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The recent stochastic signal observed jointly by NANOGrav, PPTA, EPTA, andCPTA can be accounted for by scalar-induced gravitational waves (SIGWs). Thesource of the SIGWs is from the primordial curvature perturbations, and themain contribution to the SIGWs is from the peak of the primordial curvaturepower spectrum. To effectively model this peak, we apply the Taylor expansionto parameterize it. With the Taylor expansion parameterization, we applyBayesian methods to constrain the primordial curvature power spectrum based onthe NANOGrav 15-year data set. The constraint on the primordial curvature powerspectrum possesses a degree of generality, as the Taylor expansion caneffectively approximate a wide range of function profiles.

Constraints on the Primordial Curvature Power Spectrum by Pulsar Timing Array Data: A Polynomial Parameterization Approach