Reconstructing primordial black hole power spectra from gravitational waves

A novel methodology for analyzing the relation between the energy density in gravitational waves and
primordial power spectra is developed. Focusing on scalar-induced gravitational radiation, this method-
ology 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.