# Angpow: a software for the fast computation of accurate tomographic power spectra

## TL;DR

Angpow is a software tool designed to rapidly and accurately compute angular power spectra between redshift bins, facilitating cosmological analyses without relying on the Limber approximation, especially useful for large parameter space explorations.

## Contribution

This paper introduces Angpow, a novel software that efficiently computes angular power spectra using Chebyshev polynomial basis and Clenshaw-Curtis quadrature, improving over traditional methods.

## Key findings

- Angpow achieves fast computation of $C_\ell(z_1,z_2)$ spectra.
- It accurately handles auto and cross-correlations without Limber approximation.
- Validated results match other codes and demonstrate high performance.

## Abstract

The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular the matter power spectrum $P(k)$ brings information about the cosmological distance evolution and the galaxy clustering together. However the building of $P(k)$ from galaxy catalogues needs a cosmological model to convert angles on the sky and redshifts into distances, which leads to difficulties when comparing data with predicted $P(k)$ from other cosmological models, and for photometric surveys like LSST. The angular power spectrum $C_\ell(z_1,z_2)$ between two bins located at redshift $z_1$ and $z_2$ contains the same information than the matter power spectrum, is free from any cosmological assumption, but the prediction of $C_\ell(z_1,z_2)$ from $P(k)$ is a costly computation when performed exactly. The Angpow software aims at computing quickly and accurately the auto ($z_1=z_2$) and cross ($z_1 \neq z_2$) angular power spectra between redshift bins. We describe the developed algorithm, based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. We validate the results with other codes, and benchmark the performance. Angpow is flexible and can handle any user defined power spectra, transfer functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the $C_\ell(z_1,z_2)$ comparison with data. We emphasize that the Limber's approximation, often used to fasten the computation, gives wrong $C_\ell$ values for cross-correlations.