Imprints of Primordial Non-Gaussianity on Gravitational Wave Spectrum

Abstract: Although Cosmic Microwave Background and Large Scale Structure probe the largest scales of our universe with ever increasing precision, our knowledge about the smaller scales is still very limited other than the bounds on Primordial Black Holes. We show that the statistical properties of the small scale quantum fluctuations can be probed via the stochastic gravitational wave background, which is induced as the scalar modes re-enter the horizon. We found that even if scalar curvature fluctuations have a subdominant non-Gaussian component, these non-Gaussian perturbations can source a dominant portion of the induced GWs. Moreover, the GWs sourced by non-Gaussian scalar fluctuations peaks at a higher frequency and this can result in distinctive observational signatures. We found that the sensitive next-generation-interferometers, which will/could reach $\Omega_{GW}h^2 \sim 10^{-15}$ (such as PTA-SKA, LISA, DECIGO, BBO, CE, ET), can probe $f_{NL} \sim 0.5$ which is even better than the predictions of the next generation CMB experiments. If the induced GW background is detected, but not the signatures arising from the non-Gaussian component, $\zeta = \zeta_G + f_{\rm NL} \, \zeta_G^{2}$, this translates into bounds on $f_{\rm NL}$ depending on the amplitude and the width of the GW signal. If the induced GW background is not detected at all, this translates into bounds on scalar fluctuations. The results are independent from the fact that whether PBH are DM or completely negligible part of the current energy density.