs bosons of the Standard Model, we find that rare three-body inflaton decays into a Higgs boson plus one light and one heavy neutrino allow leptogenesis even for T rh < M 1 if the inflaton mass is of order 1012 GeV or higher; in the polynomial inflation scenario this requires ϕ 0 ≳ 2.5 MP . This novel mechanism of non-thermal leptogenesis is quite generic, since the coupling leading to the three-body final state is required in the type I see-saw mechanism. (ii) If the inflaton decays into two fermions, the flatness of the potential implies a lower reheating temperature. In this case inflaton decay to two N 1 still allows successful non-thermal leptogenesis if ϕ 0 ≳ 0.1 MP and T rh ≳ 106 GeV.

Supersymmetric baryogenesis in a hybrid inflation model

We study baryogenesis in a hybrid inflation model which is embedded to the minimal supersymmetric model with right-handed neutrinos. Inflation is induced by a linear combination of the right-handed sneutrinos and its decay reheats the universe. The decay products are stored in conserved numbers, which are transported under the interactions in equilibrium as the temperature drops down. We find that at least a few percent of the initial lepton asymmetry is left under the strong wash-out due to the lighter right-handed (s)neutrinos. To account for the observed baryon number and the active neutrino masses after a successful inflation, the inflaton mass and the Majorana mass scale should be 1013 GeV and mathcal{O} (109–1010) GeV, respectively.

The Warm Inflation Story

Warm inflation has normalized two ideas in cosmology, that in the early universe the initial primordial density perturbations generally could be of classical rather than quantum origin and that during inflation, particle production from interactions amongst quantum field, and its backreaction effects, can occur concurrent with inflationary expansion. When we first introduced these ideas, both were met with resistance, but today they are widely accepted as possibilities with many models and applications based on them, which is an indication of the widespread influence of warm inflation. Open quantum field theory, which has been utilized in studies of warm inflation, is by now a relevant subject in cosmology, in part due to this early work. In this review I first discuss the basic warm inflation dynamics. I then outline how to compute warm inflation dynamics from first-principles quantum field theory (QFT) and in particular how a dissipative term arises. Warm inflation models can have an inflaton mass bigger than the Hubble scale and the inflaton field excursion can remain sub-Planckian, thus overcoming the most prohibitive problems of inflation model building. I discuss the early period of my work in developing warm inflation that helped me arrive at these important features of its dynamics. Inflationary cosmology today is immersed in hypothetical models, which by now are acting as a diversion from reaching any endgame in this field. I discuss better ways to approach model selection and give necessary requirements for a well constrained and predictive inflation model. A few warm inflation models are pointed out that could be developed to this extent. I discuss how, at this stage, more progress would be made in this subject by taking a broader view on the possible early universe solutions that include not just inflation but the diverse range of options.

Leptogenesis via inflaton mass terms in nonminimally coupled inflation

We consider a model of baryogenesis based on adding lepton number-violating quadratic mass terms to the inflaton potential of a non-minimally coupled inflation model. The $L$-violating mass terms generate a lepton asymmetry in a complex inflaton field via the mass term Affleck-Dine mechanism, which is transferred to the Standard Model (SM) sector when the inflaton decays to right-handed (RH) neutrinos. The model is minimal in that it requires only the SM sector, RH neutrinos, and a non-minimally coupled inflaton sector. We find that baryon isocurvature fluctuations can be observable in metric inflation but are negligible in Palatini inflation. The model is compatible with reheating temperatures that may be detectable in the observable primordial gravitational waves predicted by metric inflation.

New one-parametric extension of the Starobinsky inflationary model

We propose a one-parametric extension of the Starobinsky R + R 2 model by adding the term. The parameter m is the inflaton mass, which is determined in the same way as in the Starobinsky model, and β is a dimensionless constant. Using the Einstein frame and the scalar field potential, we get the inflationary parameters of the model proposed. The value of the tensor-to-scalar ratio r can be significantly larger than in the Starobinsky model. The considered inflationary model is in a good agreement with the current observational data. The corresponding scalar field potential is a polynomial of the exponential function.

On the superstring-inspired quantum correction to the Starobinsky model of inflation

Superstring/M-theory is the theory of quantum gravity that can provide the UV-completion to viable inflation models. We modify the Starobinsky inflation model by adding the Bel-Robinson tensor Tμνλρ squared term proposed as the leading quantum correction inspired by superstring theory. The (R + 1/6m 2 R 2 - β/8m 6 T 2) model under consideration has two parameters: the inflaton mass m and the string-inspired positive parameter β. We derive the equations of motion in the Friedmann-Lemaitre-Robertson-Walker universe and investigate its solutions. We find the physical bounds on the value of the parameter β by demanding the absence of ghosts and consistency of the derived inflationary observables with the measurements of the cosmic microwave background radiation.

Post-inflationary dark matter bremsstrahlung

Dark matter may only interact with the visible sector efficiently at energy scales above the inflaton mass, such as the Planck scale or the grand unification scale. In such a scenario, the dark matter is mainly produced out of equilibrium during the period of reheating, often referred to as UV freeze-in. We evaluate the abundance of the dark matter generated from bremsstrahlung off the inflaton decay products assuming no direct coupling between the inflaton and the dark matter. This process generally dominates the production of dark matter for low reheating temperatures where the production through the annihilations of particle in the thermal plasma becomes inefficient. We find that the bremsstrahlung process dominates for reheating temperatures T RH ≲ 1010 GeV, and produces the requisite density of dark matter for a UV scale ≃ 1016 GeV. As examples, we calculate numerically the yield of the dark matter bremsstrahlung through gravitation and dimension-6 vector portal effective interactions.

Measuring the inflaton coupling in the CMB

We study the perspectives to extract information about the microphysical parameters that governed the reheating process after cosmic inflation from CMB data. We identify conditions under which the inflaton coupling to other fields can be constrained for a given model of inflation without having to specify the details of the particle physics theory within which this model is realised. This is possible when the effective potential during reheating is approximately parabolic, and when the coupling constants are smaller than an upper bound that is determined by the ratios between the inflaton mass and the Planck mass or the scale of inflation. We consider scalar, Yukawa, and axion-like interactions and estimate that these conditions can be fulfilled if the inflaton coupling is comparable to the electron Yukawa coupling or smaller, and if the inflaton mass is larger than 105 GeV. Constraining the order of magnitude of the coupling constant requires measuring the scalar-to-tensor ratio at the level of 10-3, which is possible with future CMB observatories. Such a measurement would provide an important clue to understand how a given model of inflation may be embedded into a more fundamental theory of nature.

Momentum distribution of dark matter produced in inflaton decay: Effect of inflaton mediated scatterings

Postinflationary reheating is a widely discussed mechanism for nonthermal production of dark matter (DM). In this scenario the momentum distribution of the produced DM particles is usually taken to be the one obtained at reheating, redshifted at later times due to the expansion of the Universe. However, since in such a scenario both the DM and the standard model (SM) fields couple to the inflaton, the DM particles necessarily undergo self-scatterings, as well as elastic and inelastic scattering reactions with the SM bath, all of which proceed through $s$-channel or $t$-channel inflaton exchange. We compute the momentum distribution of the DM particles including the effect of these scatterings, and find that the distributions can be significantly altered, even though DM remains nonthermal throughout the cosmological evolution. We observe that if the inflaton dominantly couples to the SM Higgs boson through a renormalizable interaction, then reheating temperatures and inflaton masses at the TeV scale lead to a large effect from the scattering processes, with the DM-inflaton coupling constrained by the DM density. The scattering effects are found to be sensitive to the duration of the reheating process---larger the duration, more momentum modes are filled at reheating, leading to an enhanced scattering probability. We also obtain the free-streaming length of such DM using the resulting nonthermal momentum distribution, which can be used to estimate the implications of the Lyman-$\ensuremath{\alpha}$ constraints on the DM mass. It is observed that in the scenarios considered, including the scattering effects can reduce the DM average velocity at matter-radiation equality, and its free-streaming length, by up to a factor of 40, thereby making the constraints on light DM produced in inflaton decay significantly weaker.

Inflation, SUSY breaking, and primordial black holes in modified supergravity coupled to chiral matter

We propose a novel model of the modified (Starobinsky-like) old-minimal-type supergravity coupled to a chiral matter superfield, that can simultaneously describe multi-field inflation, primordial black hole (PBH) formation, dark matter (DM), and spontaneous supersymmetry (SUSY) breaking after inflation in a Minkowski vacuum. The PBH masses in our supergravity model of double slow-roll inflation, with a short phase of “ultra-slow-roll” between two slow-roll phases, are close to 10^{18} g. We find that a significant PBH fraction in the allowed mass window can be supplemented by spontaneous SUSY breaking in the vacuum with the gravitino mass close to the scalaron (inflaton) mass M of the order 10^{13} GeV. Our supergravity model favors the composite nature of DM as a mixture of PBH and heavy gravitinos as the lightest SUSY particles. The composite DM significantly relaxes fine-tuning needed for the whole PBH-DM. The PBH-DM fraction is derived, and the second-order gravitational wave background induced by the enhanced scalar perturbations is calculated. Those gravitational waves may be accessible by the future space-based gravitational interferometers.

Gravitational dark matter: Free streaming and phase space distribution

Gravitational dark matter (DM) is the simplest possible scenario that has recently gained interest in the early Universe cosmology. In this scenario, DM is assumed to be produced from the scattering of inflatons through the gravitational interaction during reheating. Gravitational production from the radiation bath will be ignored as our analysis shows it to be suppressed for a wide range of reheating temperatures $({T}_{\mathrm{re}})$. Ignoring any other internal parameters except the DM mass $({m}_{Y})$ and spin, a particular inflation model such as $\ensuremath{\alpha}$ attractor, with a specific scalar spectral index $({n}_{s})$ has been shown to uniquely fix the DM mass of the present Universe. For fermion type DM, we found the mass ${m}_{f}$ should be within $({10}^{4}--{10}^{13})\text{ }\text{ }\mathrm{GeV}$, and for boson/vector type DM, the mass ${m}_{s}/{m}_{X}$ turned out to be within $(1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}/9.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}--{10}^{13})\text{ }\text{ }\mathrm{GeV}$. Interestingly, if the inflaton equation of state ${\ensuremath{\omega}}_{\ensuremath{\phi}}\ensuremath{\rightarrow}1/3$, the DM mass also approaches towards unique value, ${m}_{f}\ensuremath{\sim}{10}^{10}\text{ }\text{ }\mathrm{GeV}$ and ${m}_{s}({m}_{X})\ensuremath{\sim}{10}^{3}(8\ifmmode\times\else\texttimes\fi{}{10}^{3})\text{ }\text{ }\mathrm{GeV}$. We further analyzed the phase space distribution ${f}_{Y}$ and free streaming length ${\ensuremath{\lambda}}_{\mathrm{fs}}$ of these gravitationally produced DM. ${f}_{Y}$, which is believed to encode important information about DM, contains a characteristic primary peak at the initial time where the gravitational production is maximum for both fermionic and bosonic DM. Apart from this fermionic phase space, the distribution function contains an additional peak near the inflaton and fermion mass equality (${m}_{Y}\ensuremath{\sim}{m}_{\ensuremath{\phi}}$) arising for ${\ensuremath{\omega}}_{\ensuremath{\phi}}&gt;5/9$. Furthermore, the height of this additional peak turned out to be increasing with decreasing ${T}_{\mathrm{re}}$ and at some point, dominates over the primary one. Since reheating is a causal process and DM is produced during this phase, gravitational instability forming small-scale DM structures during this period will encode those phase space information and be observed at present. The crucial condition of forming such a small-scale DM structure during reheating suggests that the ${\ensuremath{\lambda}}_{\mathrm{fs}}$ must be less than the length scale associated with the mode reentering the Hubble radius at the end of reheating ${\ensuremath{\lambda}}_{\mathrm{re}}$, which has been analyzed in detail. We further estimate in detail the range of scales within which the above condition will be satisfied for different masses of scalar, fermionic, and vector DM. Finally, we end by stating the fact that all our results are observed to be insensitive on the parameter $\ensuremath{\alpha}$ of the inflaton potential within the allowed range set by the latest Planck and BICEP/Keck results.

Q-balls in nonminimally coupled Palatini inflation and their implications for cosmology

We demonstrate the existence of Q-balls in nonminimally coupled inflation models with a complex inflaton in the Palatini formulation of gravity. We show that there exist Q-ball solutions which are compatible with inflation and we derive a window in the inflaton mass squared for which this is the case. In particular, we confirm the existence of Q-ball solutions with $\ensuremath{\phi}\ensuremath{\sim}{10}^{17}--{10}^{18}\text{ }\text{ }\mathrm{GeV}$, consistent with the range of field values following the end of slow-roll Palatini inflation. We study the Q-balls and their properties both numerically and in an analytical approximation. The existence of such Q-balls suggests that the complex inflaton condensate can fragment into Q-balls, and that there may be an analogous process for the case of a real inflaton with fragmentation to neutral oscillons. We discuss the possible postinflationary cosmology following the formation of Q-balls, including an early Q-ball matter domination (eMD) period and the effects of this on the reheating dynamics of the model, gravitational wave signatures which may be detectable in future experiments, and the possibility that Q-balls could lead to the formation of primordial black holes (PBHs). In particular, we show that Palatini Q-balls with field strengths typical of inflaton condensate fragmentation can directly form black holes with masses around 500 kg or more when the self-coupling is $\ensuremath{\lambda}=0.1$, resulting in very low (less than 100 GeV) reheating temperatures from black hole decay, with smaller black hole masses and larger reheating temperatures possible for smaller values of $\ensuremath{\lambda}$. Q-ball dark matter from nonminimally coupled Palatini inflation may also be a direction for future work.

Gravitational collapse in the postinflationary Universe

The Universe may pass through an effectively matter-dominated epoch between inflation and Big Bang Nucleosynthesis during which gravitationally bound structures can form on subhorizon scales. In particular, the inflaton field can collapse into inflaton halos, forming "large scale" structure in the very early universe. We combine N-body simulations with high-resolution zoom-in regions in which the non-relativistic Schr\"odinger-Poisson equations are used to resolve the detailed, wave-like structure of inflaton halos. Solitonic cores form inside them, matching structure formation simulations with axion-like particles in the late-time universe. We denote these objects \textit{inflaton stars}, by analogy with boson stars. Based on a semi-analytic formalism we compute their overall mass distribution which shows that some regions will reach overdensities of $10^{15}$ if the early matter-dominated epoch lasts for 20 $e$-folds. The radii of the most massive inflaton stars can shrink below the Schwarzschild radius, suggesting that they could form primordial black holes prior to thermalization.