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In cosmology, we routinely choose between models to describe our data, and can incur biases due to insufficient models or lose constraining power with overly complex models. In this paper, we propose an empirical approach to model selection that explicitly balances parameter bias against model complexity. Our method uses synthetic data to calibrate the relation between bias and the χ2 difference between models. This allows us to interpret χ2 values obtained from real data (even if catalogues are blinded) and choose a model accordingly. We apply our method to the problem of intrinsic alignments – one of the most significant weak lensing systematics, and a major contributor to the error budget in modern lensing surveys. Specifically, we consider the example of the Dark Energy Survey Year 3 (DES Y3), and compare the commonly used non-linear alignment (NLA) and tidal alignment and tidal torque (TATT) models. The models are calibrated against bias in the Ωm–S8 plane. Once noise is accounted for, we find that it is possible to set a threshold Δχ2 that guarantees an analysis using NLA is unbiased at some specified level Nσ and confidence level. By contrast, we find that theoretically defined thresholds (based on, e.g. p-values for χ2) tend to be overly optimistic, and do not reliably rule out cosmological biases up to ∼1–2σ. Considering the real DES Y3 cosmic shear results, based on the reported difference in χ2 from NLA and TATT analyses, we find a roughly $30{{\ \rm per\ cent}}$ chance that were NLA to be the fiducial model, the results would be biased (in the Ωm–S8 plane) by more than 0.3σ. More broadly, the method we propose here is simple and general, and requires a relatively low level of resources. We foresee applications to future analyses as a model selection tool in many contexts.

 

Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

 

ABSTRACT Galaxy intrinsic alignments (IAs) have long been recognized as a significant contaminant to weak lensing-based cosmological inference. In this paper we seek to quantify the impact of a common modelling assumption in analytic descriptions of IAs: that of spherically symmetric dark matter haloes. Understanding such effects is important as the current generation of IA models are known to be limited, particularly on small scales, and building an accurate theoretical description will be essential for fully exploiting the information in future lensing data. Our analysis is based on a catalogue of 113 560 galaxies between z = 0.06 and 1.00 from massiveblack-ii, a hydrodynamical simulation of box length $100 \, h^{-1}$ Mpc. We find satellite anisotropy contributes at the level of $\ge 30\!-\!40{{\ \rm per\ cent}}$ to the small-scale alignment correlation functions. At separations larger than $1 \, h^{-1}$ Mpc the impact is roughly scale independent, inducing a shift in the amplitude of the IA power spectra of $\sim 20{{\ \rm per\ cent}}$. These conclusions are consistent across the redshift range and between the massiveblack-ii and the illustris simulations. The cosmological implications of these results are tested using a simulated likelihood analysis. Synthetic cosmic shear data are constructed with the expected characteristics (depth, area, and number density) of a future LSST-like survey. Our results suggest that modelling alignments using a halo model based upon spherical symmetry could potentially induce cosmological parameter biases at the ∼1.5σ level for S8 and w. 

We present direct constraints on galaxy intrinsic alignments (IAs) using the Dark Energy Survey Year 3 (DES Y3), the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and its precursor, the Baryon Oscillation Spectroscopic Survey (BOSS). Our measurements incorporate photometric red sequence (redMaGiC) galaxies from DES with median redshift z ∼ 0.2–1.0, luminous red galaxies from eBOSS at z ∼ 0.8, and also an SDSS-III BOSS CMASS sample at z ∼ 0.5. We measure two-point IA correlations, which we fit using a model that includes lensing, magnification, and photometric redshift error. Fitting on scales 6 Mpc h−1 < rp < 70 Mpc h−1, we make a detection of IAs in each sample, at 5σ–22σ (assuming a simple one-parameter model for IAs). Using these red samples, we measure the IA–luminosity relation. Our results are statistically consistent with previous results, but offer a significant improvement in constraining power, particularly at low luminosity. With this improved precision, we see detectable dependence on colour between broadly defined red samples. It is likely that a more sophisticated approach than a binary red/blue split, which jointly considers colour and luminosity dependence in the IA signal, will be needed in future. We also compare the various signal components at the best-fitting point in parameter space for each sample, and find that magnification and lensing contribute $\sim 2\!-\!18~{{\ \rm per\ cent}}$ of the total signal. As precision continues to improve, it will certainly be necessary to account for these effects in future direct IA measurements. Finally, we make equivalent measurements on a sample of emission-line galaxies from eBOSS at z ∼ 0.8. We constrain the non-linear alignment amplitude to be $A_1=0.07^{+0.32}_{-0.42}$ (|A1| < 0.78 at 95 per cent CL).