Constraining the inflaton potential with gravitational waves from oscillons

TL;DR

The paper investigates how oscillon formation after inflation can drive an early matter-dominated epoch and generate a strong second-order gravitational-wave signal during the rapid oscillon decay. By computing the induced GW spectrum from oscillon-number fluctuations and applying the bound on $\Delta N_{\rm eff}$ from BBN and the CMB, the authors translate GW constraints into bounds on the inflaton mass $m$ and self-interactions $g$ and $\lambda$ for several representative potentials (including $\alpha$-attractor T-model, axion monodromy, and hilltop forms). They show the GW peak typically lies at ultra-high frequencies around $f_{\rm peak}\sim 10^{7}$ Hz, which often lies beyond direct detection but provides a powerful probe of reheating physics and inflaton microphysics that are inaccessible to CMB observations. The results highlight the importance of post-inflationary dynamics for inflaton potentials and motivate further non-linear simulations and exploration of high-frequency GW detectors to fully exploit this signature.

Abstract

Under certain conditions, the oscillating inflaton condensate filling the Universe after inflation can fragment and form so-called oscillons. These long-lived soliton-like field configurations can dominate the Universe for several $e$-folds of expansion, leading to an early matter-dominated phase preceding the standard radiation era. In this paper we show how the rapid final decay of the oscillons leads to an enhanced production of induced gravitational waves, whose energy density can saturate the observational bound on the effective number of relativistic species. We leverage this bound to constrain the inflaton mass, cubic, and quartic self-coupling in generic models that admit oscillon formation, providing novel and complementary constraints in regions of parameter space that are inaccessible with cosmic microwave background observations alone.

Figures (5)

• Figure 1: Some representative examples of the potentials \ref{['eq:Tanh-potential', 'eq:Monodromy-potential', 'eq:Hilltop-potential']} for different values of $n$, $q$ and $p$, respectively. The dashed line marks the quadratic minimum in the two cases. For a few examples, we also mark the field values $\phi_*$ and $\phi_e$, corresponding to scales that exit the horizon $N_*$$e$-folds before the end of inflation (at $\phi_e$), with circles and stars, respectively. In order to fix $\phi_*$ and $\phi_e$ for illustration purposes, we chose $M=0.1M_{\rm Pl}$ for the T-model ($n=1$), and $M=2M_{\rm Pl}$ for the plateau ($q=-1$) and $p=6$ cases.
• Figure 2: The present day spectral energy density of gravitational waves $\Omega_{\rm GW,0}(f)$ induced after oscillon decay for some representative models. We fixed $\beta=0.8$ and two illustrative values of $M$ shown with solid and dashed curves, respectively. The horizontal red dashed line marks the (integrated) BBN bound on $\Delta N_{\rm eff}$, and the light gray curve indicates the projected sensitivity of resonant cavities Herman:2022fau.
• Figure 3: Here we show the allowed and excluded parameter space in the $(m,\lambda)$-plane for the symmetric potentials \ref{['eq:Tanh-potential', 'eq:Monodromy-potential']} ($\alpha$-attractor T-model and generalized monodromy), and in the $(m,g)$-plane for the asymmetric hilltop potential \ref{['eq:Hilltop-potential']}. Each line marks one specific model. The green shaded area is allowed parameter space, the red shaded region is ruled out by induced GW overproduction violating the BBN bound. The gray shaded area shows the forecasted constraint from next generation CMB missions ($r<10^{-3}$) and the hatched area marks the strong-coupling region where $\lambda>1$ and quantum backreaction has to be taken into account. We assume that oscillon formation becomes efficient at $M\lesssim0.05M_{\rm Pl}$Amin:2011hj. We fixed $\beta=0.8$ in all cases, and for the generalized monodromy model with $q=5,10$ we conservatively assumed the same lifetime as for $q=0$. Varying $\beta$ or the lifetime slightly shifts the boundary of the region ruled out by the BBN constraint. For the $\alpha$-attractor T-model we vary $N_*$ to show the range of variation within the observational errorbars, while for the other models we fix the central value from $Planck$ for $n_s$ and focus on the variation with the model parameters $q$ and $p$.
• Figure 4: Evolution of the gravitational potential $\Phi$ as a function of the number of $e$-folds since the time of oscillon formation, $N-N_{\rm f}$, with isocurvature initial conditions and for initial energy density fraction $\beta=0.8$. With solid lines we show the result of numerical integration of \ref{['eq:PhiEq', 'eq:SEq']} for two modes which are initially sub- ($k/k_{\rm f}=10^{3}$) and superhorizon ($k/k_{\rm f}=10^{-3}$). The initial conditions are set at the time of formation, $\Phi_{\rm f}=0$, and we fixed $S_{\rm f}=1$ for the plot. The dotted and dashed lines superimposed on the numerical solution represent the analytical approximations \ref{['eq:Phi_chi_Super']} and \ref{['eq:Phi_MD_Sub']} for the super- and subhorizon regimes, respectively. See how the potential is quickly generated on both scales and approaches the plateau value fast.
• Figure 5: The parameter space for the asymmetric hilltop potential \ref{['eq:Hilltop-potential']} in the $(m,\lambda)$ plane with the same specifications as in \ref{['fig:parameter_space']}. Note that $\lambda$ is negative and we plot the absolute value.