New constraints on primordial non-Gaussianity from missing two-loop contributions of scalar induced gravitational waves

Abstract

We analyze the energy density spectrum of scalar induced gravitational waves (SIGWs) using the NANOGrav 15-year data set, thereby constraining the primordial non-Gaussian parameter ${f}_{\mathrm{NL}}$. For the first time, we calculate the seventeen missing two-loop diagrams proportional to ${f}_{\mathrm{NL}}{A}_{\ensuremath{\zeta}}^{3}$ that correspond to the two-point correlation function $⟨{h}_{\mathbf{k}}^{\ensuremath{\lambda},(3)}{h}_{{\mathbf{k}}^{\ensuremath{'}}}^{{\ensuremath{\lambda}}^{\ensuremath{'}},(2)}⟩$ for local-type primordial non-Gaussianity. The total energy density spectrum of SIGWs can be significantly suppressed by these two-loop diagrams. If SIGWs dominate the stochastic gravitational wave backgrounds observed in pulsar timing array experiments, the parameter interval ${f}_{\mathrm{NL}}\ensuremath{\in}[\ensuremath{-}5,\ensuremath{-}1]$ is notably excluded based on NANOGrav 15-year data set. After taking into account abundance of primordial black holes and the convergence of the cosmological perturbation expansion, we find that the only possible parameter range for ${f}_{\mathrm{NL}}$ might be $\ensuremath{-}1\ensuremath{\le}{f}_{\mathrm{NL}}<0$.