KiDS-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis

Abstract

We present the methodology for a joint cosmological analysis of weak gravitational lensing from the fourth data release of the ESO Kilo-Degree Survey (KiDS-1000) and galaxy clustering from the partially overlapping Baryon Oscillation Spectroscopic Survey (BOSS) and the 2-degree Field Lensing Survey (2dFLenS). Cross-correlations between BOSS and 2dFLenS galaxy positions and source galaxy ellipticities have been incorporated into the analysis, necessitating the development of a hybrid model of non-linear scales that blends perturbative and non-perturbative approaches, and an assessment of signal contributions by astrophysical effects. All weak lensing signals were measured consistently via Fourier-space statistics that are insensitive to the survey mask and display low levels of mode mixing. The calibration of photometric redshift distributions and multiplicative gravitational shear bias has been updated, and a more complete tally of residual calibration uncertainties was propagated into the likelihood. A dedicated suite of more than 20 000 mocks was used to assess the performance of covariance models and to quantify the impact of survey geometry and spatial variations of survey depth on signals and their errors. The sampling distributions for the likelihood and the χ2 goodness-of-fit statistic have been validated, with proposed changes for calculating the effective number of degrees of freedom. The prior volume was explicitly mapped, and a more conservative, wide top-hat prior on the key structure growth parameter S8 = σ8 (Ωm/0.3)1/2 was introduced. The prevalent custom of reporting S8 weak lensing constraints via point estimates derived from its marginal posterior is highlighted to be easily misinterpreted as yielding systematically low values of S8, and an alternative estimator and associated credible interval are proposed. Known systematic effects pertaining to weak lensing modelling and inference are shown to bias S8 by no more than 0.1 standard deviations, with the caveat that no conclusive validation data exist for models of intrinsic galaxy alignments. Compared to the previous KiDS analyses, S8 constraints are expected to improve by 20% for weak lensing alone and by 29% for the joint analysis.

Euclid: Impact of non-linear and baryonic feedback prescriptions on cosmological parameter estimation from weak lensing cosmic shear

“…Such an argument can be repeated for all the bins combinations and the multipoles thus explaining why the FoM is still dependent on the non-linear recipe even with these very conservative scale cuts, a result in agreement with what was discussed in Taylor et al (2018a). Therefore, in order to remove completely the dependence on the non-linear description from the analysis, different approaches are needed, for example using band powers rather than a C ( ) analysis (Joachimi et al 2021). The results of this paper have been obtained using both Fisher matrix and MCMC codes.…”

Cosmology from weak lensing alone and implications for the Hubble tension

“…not competitive with even current measurements. The conditional error on H 0 fixing all other parameters is 0.16%, 10 The dominant non-Gaussian contribution to the covariance of cosmic shear two-point functions is that from super-sample covariance (SSC; Takada & Hu 2013;Barreira et al 2018;Joachimi et al 2021). The SSC covariance can be approximated as a rank-1 update to the total covariance matrix (Lacasa & Grain 2019), with degradations to parameter constraints roughly determined by the alignment of the power spectrum response to a largescale density fluctuation with the response to the parameter of interest.…”

Geometry versus growth

“…Angular power spectra are not directly measurable from a restricted survey footprint. We employed band powers derived from angular correlation function measurements; see Joachimi et al (2021), van Uitert et al (2018, Schneider et al (2002) for a detailed description. Band powers can be modelled as linear functionals of the angular convergence power spectra,…”

“…for a band indexed by l, where the filter function W l EE is given by equation 26 of Joachimi et al (2021). The normalisation, N l , is defined such that the band powers trace 2 C κ ( ) at the logarithmic centre of the bin, N l = ln( up,l ) − ln( lo,l ) with up,l and lo,l defining the edges of the top-hat band selection function for the bin indexed by l. Here, we have assumed that the model does not predict any B-modes, and we will only use the E-mode band powers in our analysis.…”

“…The corresponding KiDS-1000 cosmic shear likelihood is publicly available in the KiDS Cosmology Analysis Pipeline 3 (KCAP) together with a MontePython interface 4 that wraps the KCAP functionality. This likelihood requires two additional astrophysical nuisance parameters: the amplitude of intrinsic galaxy alignments A IA and the baryonic feedback parameter A bary ; see Joachimi et al (2021) for further details. Furthermore, five additional nuisance parameters δ z allow for a shift of the mean of the redshift distribution in each tomographic bin within informative Gaussian prior set by the calibration procedure.…”