Reconstructing Primordial Black Hole Power Spectra from Gravitational Waves

A novel methodology for analysing the relation between the energy density in gravitational waves and primordial power spectra is developed. Focusing on scalar-induced gravitational radiation, this methodology is applied to a number of scenarios for the primordial black hole formation. Being differed from conventional Bayesian approaches, its advantages include directness and computational efficiency, which are crucial for handling the complex data characteristic of gravitational wave research. As an important application, it is demonstrated that this methodology allows for the systematic reconstruction of power spectra across all scenarios using current pulsar timing array data, providing a clear example of its potential in gravitational wave analysis.