Towards forecasting cosmological constraints from velocity angular power spectrum of type Ia supernovae

Abstract

Galaxies’ peculiar velocities provide a powerful probe of cosmic structure growth through their correlations. However, measuring these velocities requires distance indicators. Type Ia supernovae (SNe Ia) serve as fundamental distance indicators due to their nature as standardizable candles, offering superior distance estimates compared to galaxy scaling relations, which have traditionally been used due to the limited number of detected SNe Ia. With the upcoming Rubin Observatory Legacy Survey of Space and Time (Rubin LSST) set to detect one million of SNe Ia, we have an opportunity to leverage them for peculiar velocity studies. Yet, current methods rely on 3D statistical estimators, which are ill-suited for Rubin LSST’s photometric data. Without a robust alternative, we risk failing to fully exploit Rubin LSST’s vast dataset for cosmic structure studies. To address this challenge, we investigate the application of angular power spectrum analysis to velocity fields. We examine the velocity-density field relationship, compute the velocity angular power spectrum, and compare it with existing literature. Due to computational challenges posed by highly oscillatory functions, we implement the Limber approximation—a calculation not previously applied to velocity fields. We find that while efficient at small angular scales, this approximation introduces significant errors at large scales, as expected. Additionally, we assess whether LSST’s large photometric sample could compensate for photometric redshift imprecision. Through the signal-to noise analysis, we demonstrate that precise redshift measurements are important to PV studies. This work represents a critical step toward enabling cosmological parameter forecasts using SNe Ia peculiar velocities in the Rubin LSST era.