Preheating after multifield inflation with nonminimal couplings, III: Dynamical spacetime results

This paper concludes our semi-analytic study of preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. Using the covariant framework of paper I in this series, we extend the rigid-spacetime results of paper II by considering both the expansion of the universe during preheating, as well as the effect of the coupled metric perturbations on particle production. The adiabatic and isocurvature perturbations are governed by different effective masses that scale differently with the nonminimal couplings and evolve differently in time. The effective mass for the adiabatic modes is dominated by contributions from the coupled metric perturbations immediately after inflation. The metric perturbations contribute an oscillating tachyonic term that enhances an early period of significant particle production for the adiabatic modes, which ceases on a time-scale governed by the nonminimal couplings $\xi_I$. The effective mass of the isocurvature perturbations, on the other hand, is dominated by contributions from the fields' potential and from the curvature of the field-space manifold (in the Einstein frame), the balance between which shifts on a time-scale governed by $\xi_I$. As in papers I and II, we identify distinct behavior depending on whether the nonminimal couplings are small ($\xi_I \lesssim {\cal O} (1)$), intermediate ($\xi_I \sim {\cal O} (1 - 10)$), or large ($\xi_I \geq 100$).

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title: Non-minimal Inflationary Attractors
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title: On reaching the adiabatic limit in multi-field inflation
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title: Nonperturbative Dynamics Of Reheating After Inflation: A Review
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title: General relativistic effects in preheating
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title: Metric preheating and limitations of linearized gravity
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title: Restoring the sting to metric preheating
abstract: The relative growth of field and metric perturbations during preheating is sensitive to initial conditions set in the preceding inflationary phase. Recent work suggests this may protect super-Hubble metric perturbations from resonant amplification during preheating. We show that this possibility is fragile and sensitive to the specific form of the interactions between the inflaton and other fields. The suppression is naturally absent in two classes of preheating in which either: (1) the vacua of the noninflaton fields during inflation are deformed away from the origin; or (2) the effective masses of noninflaton fields during inflation are small but during preheating are large. Unlike the simple toy model of a g2Φ2χ2 coupling, most realistic particle physics models contain these other features. Moreover, they generically lead to both adiabatic and isocurvature modes and non-Gaussian scars on super-Hubble scales. Large-scale coherent magnetic fields may also appear naturally.

title: Parametric amplification of metric fluctuations during reheating in two field models
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title: When can preheating affect the CMB
abstract: We discuss the principles governing the selection of inflationary models for which preheating can affect the CMB. This is a (fairly small) subset of those models which have nonnegligible entropy/isocurvature perturbations on large scales during inflation. We study new models which belong to this class—two-field inflation with negative nonminimal coupling and hybrid/double/supernatural inflation models where the tachyonic growth of entropy perturbations can lead to the variation of the curvature perturbation, R , on super-Hubble scales. Finally, we present evidence against recent claims for the variation of R in the absence of substantial super-Hubble entropy perturbations.

title: Lattice calculation of non-Gaussianity from preheating
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title: Non-Gaussian curvature spikes from chaotic billiards in inflation preheating.
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title: Anisotropies in the gravitational wave background from preheating.
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title: Parametric Resonance of Entropy Perturbations in Massless Preheating
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title: Equation of State and Duration to Radiation Domination after Inflation.
abstract: We calculate the equation of state after inflation and provide an upper bound on the duration before radiation domination by taking the nonlinear dynamics of the fragmented inflaton field into account. A broad class of single-field inflationary models with observationally consistent flattening of the potential at a scale M away from the origin, V(ϕ)∝|ϕ|^{2n} near the origin, and where the couplings to other fields are ignored, is included in our analysis. We find that the equation of state parameter w→0 for n=1 and w→1/3 (after sufficient time) for n≳1. We calculate how the number of e-folds to radiation domination depends on both n and M when M∼m_{Pl}, whereas when M≪m_{Pl}, we find that the duration to radiation domination is negligible. Our results are explained in terms of a linear instability analysis in an expanding universe and scaling arguments, and are supported by 3+1-dimensional lattice simulations. We show that our upper bound on the postinflationary duration before radiation domination reduces the uncertainty in inflationary observables even when couplings to additional light fields are included (at least under the assumption of perturbative decay).

title: Parametric Resonance in the Early Universe - A Fitting Analysis
abstract: Particle production via parametric resonance in the early Universe, is a nonperturbative, non-linear and out-of-equilibrium phenomenon. Although it is a well studied topic, whenever a new scenario exhibits parametric resonance, a full re-analysis is normally required. To avoid this tedious task, many works present often only a simplified linear treatment of the problem. In order to surpass this circumstance in the future, we provide a fitting analysis of parametric resonance through all its relevant stages: initial linear growth, non-linear evolution, and relaxation towards equilibrium. Using lattice simulations in an expanding grid in 3 + 1 dimensions, we parametrize the dynamics outcome scanning over the relevant ingredients: role of the oscillatory field, particle coupling strength, initial conditions, and background expansion rate. We emphasize the inaccuracy of the linear calculation of the decay time of the oscillatory field, and propose a more appropriate definition of this scale based on the subsequent non-linear dynamics. We provide simple fits to the relevant time scales and particle energy fractions at each stage. Our fits can be applied to post-inflationary preheating scenarios, where the oscillatory field is the inflaton, or to spectator-field scenarios, where the oscillatory field can be e.g. a curvaton, or the Standard Model Higgs.

title: Towards the theory of reheating after inflation
abstract: Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance called preheating. It may occur in an expanding universe if the initial amplitude of oscillations of the inflaton field is large enough. We investigate a simple model of a massive inflaton field coupled to another scalar field X. Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is different from the parametric resonance in the case when the expansion of the universe is neglected. Quantum fields interacting with the oscillating inflaton field experience a series of kicks which occur with phases uncorrelated to each other. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and backreaction of produced particles, including the effects of rescattering. The process of preheating can be divided into several distinct stages. At the first stage the backreaction of created particles is not important. At the second stage backreaction increases the frequency of oscillations of the inflaton field, which makes the process even more efficient than before. Then the effects related to scattering of X-particles terminate the resonance. We calculate the density of X-particles and their quantum fluctuations with all backreaction effects taken into account. This allows us to find the range of masses and coupling constants for which one has efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.

title: Post-inflation reheating in an expanding universe.
abstract: An analytic means of studying the resonant decay of the inflaton field is developed for the case of background expansion H # 0. It is shown that the parametric resonance in the in0aton’s decay need not disappear when the expansion of the universe is taken into account, although the total number of particles produced is fewer than that in the H Y 0 case.

title: Geometric Reheating after Inflation
abstract: Inflationary reheating via resonant production of non-minimally coupled scalar particles with only gravitational coupling is shown to be extremely strong, exhibiting a negative coupling instability for $\xi<0$ and a wide resonance decay for $\xi \gg 1$. Since non-minimal fields are generic after renormalisation in curved spacetime, this offers a new paradigm in reheating - one which naturally allows for efficient production of the massive bosons needed for GUT baryogenesis. We also show that both vector and tensor fields are produced resonantly during reheating, extending the previously known correspondences between bosonic fields of different spins during preheating.

title: Resonant particle production with non-minimally coupled scalar fields in preheating after inflation
abstract: We investigate a resonant particle production of a scalar field $\chi$ coupled non-minimally to a spacetime curvature $R$ ($\xi R \chi^2$) as well as to an inflaton field $\phi$ ($g^2\phi^2\chi^2$). In the case of $g<3 \times 10^{-4}$, $\xi$ effect assists $g$-resonance in certain parameter regimes. However, for $g>3 \times 10^{-4}$, $g$-resonance is not enhanced by $\xi$ effect because of $\xi$ suppression effect as well as a back reaction effect. If $\xi \approx -4$, the maximal fluctuation of produced $\chi$-particle is $\sqrt{<\chi^2>}_{max} \approx 2 \times 10^{17}$ GeV for $g<1 \times 10^{-5}$, which is larger than the minimally coupled case with $g \approx 1 \times 10^{-3}$.

title: Pseudostable bubbles.
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title: Inflaton Fragmentation and Oscillon Formation in Three Dimensions
abstract: Analytical arguments suggest that a large class of scalar field potentials permit the existence of oscillons -- pseudo-stable, non-topological solitons -- in three spatial dimensions. In this paper we numerically explore oscillon solutions in three dimensions. We confirm the existence of these field configurations as solutions to the Klein-Gorden equation in an expanding background, and verify the predictions of Amin and Shirokoff for the characteristics of individual oscillons for their model. Further, we demonstrate that significant numbers of oscillons can be generated via fragmentation of the inflaton condensate, consistent with the analysis of Amin. These emergent oscillons can easily dominate the post-inflationary universe. Finally, both analytic and numerical results suggest that oscillons are stable on timescales longer than the post-inflationary Hubble time. Consequently, the post-inflationary universe can contain an effective matter-dominated phase, during which it is dominated by localized concentrations of scalar field matter.

title: Gravitational waves from oscillon preheating
abstract: A bstractOscillons 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. However, a significant stochastic gravitational wave background may be generated during preheating itself (i.e, when oscillons are forming), and in this case the characteristic size of the oscillons is imprinted on the gravitational wave power spectrum, which has multiple, distinct peaks.

title: End of inflation, oscillons, and matter-antimatter asymmetry
abstract: The dynamics at the end of inflation can generate an asymmetry between particles and antiparticles of the inflaton field. This asymmetry can be transferred to baryons via decays, generating a baryon asymmetry in our Universe. We explore this idea in detail for a complex inflaton governed by an observationally consistent\char22{}``flatter than quadratic''\char22{}potential with a weakly broken global $U(1)$ symmetry. We find that most of the inflaton asymmetry is locked in nontopological soliton-like configurations (oscillons) produced copiously at the end of inflation. These solitons eventually decay into baryons and generate the observed matter-antimatter asymmetry for a range of model parameters. Through a combination of three dimensional lattice simulations and a detailed linearized analysis, we show how the inflaton asymmetry depends on the fragmentation, the magnitude of the symmetry breaking term and initial conditions at the end of inflation. We discuss the final decay into baryons, but leave a detailed analysis of the inhomogeneous annihilation, reheating and thermalization to future work. As part of our work, we pay particular attention to generating multifield initial conditions for the field fluctuations (including metric perturbations) at the end of inflation for lattice simulations.

title: Equation of State and Duration to Radiation Domination after Inflation.
abstract: We calculate the equation of state after inflation and provide an upper bound on the duration before radiation domination by taking the nonlinear dynamics of the fragmented inflaton field into account. A broad class of single-field inflationary models with observationally consistent flattening of the potential at a scale M away from the origin, V(ϕ)∝|ϕ|^{2n} near the origin, and where the couplings to other fields are ignored, is included in our analysis. We find that the equation of state parameter w→0 for n=1 and w→1/3 (after sufficient time) for n≳1. We calculate how the number of e-folds to radiation domination depends on both n and M when M∼m_{Pl}, whereas when M≪m_{Pl}, we find that the duration to radiation domination is negligible. Our results are explained in terms of a linear instability analysis in an expanding universe and scaling arguments, and are supported by 3+1-dimensional lattice simulations. We show that our upper bound on the postinflationary duration before radiation domination reduces the uncertainty in inflationary observables even when couplings to additional light fields are included (at least under the assumption of perturbative decay).

title: Violent Preheating in Inflation with Nonminimal Coupling
abstract: We study particle production at the preheating era in inflation models with nonminimal coupling $\xi \phi^2R$ and quartic potential $\lambda \phi^4/4$ 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 inflaton field, which may be understood as a consequence of the short time scale during which the effective potential or kinetic term changes suddenly. The produced particles typically have very high momenta $k \lesssim \sqrt{\lambda}M_\text{P}$. The production might be so strong that almost all the energy of the inflaton is carried away within one oscillation for $\xi^2\lambda \gtrsim {\mathcal O}(100)$. This may partly change the conventional understandings of the (p)reheating after inflation with the nonminimal coupling to gravity such as Higgs inflation. We also discuss the possibility of unitarity violation at the preheating stage.

title: Gauge-preheating and the end of axion inflation
abstract: 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 m22 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 transfers all of its energy to the gauge fields within a few oscillations. In most cases, we find that the gauge fields on sub-horizon scales end preheating in an unpolarized state due to the existence of strong rescattering between the inflaton and gauge-field modes. We also present a preliminary study of an axion monodromy model coupled to U(1) gauge fields, seeing a similarly efficient preheating behavior as well as indications that the coupling strength has an effect on the creation of oscillons.

title: Magnetogenesis from axion inflation
abstract: In this work we compute the production of magnetic fields in models of axion inflation coupled to the hypercharge sector of the Standard Model through a Chern-Simons interaction term. We make the simplest choice of a quadratic inflationary potential and use lattice simulations to calculate the magnetic field strength, helicity and correlation length at the end of inflation. For small values of the axion-gauge field coupling strength the results agree with no-backreaction calculations and estimates found in the literature. For larger couplings the helicity of the magnetic field differs from the no-backreaction estimate and depends strongly on the comoving wavenumber. We estimate the post-inflationary evolution of the magnetic field based on known results for the evolution of helical and non-helical magnetic fields. The magnetic fields produced by axion inflation with large couplings to $U(1)_Y$ can reach $B_{\rm eff} \gtrsim 10^{-16}\, {\rm G}$, exhibiting a field strength $B_{\rm phys} \approx 10^{-13}\, {\rm G}$ and a correlation length $\lambda_{\rm phys}\approx10\, {\rm pc}$. This result is insensitive to the exact value of the coupling, as long as the coupling is large enough to allow for instantaneous preheating. Depending on the assumptions for the physical processes that determine blazar properties, these fields can be found consistent with blazar observations based on the value of $B_{\rm eff}$. Finally, the intensity of the magnetic field for large coupling can be enough to satisfy the requirements for a recently proposed baryogenesis mechanism, which utilizes the chiral anomaly of the Standard Model.

title: Preheating with nonminimal kinetic terms.
abstract: We present the first (3+1)-dimensional numerical simulations of scalar fields with nonminimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld inflaton coupled to a canonical matter field. The simulations represent the full nonlinear theory in the presence of an expanding universe. We show that parametric resonance in the matter field along with self-resonance in the inflaton repopulate the universe with matter particles as efficiently as in traditional preheating.

title: Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field
abstract: We consider the renormalization group improvement in the theory of the Standard Model Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. It suggests the range of the Higgs mass $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$ compatible with the current CMB data (the lower WMAP bound on $n_s$), which is close to the widely accepted range dictated by the electroweak vacuum stability and perturbation theory bounds. We find the phenomenon of asymptotic freedom induced by this non-minimal curvature coupling, which brings the theory to the weak coupling domain everywhere except at the lower and upper boundary of this range. The renormalization group running of the basic quantity ${\boldmath $A_I$}$ -- the anomalous scaling in the non-minimally coupled Standard Model, which analytically determines all characteristics of the CMB spectrum -- brings ${\boldmath $A_I$}$ to small negative values at the inflation scale. This property is crucial for the above results and may also underlie the formation of initial conditions for the inflationary dynamics in quantum cosmology.

title: Power-counting and the validity of the classical approximation during inflation
abstract: We use the power-counting formalism of effective field theory to study the size of loop corrections in theories of slow-roll inflation, with the aim of more precisely identifying the limits of validity of the usual classical inflationary treatments. We keep our analysis as general as possible in order to systematically identify the most important corrections to the classical inflaton dynamics. Although most slow-roll models lie within the semiclassical domain, we find the consistency of the Higgs-Inflaton scenario to be more delicate due to the proximity between the Hubble scale during inflation and the upper bound allowed by unitarity on the new-physics scale associated with the breakdown of the semiclassical approximation within the effective theory. Similar remarks apply to curvature-squared inflationary models.

title: Primordial perturbations from multifield inflation with nonminimal couplings
abstract: Realistic models of particle physics include many scalar fields. These fields generically have nonminimal couplings to the Ricci curvature scalar, either as part of a generalized Einstein theory or as necessary counterterms for renormalization in curved background spacetimes. We develop a gauge-invariant formalism for calculating primordial perturbations in models with multiple nonminimally coupled fields. We work in the Jordan frame (in which the nonminimal couplings remain explicit) and identify two distinct sources of entropy perturbations for such models. One set of entropy perturbations arises from interactions among the multiple fields. The second set arises from the presence of nonminimal couplings. Neither of these varieties of entropy perturbations will necessarily be suppressed in the long-wavelength limit, and hence they can amplify the curvature perturbation zeta, even for modes that have crossed outside the Hubble radius. Models that overproduce long-wavelength entropy perturbations endanger the close fit between predicted inflationary spectra and empirical observations.