Discreteness Effects in the Post-Reconstruction Galaxy Power Spectrum

Recent studies have increasingly recognized the value of analyzing the post-reconstruction galaxy power spectrum for investigations into redshift space distortion (RSD) effects. In this paper, we present a novel theoretical model for the post-reconstruction galaxy power spectrum, designed for RSD analyses. In particular, we emphasize the importance of accounting for discrete effects arising from the reconstruction displacement vector, which have been overlooked. We specifically calculate these discrete effects, i.e., shot noise terms, within the framework of standard perturbation theory at the 1-loop level. In addition, we adopt a formulation that accounts for infrared (IR) effects to accurately model the non-linear damping of the Baryon Acoustic Oscillation (BAO) signal. Our model comprehensively integrates key physical phenomena relevant to the post-reconstruction galaxy power spectrum, such as gravitational non-linearities, RSD effects, bias effects, reconstruction effects, reconstruction-specific shot-noise effects, and the non-linear damping of the reconstructed BAO signal, thereby making it applicable to post-reconstruction RSD analyses.