The flat-sky approximation to galaxy number counts - redshift space correlation function

We study the flat-sky approximation for galaxy number counts including relativistic effects, and assess its performance and accuracy with respect to the full-sky result. We find an agreement of up to 5% for the local and lensing contributions to the 2-point correlation function and its multipoles at $z > 0.5$, and up to 1% for the multipoles alone at $z > 1$ and separations $\lesssim 250$ Mpc/$h$, with a speed-up of over a factor of 1000. Using a semi-analytic method, which has been implemented in a new version of the code COFFE, along with the Limber approximation for the integrated contributions, we further increase the performance, allowing the computation of the flat-sky multipoles to be done over 10000 times faster than in the full-sky calculation, which could be used to greatly speed-up Markov chain Monte Carlo sampling for cosmological parameter estimation.Comment: 32 pages, 8 figures. Code available at https://github.com/JCGoran/coff

COFFE: a code for the full-sky relativistic galaxy correlation function

We present a public version of the code COFFE (COrrelation Function Full-sky Estimator) available at https://github.com/JCGoran/coffe. The code computes the galaxy two-point correlation function and its multipoles in linear perturbation theory, including all relativistic and wide angle corrections. COFFE also calculates the covariance matrix for two physically relevant estimators of the correlation function multipoles. We illustrate the usefulness of our code by a simple but relevant example: a forecast of the detectability of the lensing signal in the multipoles of the two-point function. In particular, we show that lensing should be detectable in the multipoles of the two-point function, with a signal-to-noise larger than 10, in future surveys like Euclid or the SKA.Comment: Code available at https://github.com/JCGoran/coff

The 2-point Correlation Function of Galaxy Number Counts

This thesis investigates two important subjects in cosmology: the 2-point functions of the galaxy number counts, and the vorticity field of matter. In the first four chapters, we make a general treatment of the galaxy number counts, and discuss contributions to it using perturbation theory. These results are then used to construct the fully relativistic correlation function, which is valid beyond the flat-sky approximation. A publicly available code is provided for a fast and accurate numerical evaluation of the 2-point function and its multipoles, which allows us to make accurate and precise predictions on cosmological parameters from future and planned experiments. Lastly, we study the mechanism responsible for the fact that galaxies rotate, the vorticity field of matter, using numerical methods