Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework

By F. V. D. Bosch, S. More, M. Cacciato, H. Mo, Xiaohu Yang. 2012

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We present a new method that simultaneously solves for cosmology and galaxy bias on non-linear scales. The method uses the halo model to analytically describe the (non-linear) matter distribution, and the conditional luminosity function (CLF) to specify the halo occupation statistics. For a given choice of cosmological parameters, this model can be used to predict the galaxy luminosity function, as well as the two-point correlation functions of galaxies, and the galaxy-galaxy lensing signal, both as a function of scale and luminosity. These observables have been reliably measured from the Sloan Digital Sky Survey. In this paper, the first in a series, we present the detailed, analytical model, which we test against mock galaxy redshift surveys constructed from high-resolution numerical N-body simulations. We demonstrate that our model, which includes scale dependence of the halo bias and a proper treatment of halo exclusion, reproduces the three-dimensional galaxy-galaxy correlation and the galaxy-matter cross-correlation (which can be projected to predict the observables) with an accuracy better than 10 (in most cases 5) per cent. Ignoring either of these effects, as is often done, results in systematic errors that easily exceed 40 per cent on scales of similar to 1 h(-1) Mpc, where the data are typically most accurate. Finally, since the projected correlation functions of galaxies are never obtained by integrating the redshift-space correlation function along the line of sight out to infinity, simply because the data only cover a finite volume, they are still affected by residual redshift-space distortions (RRSDs). Ignoring these, as done in numerous studies in the past, results in systematic errors that easily exceed 20 per cent on large scales (r(p) greater than or similar to 10 h(-1) Mpc). We show that it is fairly straightforward to correct for these RRSDs, to an accuracy better than similar to 2 per cent, using a mildly modified version of the linear Kaiser formalism.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bc64088b693ea1ef25be1e30340a16a85f89e3b1

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Citations in the corpus

Galaxy assembly bias: a significant source of systematic error in the galaxy–halo relationship (2013, methodology): “The two most widely used models of the galaxy-halo connection are the Halo Occupation Distribution (HOD, e.g., Berlind & Weinberg 2002; Zheng et al. 2005) and the Conditional Luminosity Function (CLF, e.g., Yang et al. 2003; van den Bosch et al. 2013).”
The first-year shear catalog of the Subaru Hyper Suprime-Cam Subaru Strategic Program Survey (2017, methodology): “We constrain a simple 5 parameter HOD (see e.g, White et al. 2011) based on the analytical modelling framework developed in van den Bosch et al. (2013)20.”
Mapping stellar content to dark matter haloes using galaxy clustering and galaxy–galaxy lensing in the SDSS DR7 (2015, methodology): “Furthermore, the HOD is potentially a powerful tool to constrain cosmology (Yoo et al. 2006; Zheng & Weinberg 2007; van den Bosch et al. 2013; Cacciato et al. 2013; More et al. 2014), by exploiting the average bias vs. mass relation of the dark matter halos revealed by the galaxies they contain.”
Intrinsic alignments of SDSS-III BOSS LOWZ sample galaxies (2014, methodology): “…a different redshift range, z ∈ [0.2, 0.4], (ii) use a smaller area DR9 sample, (iii) neglect redshift space distortions which can affect the large scale bias (see e.g., van den Bosch et al. 2013), and (iv) use a FKP weighting scheme which favourably weights the large bias high redshift galaxies.”
The DESI Experiment Part I: Science,Targeting, and Survey Design (2016, background): “variance [65]. But the search can be extended via spectroscopic detection of clusters and groups, along with galaxy halo occupation modeling, to measure the amplitude of clustering by halo abundances [66, 67]. The maps can also be correlated with weak lensing maps (e.g., from DES, LSST, Euclid, or C”
The Canadian Cluster Comparison Project: detailed study of systematics and updated weak lensing masses (2015, background): “The contribution from the clustering of haloes, the two-halo term, is in its most basic implementation proportional to the linear matter power spectrum (but see e.g. van den Bosch et al. 2013, for a more sophisticated implementation).”
hmcode-2020: improved modelling of non-linear cosmological power spectra with baryonic feedback (2020, background): “…2011; Philcox et al. 2020); lack of non-linear halo bias (e.g., Smith et al. 2007); missing halo exclusion (e.g., Cacciato et al. 2012; van den Bosch et al. 2013); assuming spherical haloes (Smith & Watts 2005); fixed halo properties at fixed mass (e.g., Giocoli et al. 2010); ignoring…”
The VIMOS Public Extragalactic Redshift Survey (VIPERS) - Galaxy clustering and redshift-space distortions at z ≃ 0.8 in the first data release (2013, methodology): “We follow the formalism of van den Bosch et al. (2013) to define the projected correlation in the context of this model.”
A 2.5 per cent measurement of the growth rate from small-scale redshift space clustering of SDSS-III CMASS galaxies (2014, background): “(5) πmax is traditionally chosen to be large (80 h−1 Mpc in this work) so that the sensitivity of wp to RSD is minimal (but see van den Bosch et al. 2013).”
Lensing is Low: Cosmology, Galaxy Formation, or New Physics? (2016, methodology): “Analytic HOD models may be able to marginalize over baryonic effects by allowing the concentration of the satellite distribution and the concentration of the parent dark matter halo to vary as free parameters (e.g. van den Bosch et al. 2013; Reddick et al. 2014).”
COSMOLIKE - cosmological likelihood analyses for photometric galaxy surveys (2016, methodology): “For the latter, we replace equation (9) by a HOD model (e.g. Berlind & Weinberg 2002; Zheng et al. 2005; van den Bosch et al. 2013), which describe the relation between galaxies and mass in terms of the probability that a halo of given mass contains Ng galaxies.”