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 $f_{\mathrm{NL}}{A}_{\zeta }^3$ that correspond to the two-point correlation function $⟨h_{\mathbf{k}}^{\lambda ,(3)}{h}_{{\mathbf{k}}^{\prime }}^{{\lambda }^{\prime },(2)}⟩$ 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 $f_{\mathrm{NL}}\in [-5,-1]$ 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 $-1\le f_{\mathrm{NL}}<0$.

Close

PrevNext

View figure in article

• Cosmological parameters
• Gravitational wave sources
• Gravitational waves
• Inflation