Isolating relativistic effects in large-scale structure

We present a fully relativistic calculation of the observed galaxy number counts in the linear regime. We show that besides the density fluctuations and redshift-space distortions, various relativistic effects contribute to observations at large scales. These effects all have the same physical origin: they result from the fact that our coordinate system, namely the galaxy redshift and the incoming photons' direction, is distorted by inhomogeneities in our universe. We then discuss the impact of the relativistic effects on the angular power spectrum and on the two-point correlation function in configuration space. We show that the latter is very well adapted to isolate the relativistic effects since it naturally makes use of the symmetries of the different contributions. In particular, we discuss how the Doppler effect and the gravitational redshift distortions can be isolated by looking for a dipole in the cross-correlation function between a bright and a faint population of galaxies.Comment: 26 pages, 7 figures. Invited contribution to a Classical and Quantum Gravity focus issue on "Relativistic Effects in Cosmology", edited by Kazuya Koyam

Three-point phase correlations: A new measure of non-linear large-scale structure

We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the non-linear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F_2, which governs the non-linear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a 1-sigma agreement for separations r<30 Mpc/h. Fitting formulae for the power spectrum and the non-linear coupling kernel at small scales allow us to extend our prediction into the strongly non-linear regime where we find a 1-sigma agreement with the simulations for r<2 Mpc/h. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the bias, in the regime where the bias is local and linear. Furthermore, the variance of the line correlation is independent of the Gaussian variance on the modulus of the density field. This suggests that the line correlation can probe more precisely the non-linear regime of gravity, with less contamination from the power spectrum variance.Comment: 11 pages, 5 figures. v2: replacement of the low resolution simulations, more precise quantification of the agreement with simulations, references added. Matches published version. Our code to calculate the line correlation is available at http://blue-shift.ch/phas

Measurement of the dipole in the cross-correlation function of galaxies

It is usually assumed that in the linear regime the two-point correlation function of galaxies contains only a monopole, quadrupole and hexadecapole. Looking at cross-correlations between different populations of galaxies, this turns out not to be the case. In particular, the cross-correlations between a bright and a faint population of galaxies contain also a dipole. In this paper we present the first attempt to measure this dipole. We discuss the four types of effects that contribute to the dipole: relativistic distortions, evolution effect, wide-angle effect and large-angle effect. We show that the first three contributions are intrinsic anti-symmetric contributions that do not depend on the choice of angle used to measure the dipole. On the other hand the large-angle effect appears only if the angle chosen to extract the dipole breaks the symmetry of the problem. We show that the relativistic distortions, the evolution effect and the wide-angle effect are too small to be detected in the LOWz and CMASS sample of the BOSS survey. On the other hand with a specific combination of angles we are able to measure the large-angle effect with high significance. We emphasise that this large-angle dipole does not contain new physical information, since it is just a geometrical combination of the monopole and the quadrupole. However this measurement, which is in excellent agreement with theoretical predictions, validates our method for extracting the dipole from the two-point correlation function and it opens the way to the detection of relativistic effects in future surveys like e.g. DESI.Comment: 15 pages, 17 figures. v2: 20 pages, 17 figures. Section IIIc partly rewritten, new section IIId, new figures 16 and 17. Main results unchanged. Matches published version in JCA

Optimising the measurement of relativistic distortions in large-scale structure

It has been shown recently that relativistic distortions generate a dipolar modulation in the two-point correlation function of galaxies. To measure this relativistic dipole it is necessary to cross-correlate different populations of galaxies with for example different luminosities or colours. In this paper, we construct an optimal estimator to measure the dipole with multiple populations. We show that this estimator increases the signal-to-noise of the dipole by up to 35 percent. Using 6 populations of galaxies, in a survey with halos and number densities similar to those of the millennium simulation, we forecast a cumulative signal-to-noise of 4.4. For the main galaxy sample of SDSS at low redshift z<0.2 our optimal estimator predicts a cumulative signal-to-noise of 2.4. Finally we forecast a cumulative signal-to-noise of 7.4 in the upcoming DESI survey. These forecasts indicate that with the appropriate choice of estimator the relativistic dipole should be detectable in current and future surveys.Comment: 20 pages, 8 figures. v2: 19 pages, 6 figures. Explicit derivation of the cancellation of the cosmic variance added. Some references added, minor changes to the text, main results unchanged. Matches version published in JCA