Stochastic Gravitational Waves from Modulated Reheating

TL;DR

The paper investigates whether a spectator field with Higgs-like couplings can source observable scalar-induced gravitational waves through modulated reheating in an $R^2$ inflation framework. It computes the spectator-driven curvature perturbation using the δN formalism and a stochastic de Sitter equilibrium for the spectator, then evaluates the second-order GW production via a convolution of the curvature power spectrum. The main finding is that the gravitational wave signal is generically too small unless the couplings are large, in which case detectability by future experiments like BBO/DECIGO is marginal and may clash with perturbativity and Planck non-Gaussianity bounds. The results highlight a tension between achieving sizable small-scale GWs and satisfying large-scale constraints, suggesting limited prospects for probing Higgs-like spectator physics through stochastic GWs in this framework, with caveats related to finite-volume effects and potential mean-field regimes.

Abstract

We investigate scalar-induced stochastic gravitational waves from adiabatic curvature perturbations sourced by a spectator field via the modulated reheating mechanism. We consider a spectator scalar with Higgs-like couplings and inflaton decay via shift symmetric dimension-five operators. The spectator is assumed to be in the Sitter vacuum and it sources blue-tilted, strongly non-Gaussian curvature perturbations which can dominate the spectrum on small scales $k \gg \rm{Mpc}^{-1}$. We find that the setup could generate a gravitational wave signal testable by surveys like BBO and DECIGO but only for large coupling values not expected in low-energy particle physics setups that can be perturbatively extrapolated up to the inflationary scale.

Figures (6)

• Figure 1: The spectator sourced power spectrum ${\cal P}_{\zeta_\chi}$ (left panels) and the gravitational wave density fraction today $\Omega_{\rm GW,0}$ sourced by it (right panels). Upper (lower) panels show results for the vector (fermion) decay channel for different values of the coupling $g$$(y_{\psi})$ and $\lambda = 10^{-5}$. In the upper (lower) panels $\xi=0.0266$ ($\xi = 0.0262$). The dashed lines (lowest curves) show the results for coupling values equal to the SM weak gauge coupling $g_1$ and the top Yukawa coupling $y_{\rm t}$ evaluated at $\mu = H$. The grey lines in the left panels show the inflaton sourced power spectrum ${\cal P}_{\zeta_\phi}$. The right panels also show the power-law integrated sensitivity curves with SNR $=1$ for $\mu$-Ares (grey dashed-dotted), BBO (red dashed), LISA (red solid), DECIGO (grey dashed), ET (blue), CE (blue dashed), and Ultimate DECIGO (red dashed-dotted).
• Figure 2: The top row shows the GW spectral density today at $f=0.15~{\rm Hz}$ as function of $\xi$ and $g$ for $\lambda=10^{-5},\,10^{-3},\,10^{-1}$ (from left to right). The bottom row shows the same as function of $\xi$ and $y_\psi$. The (conservative) non-Gaussianity bound $P_{\zeta_\chi}(k_*) < 10^{-12}$ is violated to the left of the grey dashed lines and in the white region $P_{\zeta_\chi}(k_*) > 5 \times 10^{-12}$. The white dotted lines show results for the SM coupling values as in Figure \ref{['fig:curves']}. The power-law integrated sensitivity curves with SNR $=1$ are shown for BBO (red dashed), DECIGO (grey dashed) and Ultimate DECIGO (red dashed-dotted).
• Figure 3: The function $\hat{I}(\kappa,\theta)$ in the bispectrum. Here $\kappa = k_2/k_1$, ${\rm cos}\theta = {\bf k}_1\cdot {\bf k}_2/(k_1 k_2)$ and the momenta are labelled such that $k_{3} \leqslant k_{1}\leqslant k_{2}$. We have set the non-minimal coupling $\xi = 0.01$ which corresponds to $\nu = 1.46$. Configurations in the white region do not satisfy the momentum conservation condition ${\bf k}_1+{\bf k}_2+{\bf k}_3=0$.
• Figure 4: The scale dependent non-linearity parameter $f_{\rm NL}$ shown as function of the ratio $\kappa = k_2/k_1$ and the angle $\theta$ between ${\bf k}_1$ and ${\bf k}_2$. The momenta are labelled such that $k_{3} \leqslant k_{1}\leqslant k_{2}$ and we have set $k_2 = 0.2 \, {\rm Mpc}^{-1}$. The other parameters are set as $\xi = 0.01$ ($\nu = 1.46$) and ${\cal P}_{\zeta_{\chi}}(k_*)/{\cal P}_{\zeta}(k_*) = 10^{-11}$ at $k_* =0.05\, {\rm Mpc}^{-1}$. Configurations in the white region do not satisfy the momentum conservation condition ${\bf k}_1+{\bf k}_2+{\bf k}_3=0$.
• Figure 5: The maximum value of the shape dependent non-linearity parameter $f^{\rm max}_{\rm NL}$ shown as function of $\xi$ and ${\cal P}_{\zeta_{\chi}}(k_*)$ where $k_* =0.05\, {\rm Mpc}^{-1}$. The hatched regions corresponds to $f^{\rm max}_{\rm NL} >4.2$ which is outside the $1\sigma$ region of Planck constraint on local non-Gaussianity $f^{\rm local}_{\rm NL} = -0.9 \pm 5.1$.