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Abstract:

The past few years have seen the emergence of a wide array of novel techniques for analyzing high-precision data from upcoming galaxy surveys, which aim to extend the statistical analysis of galaxy clustering data beyond the linear regime and the canonical two-point (2pt) statistics. We test and benchmark some of these new techniques in a community data challenge named “Beyond-2pt,” initiated during the Aspen 2022 Summer Program “Large-Scale Structure Cosmology beyond 2-Point Statistics,” whose first round of results we present here. The challenge data set consists of high-precision mock galaxy catalogs for clustering in real space, in redshift space, and on a light cone. Participants in the challenge have developed end-to-end pipelines to analyze mock catalogs and extract unknown (“masked”) cosmological parameters of the underlying ΛCDM models with their methods. The methods represented are density-split clustering, nearest neighbor statistics, BACCO power spectrum emulator, void statistics, LEFTfield field-level inference using effective field theory (EFT), and joint power spectrum and bispectrum analyses using both EFT and simulation-based inference. In this work, we review the results of the challenge, focusing on problems solved, lessons learned, and future research needed to perfect the emerging beyond-2pt approaches. The unbiased parameter recovery demonstrated in this challenge by multiple statistics and the associated modeling and inference frameworks supports the credibility of cosmology constraints from these methods. The challenge data set is publicly available, and we welcome future submissions from methods that are not yet represented.

Abstract:

We present a cosmological analysis of the combination of the DES-Y3, KiDS-1000 and HSC-DR1 weak lensing samples under a joint harmonic-space pipeline making use of angular scales down to ℓmax=4500, corresponding to significantly smaller scales (δθ ~ 2.4') than those commonly used in cosmological weak lensing studies. We are able to do so by accurately modelling non-linearities and the impact of baryonic effects using Baccoemu. We find S 8 ≡ σ 8√(Ωm/0.3) = 0.795+0.015 -0.017, in relatively good agreement with CMB constraints from Planck (less than ~1.8σ tension), although we obtain a low value of Ωm =0.212+0.017 -0.032, in tension with Planck at the ~3σ level. We show that this can be recast as an H0 tension if one parametrises the amplitude of fluctuations and matter abundance in terms of variables without hidden dependence on H0. Furthermore, we find that this tension reduces significantly after including a prior on the distance-redshift relationship from BAO data, without worsening the fit. In terms of baryonic effects, we show that failing to model and marginalise over them on scales ℓ ≲ 2000 does not significantly affect the posterior constraints for DES-Y3 and KiDS-1000, but has a mild effect on deeper samples, such as HSC-DR1. This is in agreement with our ability to only mildly constrain the parameters of the Baryon Correction Model with these data.

Abstract:

Context. Computing the matter power spectrum, P(k), as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used.

Aims. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert A_s to σ₈ given the other cosmological parameters.

Methods. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and σ₈. We learn the ratio between an existing low-accuracy fitting function for P(k) and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation.

Results. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between k = 9 &�پ������; 10⁻³ &�����Գܲ�; 9 h M�賦⁻¹ and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than CAMB and 36 times faster than the neural network based matter power spectrum emulator BACCO. We also provide a simple analytic approximation for σ₈ with a similar accuracy, with a root mean squared fractional error of just 0.1% when evaluated across the same range of cosmologies. This function is easily invertible to obtain A_s as a function of σ₈ and the other cosmological parameters, if preferred.

Conclusions. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.