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Register a new userCross-Correlation of spectroscopic and photometric galaxy surveys: cosmology from lensing and redshift distortions
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Cosmological galaxy surveys aim at mapping the largest volumes to test models with techniques such as cluster abundance, cosmic shear correlations or baryon acoustic oscillations (BAO), which are designed to be independent of galaxy bias. Here we explore an alternative route to constrain cosmology: sampling more moderate volumes with the cross-correlation of photometric and spectroscopic surveys. We consider the angular galaxy-galaxy autocorrelation in narrow redshift bins and its combination with different probes of weak gravitational lensing (WL) and redshift space distortions (RSD). Including the cross-correlation of these surveys improves by factors of a few the constraints on both the dark energy equation of state w(z) and the cosmic growth history, parametrized by gamma. The additional information comes from using many narrow redshift bins and from galaxy bias, which is measured both with WL probes and RSD, breaking degeneracies that are present when using each method separately. We show forecasts for a joint w(z) and gamma figure of merit using linear scales over a deep (i<24) photometric survey and a brighter (i<22.5) spectroscopic or very accurate (0.3%) photometric redshift survey. Magnification or shear in the photometric sample produce FoM that are of the same order of magnitude of those of RSD or BAO over the spectroscopic sample. However, the cross-correlation of these probes over the same area yields a FoM that is up to a factor 100 times larger. Magnification alone, without shape measurements, can also be used for these cross-correlations and can produce better results than using shear alone. For a spectroscopic follow-up survey strategy, measuring the spectra of the foreground lenses to perform this cross-correlation provides 5 times better FoM than targeting the higher redshift tail of the galaxy distribution to study BAO over a 2.5 times larger volume.
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Cosmic Microwave Background (CMB) is a powerful probe to study the early universe and various cosmological models. Weak gravitational lensing affects the CMB by changing its power spectrum, but meanwhile, it also carries information about the distribution of lensing mass and hence, the large scale structure (LSS) of the universe. When studies of the CMB is combined with the tracers of LSS, one can constrain cosmological models, models of LSS development and astrophysical parameters simultaneously. The main focus of this project is to study the cross-correlations between CMB lensing and the galaxy matter density to constrain the galaxy bias ($b$) and the amplitude scaling parameter ($A$), to test the validity of $Lambda$CDM model. We test our approach for simulations of the Planck CMB convergence field and galaxy density field, which mimics the density field of the Herschel Extragalactic Legacy Project (HELP). We use maximum likelihood method to constrain the parameters.
We outline how redshift-space distortions (RSD) can be measured from the angular correlation function w({theta}), of galaxies selected from photometric surveys. The natural degeneracy between RSD and galaxy bias can be minimized by comparing results from bins with top-hat galaxy selection in redshift, and bins based on the radial position of galaxy pair centres. This comparison can also be used to test the accuracy of the photometric redshifts. The presence of RSD will be clearly detectable with the next generation of photometric redshift surveys. We show that the Dark Energy Survey (DES) will be able to measure f(z){sigma}_8(z) to a 1{sigma} accuracy of (17 {times} b)%, using galaxies drawn from a single narrow redshift slice centered at z = 1. Here b is the linear bias, and f is the logarithmic rate of change of the linear growth rate with respect to the scale factor. Extending to measurements of w({theta}) for a series of bins of width 0.02(1 + z) over 0.5 < z < 1.4 will measure {gamma} to a 1{sigma} accuracy of 25%, given the model f = {Omega}_m(z)^{gamma}, and assuming a linear bias model that evolves such that b = 0.5 + z (and fixing other cosmological parameters). The accuracy of our analytic predictions is confirmed using mock catalogs drawn from simulations conducted by the MICE collaboration.
We investigate the impact of different observational effects affecting a precise and accurate measurement of the growth rate of fluctuations from the anisotropy of clustering in galaxy redshift surveys. We focus on redshift measurement errors, on the reconstruction of the underlying real-space clustering and on the apparent degeneracy existing with the geometrical distortions induced by the cosmology-dependent conversion of redshifts into distances. We use a suite of mock catalogues extracted from large N-body simulations, focusing on the analysis of intermediate, mildly non-linear scales and apply the standard linear dispersion model to fit the anisotropy of the observed correlation function. We verify that redshift errors up to ~0.2% have a negligible impact on the precision with which the specific growth rate beta can be measured. Larger redshift errors introduce a positive systematic error, which can be alleviated by adopting a Gaussian distribution function of pairwise velocities. This is, in any case, smaller than the systematic error of up to 10% due to the limitations of the linear dispersion model, which is studied in a separate paper. We then show that 50% of the statistical error budget on beta depends on the deprojection procedure through which the real-space correlation function is obtained. Finally, we demonstrate that the degeneracy with geometric distortions can in fact be circumvented. This is obtained through a modified version of the Alcock-Paczynski test in redshift-space, which successfully recovers the correct cosmology by searching for the solution that optimizes the description of dynamical redshift distortions. For a flat cosmology, we obtain largely independent, robust constraints on beta and OmegaM. In a volume of 2.4(Gpc/h)^3, the correct OmegaM is obtained with ~12% error and negligible bias, once the real-space correlation function is properly reconstructed.
We study the importance of gravitational lensing in the modelling of the number counts of galaxies. We confirm previous results for photometric surveys, showing that lensing cannot be neglected in a survey like LSST since it would infer a significant shift of cosmological parameters. For a spectroscopic survey like SKA2, we find that neglecting lensing in the monopole, quadrupole and hexadecapole of the correlation function also induces an important shift of parameters. For ${Lambda}$CDM parameters, the shift is moderate, of the order of 0.6${sigma}$ or less. However, for a model-independent analysis, that measures the growth rate of structure in each redshift bin, neglecting lensing introduces a shift of up to 2.3${sigma}$ at high redshift. Since the growth rate is directly used to test the theory of gravity, such a strong shift would wrongly be interpreted as the breakdown of General Relativity. This shows the importance of including lensing in the analysis of future surveys. On the other hand, for a survey like DESI, we find that lensing is not important, mainly due to the value of the magnification bias parameter of DESI, $s(z)$, which strongly reduces the lensing contribution at high redshift. We also propose a way of improving the analysis of spectroscopic surveys, by including the cross-correlations between different redshift bins (which is neglected in spectroscopic surveys) from the spectroscopic survey or from a different photometric sample. We show that including the cross-correlations in the SKA2 analysis does not improve the constraints. On the other hand replacing the cross-correlations from SKA2 by cross-correlations measured with LSST improves the constraints by 10 to 20 %. Interestingly, for ${Lambda}$CDM parameters, we find that LSST and SKA2 are highly complementary, since they are affected differently by degeneracies between parameters.
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(Omega_m,w,sigma_8)$ for an LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the $1sigma$ confidence interval in $(Omega_m,w)$ space by a factor of 8 with respect to the case of the single highest redshift bin. We also find that adding non-Gaussian information from the peak counts and higher-order moments of the convergence field and its spatial derivatives further reduces the constrained area in $(Omega_m,w)$ by a factor of 3 and 4, respectively. When we add cosmic microwave background parameter priors from Planck to our analysis, tomography improves power spectrum constraints by a factor of 3. Adding moments yields an improvement by an additional factor of 2, and adding both moments and peaks improves by almost a factor of 3, over power spectrum tomography alone. We evaluate the effect of uncorrected systematic photometric redshift errors on the parameter constraints. We find that different statistics lead to different bias directions in parameter space, suggesting the possibility of eliminating this bias via self-calibration.
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