Finite distance effects on the Hellings-Downs curve in modified gravity
The study investigates how finite distance effects modify the Overlap Reduction Function (ORF) for subluminal gravitational waves in modified gravity theories. By reformulating harmonic coefficients using spherical Bessel functions, the authors find that approximations are valid only up to a cut-off at multipole numbers around $\ell \sim \sqrt{1 - v^2kL}$. This cut-off reconciles different analytical results with autocorrelation values, confirming the ORF remains finite for $v < 1$ and correctly approaches the expected limit as angular separation goes to zero.