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    In addition to the intrinsic clustering of galaxies themselves, the spatial distribution of galaxies observed in surveys is modulated by the presence of weak lensing due to matter in the foreground. This effect, known as magnification bias, is a significant contaminant to analyses of galaxy-lensing cross-correlations and must be carefully modelled. We present a method to estimate the magnification bias in spectroscopically confirmed galaxy samples based on finite differences of galaxy catalogues while marginalizing over errors due to finite step size. We use our estimator to measure the magnification biases of the CMASS and LOWZ samples in the SDSS BOSS galaxy survey, analytically taking into account the dependence on galaxy shape for fibre and PSF magnitudes, finding αCMASS = 2.71 ± 0.02 and αLOWZ = 2.45 ± 0.02 and quantify modelling uncertainties in these measurements. Finally, we quantify the redshift evolution of the magnification bias within the CMASS and LOWZ samples, finding a difference of up to a factor of three between the lower and upper redshift bounds for the former. We discuss how to account for this evolution in modelling and its interaction with commonly applied redshift-dependent weights. Our method should be readily applicable to upcoming surveys and we make our code publicly available as part of this work.

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  2. Abstract We present a new method for consistent, joint analysis of the pre- and post-reconstruction galaxy two-point functions of the BOSS survey. The post-reconstruction correlation function is used to accurately measure the distance-redshift relation and expansion history, while the pre-reconstruction power spectrum multipoles constrain the broad-band shape and the rate-of-growth of large-scale structure. Our technique uses Lagrangian perturbation theory to self-consistently work at the level of two-point functions, i.e. directly with the measured data, without approximating the constraints with summary statistics normalized by the drag scale. Combining galaxies across the full redshift range and both hemispheres we constrain Ω m  = 0.303 ± 0.0082, H 0  = 69.23 ± 0.77 and σ 8  = 0.733 ± 0.047 within the context of ΛCDM. These constraints are consistent both with the Planck primary CMB anisotropy data and recent cosmic shear surveys. 
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    We investigate the stochastic properties of typical red galaxy samples in a controlled numerical environment. We use halo occupation distribution (HOD) modelling to create mock realizations of three separate bright red galaxy samples consistent with data sets used for clustering and lensing analyses in modern galaxy surveys. Second-order Hybrid Effective Field Theory (HEFT) is used as a field-level forward model to describe the full statistical distribution of these tracer samples, and their stochastic power spectra are directly measured and compared to the Poisson shot-noise prediction. While all of the galaxy samples we consider are hosted within haloes with sub-Poisson stochasticity, we observe that the galaxy samples themselves possess stochasticities that range from sub-Poisson to super-Poisson, in agreement with predictions from the halo model. As an application of our methodology, we place priors on the expected degree of non-Poisson stochasticity in cosmological analyses using such samples. We expect these priors will be useful in reducing the complexity of the full parameter space for future analyses using second-order Lagrangian bias models. More generally, the techniques outlined here present the first application of HEFT methods to characterize models of the galaxy–halo connection at the field level, revealing new connections between once-disparate modelling frameworks.

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  4. Abstract The Lyα forest provides one of the best means of mapping large-scale structure at high redshift, including our tightest constraint on the distance-redshift relation before cosmic noon. We describe how the large-scale correlations in the Lyα forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, small-scale physics enters the predictions, the origin of the much-discussed velocity bias and the `renormalization' of the large-scale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peak-background split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the large-scale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from small-scale physics. 
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  5. ABSTRACT We implement a model for the two-point statistics of biased tracers that combines dark matter dynamics from N-body simulations with an analytic Lagrangian bias expansion. Using Aemulus, a suite of N-body simulations built for emulation of cosmological observables, we emulate the cosmology dependence of these non-linear spectra from redshifts z = 0 to z = 2. We quantify the accuracy of our emulation procedure, which is sub-per cent at $k=1\, h \,{\rm Mpc}^{-1}$ for the redshifts probed by upcoming surveys and improves at higher redshifts. We demonstrate its ability to describe the statistics of complex tracer samples, including those with assembly bias and baryonic effects, reliably fitting the clustering and lensing statistics of such samples at redshift z ≃ 0.4 to scales of $k_{\rm max} \approx 0.6\, h\,\mathrm{Mpc}^{-1}$. We show that the emulator can be used for unbiased cosmological parameter inference in simulated joint clustering and galaxy–galaxy lensing analyses with data drawn from an independent N-body simulation. These results indicate that our emulator is a promising tool that can be readily applied to the analysis of current and upcoming data sets from galaxy surveys. 
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  8. Abstract We use luminous red galaxies selected from the imaging surveys that are being used for targeting by the Dark Energy Spectroscopic Instrument (DESI) in combination with CMB lensing maps from the Planck collaboration to probe the amplitude of large-scale structure over 0.4 ≤  z  ≤ 1. Our galaxy sample, with an angular number density of approximately 500 deg -2 over 18,000 sq.deg., is divided into 4 tomographic bins by photometric redshift and the redshift distributions are calibrated using spectroscopy from DESI. We fit the galaxy autospectra and galaxy-convergence cross-spectra using models based on cosmological perturbation theory, restricting to large scales that are expected to be well described by such models. Within the context of ΛCDM, combining all 4 samples and using priors on the background cosmology from supernova and baryon acoustic oscillation measurements, we find S 8  = σ 8 (Ω m /0.3) 0.5  = 0.73 ± 0.03. This result is lower than the prediction of the ΛCDM model conditioned on the Planck data. Our data prefer a slower growth of structure at low redshift than the model predictions, though at only modest significance. 
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