Probing non-Gaussianities with the high frequency tail of induced gravitational waves

Abstract

We investigate in detail the spectrum of gravitational waves induced by a peaked primordial curvature power spectrum generated in single field inflationary models. We argue that the $f_{\mathrm{NL}}$ parameter can be inferred by measuring the high frequency spectral tilt of the induced gravitational waves. We also show that the intrinsically non-Gaussian impact of $f_{\mathrm{NL}}$ in ${\Omega }_{\mathrm{GW}}$ is to broaden its peak, although at a negligible level in order not to overproduce primordial black holes. We discuss possible degeneracies in the high frequency spectral tilt between $f_{\mathrm{NL}}$ and a general equation of state of the universe $w$. Finally, we discuss the constraints on the amplitude, peak and slope (or equivalently, $f_{\mathrm{NL}}$) of the primordial power spectrum by combining current and future gravitational wave experiments with limits on $\mu$ distortions from the cosmic microwave background.

36 pages (17 main text + appendices), 5 figures. v2: references added. small changes. v3. one fig. added, final version. v4: found a minor typo in the kernel. Analytical approximations accordingly corrected

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