Inflaton Oscillations Research Articles

Formation and decay of oscillons after inflation in the presence of an external coupling. Part I. Lattice simulations

We investigate the formation and decay of oscillons during the post-inflationary reheating epoch from inflaton oscillations around asymptotically flat potentials V(φ) in the presence of an external coupling of the form 1/2 g 2 φ 2 χ 2. It is well-known that in the absence of such an external coupling, the attractive self-interaction term in the potential leads to the formation of copious amounts of long-lived oscillons both for symmetric and asymmetric plateau potentials. We perform a detailed numerical analysis to study the formation of oscillons in the α-attractor E- and T-model potentials using the publicly available lattice simulation codeCosmoLattice. We observe the formation of nonlinear oscillon-like structures with the average equation of state ⟨wφ ⟩ ≃ 0 for a range of values of the inflaton self-coupling λ and the external coupling g 2. Our results demonstrate that oscillons form even in the presence of an external coupling and we determine the upper bound on g 2 which facilitates oscillon formation. We also find that eventually, these oscillons decay into the scalar inflaton radiation as well as into the quanta of the offspring field χ. Thus, we establish the possibility that reheating could have proceeded through the channel of oscillon decay, along with the usual decay of the oscillating inflaton condensate into χ particles. For a given value of the self-coupling λ, we notice that the lifetime of a population of oscillons decreases with an increase in the strength of the external coupling, following an (approximately) inverse power-law dependence on g 2.

Effective action approach for preheating

We present a semiclassical non-perturbative approach for calculating the preheating process at the end of inflation. Our method involves integrating out the decayed particles within the path integral framework and subsequently determining world-line instanton solutions in the effective action. This enables us to obtain the effective action of the inflaton, with its imaginary part linked to the phenomenon of particle creation driven by coherent inflaton field oscillations. Additionally, we utilize the Bogoliubov transformation to investigate the evolution of particle density within the medium after multiple inflaton oscillations. We apply our approach to various final state particles, including scalar fields, tachyonic fields, and gauge fields. The non-perturbative approach provides analytical results for preheating that are in accord with previous methods.

Dark matter production via a non-minimal coupling to gravity

We study postinflationary scalar dark matter production via its non-minimalcoupling to gravity. During the inflaton oscillation epoch, dark matter is producedresonantly for a sufficiently large non-minimal coupling ξ ≳ 5. We find thatbackreaction on the curvature and rescattering effects typically become important for thevalues of ξ above 30, which invalidate simple estimates of the productionefficiency. At large couplings, the dark matter yield becomes almost independent of ξ, signifying approximate quasi-equilibrium in the inflaton-dark matter system.Although the analysis gets complicated by the presence of apparent negative energy in theJordan frame, this behaviour can be regularized by introducing mild dark matterself-interaction. Using lattice simulations, we delineate parameter space leading to thecorrect dark matter relic abundance.

On gravitational preheating

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 Wilson coefficients, such operators can readily account for the correct dark matter abundance.

Implications of time-dependent inflaton decay on reheating and dark matter production

We discuss the production of radiation and dark matter assuming a time-dependent inflaton decay rate during the reheating period. It is shown that the time dependence of the inflaton decay rate can substantially modify the reheating dynamics. As an illustration, a leading interaction between the inflaton ϕ and the Higgs doublet h of the form ϕ|h|2 was adopted. In the presence of such interaction, the Higgs doublet acquires a ϕ-dependent mass which generates vacuum-expectation-value due to inflaton oscillations and breaks the Standard Model gauge symmetry. This leads to a time-dependent inflaton decay rate during the reheating period, and consequently, the production of radiation and dark matter during this period is modified. Regions of the parameter space that describe the observed value of the dark matter abundance were found and compared with the standard case when inflaton the decay rate is constant.

Gravitational production of dark matter during reheating

We consider the direct $s$-channel gravitational production of dark matter during the reheating process. Independent of the identity of the dark matter candidate or its non-gravitational interactions, the gravitational process is always present and provides a minimal production mechanism. During reheating, a thermal bath is quickly generated with a maximum temperature $T_{\rm max}$, and the temperature decreases as the inflaton continues to decay until the energy densities of radiation and inflaton oscillations are equal, at $T_{\rm RH}$. During these oscillations, $s$-channel gravitational production of dark matter occurs. We show that the abundance of dark matter (fermionic or scalar) depends primarily on the combination $T_{\rm max}^4/T_{\rm RH} M_P^3$. We find that a sufficient density of dark matter can be produced over a wide range of dark matter masses: from a GeV to a ZeV.

Inflaton oscillations and post-inflationary reheating

We analyze in detail the perturbative decay of the inflaton oscillating about a generic form of its potential V(ϕ) = ϕ k , taking into account the effects of non-instantaneous reheating. We show that evolution of the temperature as a function of the cosmological scale factor depends on the spin statistics of the final state decay products when k > 2. We also include the inflaton-induced mass of the final states leading to either kinematic suppression or enhancement if the final states are fermionic or bosonic respectively. We compute the maximum temperature reached after inflation, the subsequent evolution of the temperature and the final reheat temperature. We apply our results to the computation of the dark matter abundance through thermal scattering during reheating. We also provide an example based on supersymmetry for the coupling of the inflaton to matter.

Gravitational wave spectra from oscillon formation after inflation

We systematically investigate the preheating behavior of single field inflation with an oscillon-supporting potential. We compute both the properties of the emitted gravitational waves as well as the number density and characteristics of the produced oscillons. By performing numerical simulations for a variety of potential types, we divide the analyzed potentials in two families, each of them containing potentials with varying large- or small-field dependence. We find that the shape of the spectrum and the amplitude of emitted gravitational waves have a universal feature with the peak around the physical wavenumber k/a ∼ m at the inflaton oscillation starting period, irrespective of the exact potential shape. This can be used as a smoking-gun for deducing the existence of a violent preheating phase and possible oscillon formation after inflation. Despite this apparent universality, we also find differences in the shape of the spectrum of emitted gravitational waves between the two families of potentials, leading to discriminating features between them. In particular, all potentials show the emergence of a two-peak structure in the gravitational wave spectrum, arising at the time of oscillon formation. However, potentials that exhibit efficient parametric resonance tend to smear out this structure and by the end of the simulation the two-peak structure is replaced by one broad peak in the GW spectrum. We further compute the number density and properties of the produced oscillons for each potential choice, finding differences in the number density and size distribution of stable oscillons and transient overdensities. We also perform a linear fluctuation analysis and use the corresponding Floquet charts to relate the results of our simulations to the structure of parametric resonance for the various potential types. We find that the growth rate of the scalar perturbations and the associated oscillon formation time are sensitive to the small-field shape of a potential while the macroscopic physical properties of oscillons such as the total number depend on the large-field shape of a potential.

High-frequency graviton from inflaton oscillation

We point out that there is a high-frequency tail of the stochastic inflationary gravitational wave background that scales as f−1/2 with frequency f. This contribution comes from the graviton vacuum fluctuation amplified by the inflaton coherent oscillation during the reheating stage when the inflaton is weakly coupled and the perturbative reheating picture is valid. Although the signal is typically very small, such a high-frequency tail contains information on inflaton properties such as the inflaton mass as well as the thermal history of the early Universe.

On the violent preheating in the mixed Higgs-R2 inflationary model

It has been argued that the mixed Higgs-R2 model acts as the UV extension of the Higgs inflation, pushing up its cut-off scale in the vacuum close up to the Planck scale. In this letter, we study the inflaton oscillation stage after inflation, focusing on the effective mass of the phase direction of the Higgs field, which can cause a violent preheating process. We find that the “spikes” in the effective mass of the phase direction observed in the Higgs inflation still appear in the mixed Higgs-R2 model. While the spikes appear above the cut-off scale in the Higgs-only case, they appear below the cut-off scale when the model is extended with R2 term though reheating cannot be completed in the violent particle production regime since the spikes get milder.

Production of purely gravitational dark matter

In the purely gravitational dark matter scenario, the dark matter particle does not have any interaction except for gravitational one. We study the gravitational particle production of dark matter particle in such a minimal setup and show that correct amount of dark matter can be produced depending on the inflation model and the dark matter mass. In particular, we carefully evaluate the particle production rate from the transition epoch to the inflaton oscillation epoch in a realistic inflation model and point out that the gravitational particle production is efficient even if dark matter mass is much larger than the Hubble scale during inflation as long as it is smaller than the inflaton mass.

Toward an effective field theory approach to reheating

We investigate whether effective field theory (EFT) approaches, which have been useful in examining inflation and dark energy, can also be used to establish a systematic approach to inflationary reheating. We consider two methods. First, we extend Weinberg's background EFT to the end of inflation and reheating. We establish when parametric resonance and decay of the inflaton occurs, but also find intrinsic theoretical limitations, which make it difficult to capture some reheating models. This motivates us to next consider Cheung et al.'s EFT approach, which instead focuses on perturbations and the symmetry breaking induced by the cosmological background. Adapting the latter approach to reheating implies some new and important differences compared to the EFT of inflation. In particular, there are new hierarchical scales, and we must account for inflaton oscillations during reheating, which lead to discrete symmetry breaking. Guided by the fundamental symmetries, we construct the EFT of reheating, and as an example of its usefulness we establish a new class of reheating models and the corresponding predictions for gravity wave observations. In this paper we primarily focus on the first stages of preheating. We conclude by discussing challenges for the approach and future directions. This paper builds on ideas first proposed in the paper [O. Ozsoy, G. Sengor, K. Sinha, and S. Watson, arXiv:1507.06651.].

Note on reheating inGinflation

We study particle production at the end of inflation in kinetically driven G-inflation model and show that, in spite of the fact that there are no inflaton oscillations and hence no parametric resonance instabilities, the production of matter particles due to a coupling to the evolving inflaton field can be more efficient than pure gravitational Parker particle production.

Fate of electroweak vacuum during preheating

Our electroweak vacuum may be metastable in light of the current experimental data of the Higgs/top quark mass. If this is really the case, high-scale inflation models require a stabilization mechanism of our vacuum during inflation. A possible candidate is the Higgs-inflaton/-curvature coupling because it induces an additional mass term to the Higgs during the slow roll regime. However, after inflation, the additional mass term oscillates, and it can destabilize our electroweak vacuum via production of large Higgs fluctuations during the inflaton oscillation era. In this paper, we study whether or not the Higgs-inflaton/-curvature coupling can save our vacuum by properly taking account of Higgs production during the preheating stage. We put upper bounds on the Higgs-inflaton and -curvature couplings, and discuss possible dynamics that might relax them.

On adiabatic invariant in generalized Galileon theories

We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is useful in estimating the expansion law of the universe and also the particle production rate due to the oscillation of the Hubble parameter.

Shape of the inflaton potential and the efficiency of the universe heating

It is shown that the efficiency of the universe heating by an inflaton field depends not only on the possible presence of parametric resonance in the production of scalar particles but also strongly depends on the character of the inflaton approach to its mechanical equilibrium point. In particular, when the inflaton oscillations deviate from pure harmonic ones toward a succession of step functions, the production probability rises by several orders of magnitude. This in turn leads to a much higher temperature of the universe after the inflaton decay, in comparison to the harmonic case. An example of the inflaton potential is presented which creates a proper modification of the evolution of the inflaton toward equilibrium and does not destroy the nice features of inflation.

Gravitational effects on inflaton decay

We point out that the inflaton inevitably couples to all non-conformally coupled matters gravitationally through an oscillation in the Hubble parameter or the cosmic scale factor. It leads to particle production during the inflaton oscillation regime, which is most efficient just after inflation. Moreover, the analysis is extended to the model with non-minimal inflaton couplings to gravity, in which the Hubble parameter oscillates more violently. We apply our results to the graviton production by the inflaton: gravitons are also produced just after inflation, but the non-minimal coupling does not induce inflaton decay into the graviton pair.

Consistent generation of magnetic fields in axion inflation models

There has been a growing evidence for the existence of magnetic fields in the extra-galactic regions, while the attempt to associate their origin with the inflationary epoch alone has been found extremely challenging. We therefore take into account the consistent post-inflationary evolution of the magnetic fields that are originated from vacuum fluctuations during inflation. In the model of our interest, the electromagnetic (EM) field is coupled to a pseudo-scalar inflaton ϕ through the characteristic term ϕ F̃ F, breaking the conformal invariance. This interaction dynamically breaks the parity and enables a continuous production of only one of the polarization states of the EM field through tachyonic instability. The produced magnetic fields are thus helical. We find that the dominant contribution to the observed magnetic fields in this model comes from the modes that leave the horizon near the end of inflation, further enhanced by the tachyonic instability right after the end of inflation. The EM field is subsequently amplified by parametric resonance during the period of inflaton oscillation. Once the thermal plasma is formed (reheating), the produced helical magnetic fields undergo a turbulent process called inverse cascade, which shifts their peak correlation scales from smaller to larger scales. We consistently take all these effects into account within the regime where the perturbation of ϕ is negligible and obtain Beff ∼ 10−19 G, indicating the necessity of additional mechanisms to accommodate the observations.

On the breakdown of the curvature perturbation ζ during reheating

It is known that in single scalar field inflationary models the standard curvature perturbation ζ, which is supposedly conserved at superhorizon scales, diverges during reheating at times 0ϕ̇=, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge 0φ=, where φ denotes the inflaton perturbation, breaks down when 0ϕ̇=. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of ζ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation φ in the Hamiltonian formalism and gives a well behaved curvature perturbation ζ, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

UNCERTAINTY RELATIONS FOR COSMOLOGICAL PARTICLE CREATION AND EXISTENCE OF LARGE FLUCTUATIONS IN REHEATING

We derive an uncertainty relation for the energy density and pressure of a quantum scalar field in a time-dependent, homogeneous and isotropic, classical background, which implies the existence of large fluctuations comparable to their vacuum expectation values. A similar uncertainty relation is known to hold for the field square since the field can be viewed as a Gaussian random variable. We discuss possible implications of these results for the reheating process in scalar field driven inflationary models, where reheating is achieved by the decay of the coherently oscillating inflaton field. Specifically we argue that the evolution after backreaction can seriously be altered by the existence of these fluctuations. For example, in one model the coherence of the inflaton oscillations is found to be completely lost in a very short time after backreaction starts. Therefore we argue that entering a smooth phase in thermal equilibrium is questionable in such models and reheating might destroy the smoothness attained by inflation.