Abstract
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.
Highlights
On the other hand, the transition from the inflationary epoch to the hot big-bang, a radiation dominated epoch, is much less known
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
A similar idea was recently proposed in ref. [32], though we systematically examine a larger variety of potential types and classify them based on their small-field and large-field shape
Summary
We consider a canonical scalar field coupled minimally to gravity. The relevant action is given as. The scalar field satisfies the Klein-Gordon equation, φ + 2Hφ − φ = −a2 dV , dφ (2.2). Throughout this work primes represent derivatives with respect to conformal time η, and = δij∂i∂j is the spatial Laplacian. To remove the first time-derivative, we redefine the field as ψ = aφ, leading to a ψ − ψ−. The perturbed gravitational field hij satisfying hii = 0 = ∂ihij obeys the equation, hij + 2Hhij −. Where Mp−l2 = 8πG is the reduced Planck mass, Πij ≡ Tij − gij p is the anisotropic stress and p denotes the background homogeneous pressure. The superscript TT represents the transverse-traceless part of the anisotropic stress tensor. The details for the evaluation of the gravitational wave spectrum are given for completeness in appendix A.2
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