55005423
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 ($\xi_I \geq 100$).
119517140
Particle physics models of inflation and the cosmological density perturbation
This is a review of particle-theory models of inflation, and of their predictions for the primordial density perturbation that is thought to be the origin of structure in the Universe. It contains mini-reviews of the relevant observational cosmology, of elementary field theory and of supersymmetry, that may be of interest in their own right. The spectral index n(k), specifying the scale dependence of the spectrum of the curvature perturbation, will be a powerful discriminator between models, when it is measured by Planck with accuracy Δn∼0.01. The usual formula for n is derived, as well as its less familiar extension to the case of a multi-component inflaton; in both cases the key ingredient is the separate evolution of causally disconnected regions of the Universe. Primordial gravitational waves will be an even more powerful discriminator if they are observed, since most models of inflation predict that they are completely negligible. We treat in detail the new wave of models, which are firmly rooted in modern particle theory and have supersymmetry as a crucial ingredient. The review is addressed to both astrophysicists and particle physicists, and each section is fairly homogeneous regarding the assumed background knowledge.
40765960
Multiple field inflation
Inflation offers a simple model for very early evolution of our universe and the origin of primordial perturbations on large scales. Over the last 25 years we have become familiar with the predictions of single-field models, but inflation with more than one light scalar field can alter preconceptions about the inflationary dynamics and our predictions for the primordial perturbations. I will discuss how future observational data could distinguish between inflation driven by one field, or many fields. As an example, I briefly review the curvation as an alternative to the inflaton scenario for the origin of structure.
119276716
Particle physics models of inflation and curvaton scenarios
We review the particle theory origin of inflation and curvaton mechanisms for generating large scale structures and the observed temperature anisotropy in the cosmic microwave background (CMB) radiation. Since inflaton or curvaton energy density creates all matter, it is important to understand the process of reheating and preheating into the relevant degrees of freedom required for the success of Big Bang Nucleosynthesis. We discuss two distinct classes of models, one where inflaton and curvaton belong to the hidden sector, which are coupled to the Standard Model gauge sector very weakly. There is another class of models of inflaton and curvaton, which are embedded within Minimal Supersymmetric Standard Model (MSSM) gauge group and beyond, and whose origins lie within gauge invariant combinations of supersymmetric quarks and leptons. Their masses and couplings are all well motivated from low energy physics, therefore such models provide us with a unique opportunity that they can be verified/falsified by the CMB data and also by the future collider and non-collider based experiments. We then briefly discuss the stringy origin of inflation, alternative cosmological scenarios, and bouncing universes.
118640259
Multi-field inflation and cosmological perturbations
We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.
122657123
A new improved energy-momentum tensor
Abstract We show that the matrix elements of the conventional symmetric energy-momentum tensor are cut-off dependent in renormalized perturbation theory for most renormalizable field theories. However, we argue that, for any renormalizable field theory, it is possible to construct a new energy-momentum tensor, such that the new tensor defines the same four-momentum and Lorentz generators as the conventional tensor, and, further, has finite matrix elements in every order of renormalized perturbation theory. (“Finite” means independent of the cut-off in the limit of large cut-off.) We explicitly construct this tensor in the most general case. The new tensor is an improvement over the old for another reason: the currents associated with scale transformations and conformal transformations have very simple expressions in terms of the new tensor, rather than the very complicated ones they have in terms of the old. We also show how to alter general relativity in such a way that the new tensor becomes the source of the gravitational field, and demonstrate that the new gravitation theory obtained in this way meets all the epxerimental tests that have been applied to general relativity.
117563103
Quantum Field Theory in Curved Spacetime: Frontmatter
This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.
122960409
Renormalization Group, Effective Action and Grand Unification Theories in Curved Space‐Time
Recent developments in the renormalization group approach to grand unification theories (GUT's) in curved space-time are reviewed. The new kind of asymptotical conformal invariance in “finite” GUT's in curved space-time (with torsion) is derived. A discussion of asymptotically-finite GUT's in flat and curved space-time is presented. The modifications to the renormalization group in curved space with boundary are given. Some applications of the renormalization group are discussed as well as some prospects.
119244409
A simple method for one-loop renormalization in curved space-time
We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.
14818281
The Standard Model Higgs boson as the inflaton
We argue that the Higgs boson of the Standard Model can lead to inflation and produce cosmological perturbations in accordance with observations. An essential requirement is the non-minimal coupling of the Higgs scalar field to gravity; no new particle besides already present in the electroweak theory is required.
36989201
Chaotic inflationary scenario of the Universe with a nonminimally coupled "inflaton" field.
The possibility of the realization of a chaotic inflationary scenario is investigated in curved spacetime in which the inflaton couples nonminimally with the spacetime curvature such as (1/2xiRphi/sup 2/. It is found that the coupling effect prevents the scenario from working unless xi is at least smaller than 10/sup -3/ or negative.
44769698
Designing density fluctuation spectra in inflation.
Scale-invariant (flat) fluctuation spectra are the most natural outcomes of inflation. Nonetheless current large-scale-structure observations seem to indicate more fluctuation power on large scales than flat spectra give. We consider a wide variety of models based on the chaotic inflation paradigm and sketch the effects that varying the expansion rate, structure of the potential surface, and the curvature coupling constants have on the quantum fluctuation spectra. We calculate in detail the quantum generation of fluctuation spectra by numerically solving the linearized perturbation equations for multiple scalar fields, the metric, and the radiation into which the scalars dissipate, following the evolution from inside the horizon through reheating.
44954887
Improvement on cosmological chaotic inflation through nonminimal coupling.
Models of cosmological inflation are plagued with a severe and seemingly unavoidable problem: in order to produce density perturbations of an amplitude consistent with large-scale observations, the self-coupling $\ensuremath{\lambda}$ of the inflaton field has to be tuned to an excessively small value. In all these models, however, the scalar field is taken to be minimally coupled to the scalar curvature ($\ensuremath{\xi}=0$). It is shown here that in the more general case of nonminimal coupling ($\ensuremath{\xi}\ensuremath{\ne}0$), and within the framework of Linde's chaotic inflation, the constraint on the self-coupling could be relaxed by several orders of magnitude. We are led to this conclusion by the combination of two key results. (1) Contrary to previous common belief, the curvature coupling $\ensuremath{\xi}$ can be almost arbitrarily large without upsetting the inflationary scenario. In fact, the larger $\ensuremath{\xi}$ is, the better the model behaves. (2) Considerations regarding the amplitude of density perturbations constrain the ratio $\frac{\ensuremath{\lambda}}{{\ensuremath{\xi}}^{2}}$ rather than $\ensuremath{\lambda}$. Thus, by a suitable choice of $\ensuremath{\xi}$, the self-coupling $\ensuremath{\lambda}$ can be made as large as desired. It is found that for large $\ensuremath{\xi}$ the amplitude of density perturbations is much smaller than in $\ensuremath{\xi}=0$ models: ${(\ensuremath{\delta}\frac{\ensuremath{\rho}}{\ensuremath{\rho}})|}_{\ensuremath{\xi}g1}\ensuremath{\approx}{(48N{\ensuremath{\xi}}^{2})}^{\ensuremath{-}\frac{1}{2}}{(\frac{\ensuremath{\delta}\ensuremath{\rho}}{\ensuremath{\rho}})|}_{\ensuremath{\xi}=0}$, where $N\ensuremath{\sim}70$. For example, this represents a drop of over 4 orders of magnitude for $\ensuremath{\xi}={10}^{3}$. This same value results in a dramatic 9 orders of magnitude weakening of the constraint on $\ensuremath{\lambda}$ according to our formula ${\ensuremath{\lambda}}_{\mathrm{constraint}|\ensuremath{\xi}g1}\ensuremath{\approx}48N{\ensuremath{\xi}}^{2}{\ensuremath{\lambda}}_{\mathrm{constraint}|\ensuremath{\xi}=0}$. Non-minimal coupling may thus provide a relatively simple solution to the long-standing problem of excessive density perturbations in inflationary models.
120674166
The Density Perturbation in the Chaotic Inflation with Non-Minimal Coupling
We formulate a method to rigorously evaluate the density perturbation amplitude in inflation models with non-canonical gravity. As a specific example but which contains essential features of non-canonical models, the density perturbation in the λφ^4 chaotic inflation model with non-minimal coupling ξRφ^2 is carefully investigated in terms of the Hamiltonian formalism for constrained systems. We utilize a particular conformal transformation under which the original system with a non-minimally coupled scalar field is transformed into one with a minimal coupling and derive a reduced Hamiltonian for scalar-type perturbations (which describe density perturbations) in which only the dynamical degrees of freedom are contained. We then evaluate the amplitude of density perturbations arising from vacuum fluctuations of the system. We find the amplitude in the conformally transformed metric exactly agrees with that in the original metric. Thus the result obtained in the previous papers by a rather crude approach is confirmed in a more rigorous manner; i.e., the constraint on λ is weakened if ξ is large.
9971796
Primordial spectral indices from generalized Einstein theories.
Primordial spectral indices are calculated to second order in slow-roll parameters for three closely related models of inflation, all of which contain a scalar field nonminimally coupled to the Ricci curvature scalar. In most cases, ${\mathit{n}}_{\mathit{s}}$ may be written as a function of the nonminimal curvature coupling strength \ensuremath{\xi} alone, with ${\mathit{n}}_{\mathit{s}}$(\ensuremath{\xi})\ensuremath{\le}1, although the constraints on \ensuremath{\xi} differ greatly between ``new inflation'' and ``chaotic inflation'' initial conditions. Under ``new inflation'' initial conditions, there are discrepancies between the values of ${\mathit{n}}_{\mathit{s}}$ as calculated in the Einstein frame and the Jordan frame. The sources for these discrepancies are addressed, and shown to have negligible effects on the numerical predictions for ${\mathit{n}}_{\mathit{s}}$. No such discrepancies affect the calculations under ``chaotic inflation'' initial conditions.
1982795
Primordial bispectrum from multifield inflation with nonminimal couplings
Realistic models of high-energy physics include multiple scalar fields. Renormalization requires that the fields have nonminimal couplings to the spacetime Ricci curvature scalar, and the couplings can be large at the energy scales of early-universe inflation. The nonminimal couplings induce a nontrivial field-space manifold in the Einstein frame, and they also yield an effective potential in the Einstein frame with nontrivial curvature. The ridges or bumps in the Einstein-frame potential can lead to primordial non-Gaussianities of observable magnitude. We develop a covariant formalism to study perturbations in such models and calculate the primordial bispectrum. As in previous studies of non-Gaussianities in multifield models, our results for the bispectrum depend sensitively on the fields’ initial conditions.
17488349
Multifield dynamics of Higgs inflation
Higgs inflation is a simple and elegant model in which early-universe inflation is driven by the Higgs sector of the Standard Model. The Higgs sector can support early-universe inflation if it has a large nonminimal coupling to the Ricci spacetime curvature scalar. At energies relevant to such an inflationary epoch, the Goldstone modes of the Higgs sector remain in the spectrum in renormalizable gauges, and hence their effects should be included in the model’s dynamics. We analyze the multifield dynamics of Higgs inflation and find that the multifield effects damp out rapidly after the onset of inflation, because of the gauge symmetry among the scalar fields in this model. Predictions from Higgs inflation for observable quantities, such as the spectral index of the power spectrum of primordial perturbations, therefore revert to their familiar single-field form, in excellent agreement with recent measurements. The methods we develop here may be applied to any multifield model with nonminimal couplings in which the N fields obey an SOðN Þ symmetry in field space.
14538522
Multifield inflation after Planck: the case for nonminimal couplings.
Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from Planck. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field attractor solution and predict values of the primordial spectral index and its running, the tensor-to-scalar ratio, and non-Gaussianities squarely in the observationally most-favored region. Such models can also amplify isocurvature perturbations, which could account for the low power recently observed in the cosmic microwave background power spectrum at low multipoles. Future measurements of primordial isocurvature perturbations could distinguish between the currently viable possibilities.
54016557
Multifield Inflation after Planck: Isocurvature Modes from Nonminimal Couplings
Recent measurements by the {\it Planck} experiment of the power spectrum of temperature anisotropies in the cosmic microwave background radiation (CMB) reveal a deficit of power in low multipoles compared to the predictions from best-fit $\Lambda$CDM cosmology. The low-$\ell$ anomaly may be explained by the presence of primordial isocurvature perturbations in addition to the usual adiabatic spectrum, and hence may provide the first robust evidence that early-universe inflation involved more than one scalar field. In this paper we explore the production of isocurvature perturbations in nonminimally coupled two-field inflation. We find that this class of models readily produces enough power in the isocurvature modes to account for the \emph{Planck} low-$\ell$ anomaly, while also providing excellent agreement with the other {\it Planck} results.
118443959
Non-minimal Inflationary Attractors
Recently we identified a new class of (super)conformally invariant theories which allow inflation even if the scalar potential is very steep in terms of the original conformal variables. Observational predictions of a broad class of such theories are nearly model-independent. In this paper we consider generalized versions of these models where the inflaton has a non-minimal coupling to gravity with a negative parameter ξ different from its conformal value -1/6. We show that these models exhibit attractor behavior. With even a slight increase of |ξ| from |ξ| = 0, predictions of these models for ns and r rapidly converge to their universal model-independent values corresponding to conformal coupling ξ = −1/6. These values of ns and r practically coincide with the corresponding values in the limit ξ → −∞.
51775719
Preheating after Multifield Inflation with Nonminimal Couplings, I: Covariant Formalism and Attractor Behavior
This is the first of a three-part series of papers, in which we study the preheating phase for multifield models of inflation involving nonminimal couplings. In this paper, we study the single-field attractor behavior that these models exhibit during inflation and quantify its strength and parameter dependence. We further demonstrate that the strong single-field attractor behavior persists after the end of inflation. Preheating in such models therefore generically avoids the "de-phasing" that typically affects multifield models with minimally coupled fields, allowing efficient transfer of energy from the oscillating inflaton condensate(s) to coupled perturbations across large portions of parameter space. We develop a doubly-covariant formalism for studying the preheating phase in such models and identify several features specific to multifield models with nonminimal couplings, including effects that arise from the nontrivial field-space manifold. In papers II and III, we apply this formalism to study how the amplification of adiabatic and isocurvature perturbations varies with parameters, highlighting several distinct regimes depending on the magnitude of the nonminimal couplings $\xi_I$.
56409483
On reaching the adiabatic limit in multi-field inflation
We calculate the scalar spectral index ns and the tensor-to-scalar ratio r in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account the coupling between the curvature and the isocurvature perturbations induced by the noncanonical form of the kinetic terms. This coupling enhances the curvature perturbation and suppresses the resulting tensor-to-scalar ratio to the per mille level even for values of the slow-roll parameter  ~ 0.01. Beyond these particular models, we emphasise that multifield models of inflation are a priori not predictive, unless one supplies a prescription for the post-inflationary era, or an adiabatic limit is reached before the end of inflation. We examine the conditions that enabled us to actually derive predictions in the models under study, by analysing the various contributions to the effective isocurvature mass in general two-field inflationary models. In particular, we point out a universal geometrical contribution that is important at the end of inflation, and which can be directly extracted from the inflationary Lagrangian, independently of a specific trajectory. Eventually, we point out that spectator fields can lead to oscillatory features in the time-dependent power spectra at the end of inflation. We demonstrate how these features can be model semi-analytically as well as the theoretical uncertainties they can entail.
51816008
Nonperturbative Dynamics Of Reheating After Inflation: A Review
Our understanding of the state of the universe between the end of inflation and big bang nucleosynthesis (BBN) is incomplete. The dynamics at the end of inflation are rich and a potential source of observational signatures. Reheating, the energy transfer between the inflaton and Standard Model fields (possibly through intermediaries) and their subsequent thermalization, can provide clues to how inflation fits in with known high-energy physics. We provide an overview of our current understanding of the nonperturbative, nonlinear dynamics at the end of inflation, some salient features of realistic particle physics models of reheating, and how the universe reaches a thermal state before BBN. In addition, we review the analytical and numerical tools available in the literature to study preheating and reheating and discuss potential observational signatures from this fascinating era.
119344828
Cosmological perturbation with two scalar fields in reheating after inflation
We investigate the cosmological perturbation of two-scalar field model during the reheating phase after inflation. Using the exact solution of the perturbation in long-wavelength limit, which is expressed in terms of the background quantities, we analyze the behavior of the metric perturbation. The oscillating inflaton field gives rise to the parametric resonance of the massless scalar field and this leads to the amplification of the iso-curvature mode of the metric perturbations.
18563494
General relativistic effects in preheating
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 effects on the Doppler peaks in the cosmic background radiation, primordial black hole formation, gravitational waves and nonthermal symmetry restoration.
119492414
Metric preheating and limitations of linearized gravity
Abstract During the preheating era after inflation, resonant amplification of quantum field fluctuations takes place. Recently it has become clear that this must be accompanied by resonant amplification of scalar metric fluctuations, since the two are united by Einstein's equations. Furthermore, this “metric preheating” enhances particle production, and leads to gravitational rescattering effects even at linear order . In multi-field models with strong preheating ( q ≫1), metric perturbations are driven non-linear, with the strongest amplification typically on super-Hubble scales ( k →0). This amplification is causal, being due to the super-Hubble coherence of the inflaton condensate, and is accompanied by resonant growth of entropy perturbations. The amplification invalidates the use of the linearized Einstein field equations, irrespective of the amount of fine-tuning of the initial conditions. This has serious implications on all scales – from large-angle cosmic microwave background (CMB) anisotropies to primordial black holes. We investigate the ( q , k ) parameter space in a two-field model, and introduce the time to non-linearity, t nl , as the timescale for the breakdown of the linearized Einstein equations. t nl is a robust indicator of resonance behavior, showing the fine structure in q and k that one expects from a quasi-Floquet system, and we argue that t nl is a suitable generalization of the static Floquet index in an expanding universe. Backreaction effects are expected to shut down the linear resonances, but cannot remove the existing amplification, which threatens the viability of strong preheating when confronted with the CMB. Mode–mode coupling and turbulence tend to re-establish scale invariance, but this process is limited by causality and for small k the primordial scale invariance of the spectrum may be destroyed. We discuss ways to escape the above conclusions, including secondary phases of inflation and preheating solely to fermions. The exclusion principle constrains the amplification of metric perturbations significantly. Finally we rank known classes of inflation from strongest (chaotic and strongly coupled hybrid inflation) to weakest (hidden sector, warm inflation), in terms of the distortion of the primordial spectrum due to these resonances in preheating.
11097333
Restoring the sting to metric preheating
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.
1896745
Parametric amplification of metric fluctuations during reheating in two field models
We study the parametric amplification of super-Hubble-scale scalar metric fluctuations at the end of inflation in some specific two-field models of inflation, a class of which is motivated by hybrid inflation. We demonstrate that there can indeed be a large growth of fluctuations due to parametric resonance and that this effect is not taken into account by the conventional theory of isocurvature perturbations. Scalar field interactions play a crucial role in this analysis. We discuss the conditions under which there can be nontrivial parametric resonance effects on large scales.
119431564
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.
118281084
Lattice calculation of non-Gaussianity from preheating
If light scalar fields are present at the end of inflation, their non-equilibrium dynamics such as parametric resonance or a phase transition can produce non-Gaussian density perturbations. We show how these perturbations can be calculated using non-linear lattice field theory simulations and the separate universe approximation. In the massless preheating model, we find that some parameter values are excluded while others lead to acceptable but observable levels of non-Gaussianity. This shows that preheating can be an important factor in assessing the viability of inflationary models.
11904087
Non-Gaussian curvature spikes from chaotic billiards in inflation preheating.
A new class of non-Gaussian curvature fluctuations zeta(pr)(x) identical with deltaN(chi(i)) arises from the postinflation preheating behavior of a noninflaton field chi(i). Its billiardlike chaotic dynamics imprints regular log-spaced narrow spikes in the number of preheating e-folds N(chi(i)). We perform highly accurate lattice simulations of supersymmetry-inspired quartic inflaton and coupling potentials in a separate-universe approximation to compute N(chi(i)) as a function of the (nearly homogeneous) initial condition chi(i). The superhorizon modes of chi(i)(x) result in positive spiky excursions in zeta(pr) and hence negative gravitational potential fluctuations added to the usual sign-independent inflaton-induced perturbations, observably manifested in large cosmic structures and as (polarized) temperature cosmic microwave background cold spots.
26978064
Anisotropies in the gravitational wave background from preheating.
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 χ coupled to the inflaton φ, with the only requisite that χ 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 light scalar fields. If future direct detection GW experiments are capable of detecting the GW produced by preheating, they should also be able to detect this effect. This could eventually provide a powerful way to distinguish between different inflationary and preheating scenarios.
118428943
Parametric Resonance of Entropy Perturbations in Massless Preheating
Here, we revisit the question of possible preheating of entropy modes in a two field model with a massless inflaton coupled to a matter scalar field. Using a perturbative approximation to the covariant method we demonstrate that there is indeed a parametric instability of the entropy mode which then at second order leads to exponential growth of the curvature fluctuation on super-Hubble scale. Back-reaction effects shut off the induced curvature fluctuations, but possibly not early enough to prevent phenomenological problems. This confirms previous results obtained using different methods and resolves a controversy in the literature.
206296275
Equation of State and Duration to Radiation Domination after Inflation.
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).
118753783
Parametric Resonance in the Early Universe - A Fitting Analysis
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.
119062126
Towards the theory of reheating after inflation
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.
15170152
Post-inflation reheating in an expanding universe.
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.
119410093
Geometric Reheating after Inflation
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.
119079568
Resonant particle production with non-minimally coupled scalar fields in preheating after inflation
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 $g \approx 1 \times 10^{-3}$.
28981295
Pseudostable bubbles.
The evolution of spherically symmetric unstable scalar field configurations (“bubbles”) is examined for both symmetric (SDWP) and asymmetric (ADWP) double-well potentials. Bubbles with initial static energies E0 ∼ Ecrit evolve into time-dependent, localized configurations which are very long-lived compared to characteristic time-scales in the models examined. The stability of these configurations is investigated and possible applications are briefly discussed.
119120003
Inflaton Fragmentation and Oscillon Formation in Three Dimensions
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.
119273766
Gravitational waves from oscillon preheating
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.
118343946
End of inflation, oscillons, and matter-antimatter asymmetry
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.
206296275
Equation of State and Duration to Radiation Domination after Inflation.
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).
119306205
Violent Preheating in Inflation with Nonminimal Coupling
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.
119109938
Gauge-preheating and the end of axion inflation
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.
119207802
Magnetogenesis from axion inflation
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.
15197337
Preheating with nonminimal kinetic terms.
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.
119189534
Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field
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.
15000467
Power-counting and the validity of the classical approximation during inflation
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.
17770084
Primordial perturbations from multifield inflation with nonminimal couplings
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.