Angpow: a software for the fast computation of accurate tomographic power spectra
Abstract
Aims: The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular, the matter power spectrum P(k) provides information about the cosmological distance evolution and the galaxy clustering. However the building of P(k) from galaxy catalogs requires 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 the Large Synoptic Survey Telescope (LSST). The angular power spectrum C_{ℓ}(z_{1},z_{2}) between two bins located at redshift z_{1} and z_{2} contains the same information as the matter power spectrum, and is free from any cosmological assumption, but the prediction of C_{ℓ}(z_{1},z_{2}) from P(k) is a costly computation when performed precisely.
Methods: The Angpow software aims at quickly and accurately computing the auto (z_{1} = z_{2}) and cross (z_{1} ≠ z_{2}) angular power spectra between redshift bins. We describe the developed algorithm based on developments on the Chebyshev polynomial basis and on the ClenshawCurtis quadrature method. We validate the results with other codes, and benchmark the performance.
Results: Angpow is flexible and can handle any userdefined 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_{ℓ}(z_{1},z_{2}) comparison with data. We emphasize that the Limber's approximation, often used to speed up the computation, gives incorrect C_{ℓ} values for crosscorrelations.
The C++ code is available from https://gitlab.in2p3.fr/campagne/AngPow
 Publication:

Astronomy and Astrophysics
 Pub Date:
 June 2017
 DOI:
 10.1051/00046361/201730399
 arXiv:
 arXiv:1701.03592
 Bibcode:
 2017A&A...602A..72C
 Keywords:

 largescale structure of Universe;
 methods: numerical;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 Published in Astronomy &