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Abstract:

We assess the usefulness of gradient-based samplers, such as the no-U-turn sampler (NUTS), by comparison with traditional Metropolis–Hastings (MH) algorithms, in tomographic 3 × 2 point analyses. Specifically, we use the Dark Energy Survey (DES) Year 1 data and a simulated dataset for the Large Synoptic Survey Telescope (LSST) survey as representative examples of these studies, containing a significant number of nuisance parameters (20 and 32, respectively) that affect the performance of rejection-based samplers. To do so, we implement a differentiable forward model using JAX-COSMO, and we use it to derive parameter constraints from both data sets using the NUTS algorithm implemented in NUMPYRO, and the Metropolis–Hastings algorithm as implemented in COBAYA. When quantified in terms of the number of effective number of samples taken per likelihood evaluation, we find a relative efficiency gain of O(10) in favour of NUTS. However, this efficiency is reduced to a factor ∼ 2 when quantified in terms of computational time, since we find the cost of the gradient computation (needed by NUTS) relative to the likelihood to be ∼ 4.5 times larger for both experiments. We validate these results making use of analytical multivariate distributions (a multivariate Gaussian and a Rosenbrock distribution) with increasing dimensionality. Based on these results, we conclude that gradient-based samplers such as NUTS can be leveraged to sample high-dimensional parameter spaces in Cosmology, although the efficiency improvement is relatively mild for moderate (O(50)) dimension numbers, typical of tomographic large-scale structure analyses.

Abstract:

<jats:title>Abstract</jats:title><jats:p>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 ℓ<jats:sub>max</jats:sub>=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<jats:monospace>Baccoemu</jats:monospace>. We find<jats:italic>S</jats:italic><jats:sub>8</jats:sub>≡<jats:italic>σ</jats:italic><jats:sub>8</jats:sub>√(Ω<jats:sub>m</jats:sub>/0.3) = 0.795<jats:sup>+0.015</jats:sup><jats:sub>-0.017</jats:sub>, in relatively good agreement with CMB constraints from<jats:italic>Planck</jats:italic>(less than ~1.8<jats:italic>σ</jats:italic>tension), although we obtain a low value of Ω<jats:sub>m</jats:sub>=0.212<jats:sup>+0.017</jats:sup><jats:sub>-0.032</jats:sub>, in tension with<jats:italic>Planck</jats:italic>at the ~3σ level. We show that this can be recast as an H<jats:sub>0</jats:sub>tension if one parametrises the amplitude of fluctuations and matter abundance in terms of variables without hidden dependence on H<jats:sub>0</jats:sub>. 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<jats:italic>ℓ</jats:italic>≲ 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.</jats:p>

Abstract:

We report the first detection, at very high significance (23⁢𝜎), of the cross-correlation between cosmic shear and the diffuse x-ray background, using data from the Dark Energy Survey and the ROSAT satellite. The x-ray cross-correlation signal is sensitive to the distribution of the surrounding gas in dark matter halos. This allows us to use our measurements to place constraints on key physical parameters that determine the impact of baryonic effects in the matter power spectrum. In particular, we determine the mass of halos in which feedback has expelled half of their gas content on average to be log_10⁡(M_c/M_⊙)=13.64⁢3+0.081−0.12 and the polytropic index of the gas to be Γ =1.23⁢1+0.015−0.011. This represents a first step in the direct use of x-ray cross-correlations to obtain improved constraints on cosmology and the physics of the intergalactic gas.