2017/08/31 by Vittorio Tansella, Camille Bonvin, Ruth Durrer +2
Physics and Astronomy · #Astronomy and Astrophysical Research #Astrophysics #Correlation function (quantum field theory) #Cosmology and Gravitation Theories #Function (biology) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gravitational lens #Physics #Quantum mechanics #Redshift #Relativistic quantum chemistry #Sky #Spectral density #Statistics #Weak gravitational lensing #astro-ph.CO
paper · pdf · doi:10.1088/1475-7516/2018/03/019
published as JCAP 1803 (2018) 03, 019 · 49 pages, 19 figures. v2: minor corrections, references added, typos corrected in eqs. (2.3)-(2.6). Matches version published in JCAP
openalex created_date 2017/08/08 · openalex publication_date 2018/03/12 · arxiv created 2018/04/03 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/06
We derive an exact expression for the correlation function in redshift shells including all the relativistic contributions. This expression, which does not rely on the distant-observer or flat-sky approximation, is valid at all scales and includes both local relativistic corrections and integrated contributions, like gravitational lensing. We present two methods to calculate this correlation function, one which makes use of the angular power spectrum C ℓ ( z 1 , z 2 ) and a second method which evades the costly calculations of the angular power spectra. The correlation function is then used to define the power spectrum as its Fourier transform. In this work theoretical aspects of this procedure are presented, together with quantitative examples. In particular, we show that gravitational lensing modifies the multipoles of the correlation function and of the power spectrum by a few percent at redshift z =1 and by up to 30% and more at z =2. We also point out that large-scale relativistic effects and wide-angle corrections generate contributions of the same order of magnitude and have consequently to be treated in conjunction. These corrections are particularly important at small redshift, z =0.1, where they can reach 10%. This means in particular that a flat-sky treatment of relativistic effects, using for example the power spectrum, is not consistent.