PowerFull: fast and accurate computation of the relativistic angular galaxy power spectrum including local primordial non-Gaussianity

Abstract

Current and forthcoming wide-field galaxy surveys, such as SPHEREx and Euclid, provide a unique opportunity to probe the ultra-large scales of structure formation, where primordial non-Gaussianity, often parameterized by $f_\text{NL}$, is expected to leave its most detectable imprint. At the same time, these surveys inevitably enter regimes where relativistic and wide-angle effects become significant, requiring careful modeling to extract unbiased cosmological information. We address these challenges by applying the total-angular-momentum (TAM) formalism to describe redshift-space clustering beyond the flat-sky approximation. The standard Fourier-mode description, which characterizes distortions by the angle between a mode and a line of sight, becomes ill-defined over wide fields, whereas the TAM basis naturally separates radial and angular contributions and incorporates the relevant relativistic effects. Within this framework, we provide a new parameterization of wide-angle predictions that can be compared directly with survey data. We then introduce PowerFull, a modification of the Julia-based 2-FAST package, which enables efficient computation of the full relativistic angular power spectrum. Finally, using Fisher information matrix-based analyses, we show that a survey like SPHEREx reaches $\sigma(f_\text{NL}) \sim 1$, but that neglecting the relativistic and wide-angle contributions shifts the recovered $f_\text{NL}$ by an amount of order its own uncertainty: at this precision the inferred value is biased unless the clustering is modeled consistently.