Gravitational waves from a curvaton model with blue spectrum

TL;DR

This paper investigates gravitational waves generated at second order by blue-tilted curvature perturbations in curvaton models, focusing on quadratic and axion-like potentials. By combining inflaton and curvaton fluctuations to achieve COBE-scale normalization with a blue-tilted small-scale spectrum, it computes the induced GWB from scalar perturbations and from curvaton kinetic stress, exploring both subdominant and dominant curvaton energy density regimes. The results show that the scalar-induced GWB can reach detectable levels (up to ~10^{-10}–10^{-8} in Ω_GW) with a characteristic peak determined by curvaton decay or domination, and that future detectors like LISA, DECIGO/BBO, and SKA could probe these scenarios; the axion-like model can produce a plateau signature, while the kinetic-term contribution remains subdominant under current bounds. These findings provide a promising observational handle on curvaton dynamics, small-scale curvature perturbations, and possible PBH dark matter connections.

Abstract

We investigate the gravitational wave background induced by the first order scalar perturbations in the curvaton models. We consider the quadratic and axion-like curvaton potential which can generate the blue-tilted power spectrum of curvature perturbations on small scales and derive the maximal amount of gravitational wave background today. We find the power spectrum of the induced gravitational wave background has a characteristic peak at the frequency corresponding to the scale reentering the horizon at the curvaton decay, in the case where the curvaton does not dominate the energy density of the Universe. We also find the enhancement of the amount of the gravitational waves in the case where the curvaton dominates the energy density of the Universe. Such induced gravitational waves would be detectable by the future space-based gravitational wave detectors or pulsar timing observations.

Figures (7)

• Figure 1: The deviation from $\Phi' = 0$ defined via (\ref{['deviation']}) is shown. The horizontal axis shows $r(\eta)$. The solid red line and dashed green line correspond to the inflaton and the curvaton contributions respectively.
• Figure 2: The peak values of $\Omega_{\rm GW}$ in quadratic curvaton model are shown. The horizontal axises is the spectral index $n_\sigma$. We have taken $H_{\rm inf} = 3 \times 10^{-5}M_P$ (solid red), $10^{-5}M_P$ (dashed green) and $10^{-6}M_P$ (dotted blue), $r_D = 1$ (thick lines) and $r_D = 0.1$ (thin lines) in the left panel and $H_{\rm inf} = 3 \times 10^{-5}M_P$, $r_D = 10$ (solid red), $r_D = 100$ (dashed green) and $r_D = 1000$ (dotted blue) in the right panel.
• Figure 3: The peak values of $\Omega_{\rm GW}$ in quadratic curvaton model are shown. The horizontal axises is the wave number at peak $k_{\rm peak}$ or corresponding frequency. We have taken $H_{\rm inf} = 3 \times 10^{-5}M_P$ (solid red), $10^{-5}M_P$ (dashed green) and $10^{-6}M_P$ (dotted blue), $r_D = 1$ (thick lines) and $r_D = 0.1$ (thin lines) in the left panel and $H_{\rm inf} = 3 \times 10^{-5}M_P$, $r_D = 10$ (solid red), $r_D = 100$ (dashed green) and $r_D = 1000$ (dotted blue) in the right panel.
• Figure 4: The spectrum of $\Omega_{\rm GW}$ in the quadratic curvaton model is shown as the thick solid red line. We have taken $H_{\rm inf} = 3 \times 10^{-5}M_P$, $n_\sigma = 1.3$, $r_D = 1$ (left panel) and $r_D = 10$ (right panel). The thin solid red line represents the contribution from the primordial tensor metric perturbation. We also show the sensitivity curves of LISA (dashed green), DECIGO/BBO (dotted blue), ultimate-DECIGO (small dotted magenta) and the pulsar timing observation by SKA (dash dotted cyan). The dash double-dotted orange line correspond to the current upper limit from the pulsar timing.
• Figure 5: The peak values of $\Omega_{\rm GW}$ in terms of the spectral index $n_\sigma$ in axion-like curvaton model are shown. We have taken $k_f = 10^{10}~(10^{7})~{\rm Mpc^{-1}}$ for left (right) panel, $\kappa = 1$, $H_{\rm inf} = 3 \times 10^{-5}~M_P$ (solid red), $10^{-5}~M_P$ (dashed green) and $10^{-6}~M_P$ (dotted blue), $r_D = 1$ (thick lines) and $r_D = 0.1$ (thin lines). The dash dotted cyan line shows the upper bound from the PBH overproduction.