After inflation, a period of preheating may have produced a stochastic background of high frequency gravitational waves (GWs) that would persist until today. The nature of the inflaton's coupling to Standard Model or other fields is unknown, so it is useful to ask what features such fields may typically have, and how these affect predictions for the GW's produced. Here we consider the inflaton to be coupled to a light scalar field, and show that even a very small quartic self-interaction term will reduce the amplitude of the GW spectrum. For self-coupling $λ_χ \gtrsim g^2$, where $g^2$ is the inflaton-scalar coupling, the peak energy density goes as $Ω_{\rm gw}^{(λ_χ)} / Ω_{\rm gw}^{(λ_χ=0)} \sim (g^2/λ_χ)^{2}$. A consequence is that if the universe reheats through an inflaton-Higgs coupling then the spectrum would be suppressed but the dynamics would be sensitive to the Higgs potential near the energy scale of inflation.
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.
Oscillons are long-lived, localized excitations of nonlinear scalar fields which may be copiously produced during preheating after inflation, leading to a possible oscillon-dominated phase in the early Universe. For example, this can happen after axion monodromy inflation, on which we run our simulations. We investigate the stochastic gravitational wave background associated with an oscillon-dominated phase. An isolated oscillon is spherically symmetric and does not radiate gravitational waves, and we show that the flux of gravitational radiation generated between oscillons is also small. Howe…
We study the evolution of gravitational waves through the preheating era that follows inflation. The oscillating inflaton drives parametric resonant growth of scalar field fluctuations, and although super-Hubble tensor modes are not strongly amplified, they do carry an imprint of preheating. This is clearly seen in the Weyl tensor, which provides a covariant description of gravitational waves.
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…
We study preheating in plateau inflation in the Palatini formulation of general relativity, in a special case that resembles Higgs inflation. It was previously shown that the oscillating inflaton field returns to the plateau repeatedly in this model, and this leads to tachyonic production of inflaton particles. We show that a minimally coupled spectator scalar field can be produced even more efficiently by a similar mechanism. The mechanism is purely gravitational, and the scalar field mass can be of order $10^{13}$ GeV, larger than the Hubble scale by many orders of magnitude, making this a c…
We propose a new preheating mechanism through the coupling of the gravitational field to both the inflaton and matter fields, without direct inflaton-matter couplings. The inflaton transfers power to the matter fields through interactions with gravitational waves, which are exponentially enhanced due to an inflation-graviton coupling. One such coupling is the product of the inflaton to the Pontryagin density, as in dynamical Chern-Simons gravity. The energy scales involved are constrained by requiring that preheating happens fast during matter domination.
Primordial gravitational waves provide a very important stochastic background that could be detected soon with interferometric gravitational wave antennas or indirectly via the induced patterns in the polarization anisotropies of the cosmic microwave background. The detection of these waves will open a new window into the early Universe, and therefore it is important to characterize in detail all possible sources of primordial gravitational waves. In this paper we develop theoretical and numerical methods to study the production of gravitational waves from out-of-equilibrium gauge fields at pr…
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 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,…
When a light scalar field is present during inflation, its value will vary on superhorizon scales, modulating the preheating process at the end of inflation. Consequently, the amplitude of the gravitational wave (GW) background produced during preheating will also be modulated. The observed energy density of this background will therefore appear anisotropic at different angles in the sky. We provide a master formula for the angular power spectrum C_l of the anisotropies in the GW background from preheating, valid for any scenario where the anisotropies are due to the superhorizon modulation of…
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…
The gravitational wave equations form a parametric resonance system during oscillatory reheating after inflation, when cast in terms of the electric and magnetic parts of the Weyl tensor. This is in direct analogy with preheating. For chaotic inflation with a quadratic potential, this analogy is exact. The resulting amplification of the gravitational wave spectrum begins in the broad resonance regime for chaotic inflation but quickly moves towards narrow resonance. This increases the amplitude and breaks the scale invariance of the tensor spectrum generated during inflation, an effect which ma…
We consider dark matter production during the inflaton oscillation epoch. It is conceivable that renormalizable interactions between dark matter and inflaton may be negligible. In this case, the leading role is played by higher dimensional operators generated by gravity and thus suppressed by the Planck scale. We focus on dim-6 operators and study the corresponding particle production in perturbative and non-perturbative regimes. We find that the dark matter production rate is dominated by non-derivative operators involving higher powers of the inflaton field. Even if they appear with small Wi…
We investigated the possibility that nonlinear gravitational effects influence the preheating era after inflation, using numerical solutions of the inhomogeneous Einstein field equations. We compared our results to perturbative calculations and to solutions of the nonlinear field equations in a rigid (unperturbed) spacetime, in order to isolate gravitational phenomena. We confirm the broad picture of preheating obtained from the nonlinear field equations in a rigid background, but find gravitational effects have a measurable impact on the dynamics. The longest modes in the simulation grow much…
Tachyonic preheating is realized when the inflaton repeatedly returns to a convex region of the potential during the post-inflationary oscillating phase. This will induce a strong tachyonic instability and lead to a rapid fragmentation of the coherent field that can complete within a fraction of an $e$-fold. In this paper, we study the linear regime of this process in a model-independent way. To this purpose, we construct simplified models that provide an analytic Floquet theoretic description of mode growth. This approach captures the essential features of well-motivated tachyonic preheating …
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…
Matrix inflation, or M-flation, is a string theory motivated inflationary model with three scalar field matrices and gauge fields in the adjoint representation of the $\mathbf{U}(N)$ gauge group. One of these $3N^2$ scalars appears as the effective inflaton while the rest of the fields (scalar and gauge fields) can play the role of isocurvature fields during inflation and preheat fields afterwards. There is a region in parameter space and initial field values, "the hilltop region," where predictions of the model are quite compatible with the recent Planck data. We show that in this hilltop reg…
Preheating after inflation involves large, time-dependent field inhomogeneities, which act as a classical source of gravitational radiation. The resulting spectrum might be probed by direct detection experiments if inflation occurs at a low enough energy scale. In this paper, we develop a theory and algorithm to calculate, analytically and numerically, the spectrum of energy density in gravitational waves produced from an inhomogeneous background of stochastic scalar fields in an expanding universe. We derive some generic analytical results for the emission of gravity waves by stochastic media…
General relativistic effects in the form of metric perturbations are usually neglected in the preheating era that follows inflation. We argue that in realistic multi-field models these effects are in fact crucial, and the fully coupled system of metric and quantum field fluctuations needs to be considered. Metric perturbations are resonantly amplified, breaking the scale-invariance of the primordial spectrum, and in turn stimulate scalar field resonances via gravitational rescattering. This non-gravitationally dominated nonlinear growth of gravitational fluctuations may have significant effect…
We perform a numerical study of the preheating mechanism of particle production in models of quintessential inflation and compare it with the usual gravitational production mechanism. We find that even for a very small coupling between the inflaton field and a massless scalar field, g > 10^{-9}, preheating dominates over gravitational particle production. Reheating temperatures in the range 10^{-2} GeV < T_{rh} < 10^{15} GeV can be easily obtained.
We study gravitational creation of light fermions in the presence of classical scalar metric perturbations about a flat Friedmann-Lemaitre- Robertson-Walker (FLRW) background. These perturbations can be large during preheating, breaking the conformal flatness of the background spacetime. We compute numerically the total number of particles generated by the modes of the metric perturbations which have grown sufficiently to become classical. In the absence of inhomogeneities massless fermions are not gravitationally produced, and then this effect may be relevant for abundance estimates of light …
We show that gravitational radiation is produced quite efficiently in interactions of classical waves created by resonant decay of a coherently oscillating field. For simple models of chaotic inflation in which the inflaton interacts with another scalar field, we find that today's ratio of energy density in gravitational waves per octave to the critical density of the universe can be as large as 10^{-12} at the maximal wavelength of order 10^{5} cm. In the pure $λϕ^4$ model, the maximal today's wavelength of gravitational waves produced by this mechanism is of order 10^6 cm, close to the upper…
Parametric resonance is among the most efficient phenomena generating gravitational waves (GWs) in the early Universe. The dynamics of parametric resonance, and hence of the GWs, depend exclusively on the resonance parameter $q$. The latter is determined by the properties of each scenario: the initial amplitude and potential curvature of the oscillating field, and its coupling to other species. Previous works have only studied the GW production for fixed value(s) of $q$. We present an analytical derivation of the GW amplitude dependence on $q$, valid for any scenario, which we confront against…
The stochastic gravitational wave (GW) background provides a fascinating window to the physics of the very early universe. Beyond the nearly scale-invariant primordial GW spectrum produced during inflation, a spectrum with a much richer structure is typically generated during the preheating phase after inflation (or after some other phase transition at lower energies). This raises the question of what one can learn from a future observation of the stochastic gravitational wave background spectrum about the underlying physics during preheating. Recently, it has been shown that during preheating…
We consider the interaction between perturbations in the inflaton and in the metric during the preheating phase in simple inflationary models. By numerically integrating the Einstein field equations we are able to gauge the impact of non-linear gravitational effects on preheating for the first time. In the lambda phi^4 model we find a large increase in the amplitude of sub-Hubble metric modes, beyond that due to gravitational collapse alone. There is significant mode-mode coupling and the amplification is eventually terminated by back reaction effects. We suggest that such enhancement of inhom…
The process of reheating the universe after hybrid inflation is extremely violent. It proceeds through the nucleation and subsequent collision of large concentrations of energy density in bubble-like structures, which generate a significant fraction of energy in the form of gravitational waves. We study the power spectrum of the stochastic background of gravitational waves produced at reheating after hybrid inflation. We find that the amplitude could be significant for high-scale models, although the typical frequencies are well beyond what could be reached by planned gravitational wave observ…
We investigate non-perturbative production of fermionic dark matter in the early universe. We study analytically the gravitational production mechanism accompanied by the coupling of fermions to the background inflaton field. The latter leads to the variation of effective fermion mass during preheating and makes the resulting spectrum and abundance sensitive to its parameters. Assuming fast preheating that completes in less than the inflationary Hubble time and no oscillations of the inflaton field after inflation, we find an abundant production of particles with energies ranging from the infl…
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…
We study the stochastic background of gravitational waves produced from preheating in hybrid inflation models. We investigate different dynamical regimes of preheating in these models and we compute the resulting gravity wave spectra using analytical estimates and numerical simulations. We discuss the dependence of the gravity wave frequencies and amplitudes on the various potential parameters. We find that large regions of the parameter space leads to gravity waves that may be observable in upcoming interferometric experiments, including Advanced LIGO, but this generally requires very small c…
We investigate the production of gravitational waves during preheating after inflation in the common case of field potentials that are asymmetric around the minimum. In particular, we study the impact of oscillons, comparatively long lived and spatially localized regions where a scalar field (e.g. the inflaton) oscillates with large amplitude. Contrary to a previous study, which considered a symmetric potential, we find that oscillons in asymmetric potentials associated with a phase transition can generate a pronounced peak in the spectrum of gravitational waves, that largely exceeds the linea…
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…
Metric perturbations typically strengthen field resonances during preheating. In contrast we present a model in which the super-Hubble field resonances are completely {\em suppressed} when metric perturbations are included. The model is the nonminimal Fakir-Unruh scenario which is exactly solvable in the long-wavelength limit when metric perturbations are included, but exhibits exponential growth of super-Hubble modes in their absence. This gravitationally enhanced integrability is exceptional, both for its rarity and for the power with which it illustrates the importance of including metric p…
We investigate a possibility of reheating in a scenario of D-brane inflation in a warped deformed conifold background which includes perturbative corrections to throat geometry sourced by chiral operator of dimension 3/2 in the CFT. The effective D-brane potential, in this case, belongs to the class of non-oscillatory models of inflation for which the conventional reheating mechanism does not work. We find that gravitational particle production is inefficient and leads to reheating temperature of the order of ${10^8} GeV$. We show that instant preheating is quite suitable to the present scenar…
We discuss the interaction between perturbations in the inflaton and the background during the preheating phase in simple inflationary models. By numerically solving the Einstein field equations we are able to assess the impact of non-linear gravitational effects on preheating, and to assess the accuracy of perturbative discussions of the preheating epoch.
Weak Gravity Conjecture in the sky: gravitational waves from preheating in Einstein-Maxwell-Scalar EFT
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（基础物理与数学科学学院，杭州高等研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, Blackett Laboratory, Imperial College London（帝国理工学院布莱克特物理学系）；International Centre for Theoretical Physics Asia-Pacific（亚太理论物理中心）
Gravitational Waves from Higgs Preheating after Inflaton $Z_2$-Symmetry Breaking
Southwest University of Science and Technology（西南科技大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）；Chongqing Vocational Institute of Engineering（重庆工程职业技术学院）
We discuss the possibility to measure particle couplings with stochastic gravitational wave backgrounds (SGWBs). Under certain circumstances a sequence of peaks of different amplitude and frequency -- a $stairway$ -- emerges in a SGWB spectrum, with each peak probing a different coupling. The detection of such signature opens the possibility to reconstruct couplings (spectroscopy) of particle species involved in high energy phenomena generating SGWBs. Stairway-like signatures may arise in causally produced backgrounds in the early Universe, e.g. from preheating or first order phase transitions…
We study inflationary models in which the effective potential of the inflaton field does not have a minimum, but rather gradually decreases at large $ϕ$. In such models the inflaton field does not oscillate after inflation, and its effective mass becomes vanishingly small, so the standard theory of reheating based on the decay of the oscillating inflaton field does not apply. For a long time the only mechanism of reheating in such non-oscillatory (NO) models was based on gravitational particle production in an expanding universe. This mechanism is very inefficient. We will show that it may lea…
Cosmological B-L breaking is a natural and testable mechanism to generate the initial conditions of the hot early universe. If B-L is broken at the grand unification scale, the false vacuum phase drives hybrid inflation, ending in tachyonic preheating. The decays of heavy B-L Higgs bosons and heavy neutrinos generate entropy, baryon asymmetry and dark matter and also control the reheating temperature. The different phases in the transition from inflation to the radiation dominated phase produce a characteristic spectrum of gravitational waves. We calculate the complete gravitational wave spect…
We inaugurate a framework for studying preheating and parametric resonance after inflation without resorting to any approximations, either in gravitational perturbation theory or in the evolution of the field(s). We do this by numerically solving the Einstein field equations in the post-inflationary universe. In this letter we show how to compare our results to those of gauge invariant perturbation theory. We then verify Finelli and Brandenberger's analysis (hep-ph/9809490) of super-horizon modes in $m^2ϕ^2$ inflation, showing that they are not amplified by resonant effects. Lastly, we make a …
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…
Out-of-equilibrium fermions can be created in the early Universe by non-perturbative parametric effects, both at preheating or during the thermal era. An anisotropic stress is developed in the fermion distribution, acting as a source of a stochastic background of gravitational waves (GW). We derive a general formalism to calculate the spectrum of GW produced by an ensemble of fermions, which we apply to a variety of scenarios after inflation. We discuss in detail the regularization of the source, i.e. of the unequal-time-correlator of the fermions' transverse-traceless anisotropic stress. We d…
