Bayesian forward modelling of cosmic shear data

Abstract

We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer physically plausible cosmic structures, which accounts for the non-Gaussian features of the gravitationally evolved matter distribution and light-cone effects. We test and validate our framework with realistic simulated shear data, demonstrating that the method recovers the unbiased matter distribution and the correct lensing and matter power spectrum. While the cosmology is fixed in this test, and the method employs a prior power spectrum, we demonstrate that the lensing results are sensitive to the true power spectrum when this differs from the prior. In this case, the density field samples are generated with a power spectrum that deviates from the prior, and the method recovers the true lensing power spectrum. The method also recovers the matter power spectrum across the sky, but as currently implemented, it cannot determine the radial power since isotropy is not imposed. In summary, our method provides physically plausible inference of the dark matter distribution from cosmic shear data, allowing us to extract information beyond the two-point statistics and exploiting the full information content of the cosmological fields.

Reconstructing dark matter distribution with peculiar velocities: Bayesian forward modelling with corrections for inhomogeneous Malmquist bias

“…The use of the non-linear velocity field using can also potentially break the 𝑓 𝜎 8 degeneracy through the non-linearities. This feature was already noted in the context of weak lensing by using a forward model based on Lagrangian Perturbation theory within the framework for mock weak lensing data (Porqueres et al 2021a).…”

Optimal machine-driven acquisition of future cosmological data

“…Recent extensions to the Borg framework have led to substantial improvements in cosmological parameter inference (Kodi Ramanah et al 2019;Elsner et al 2020;Schmidt et al 2020), Lyman-α (Porqueres et al 2019a(Porqueres et al , 2020 and cosmic shear (Porqueres et al 2021) reconstructions, with the field-level treatment transcending the capabilities of conventional cosmological analyses. Novel sophisticated additions to the forward model include a robust likelihood to account for unknown foreground contamination and systematics (Porqueres et al 2019b) and machine learning-based galaxy bias models (Charnock et al 2020).…”

“…Therefore, the inference carried out in previous studies by Jasche & Wandelt (2013), , transcends the limitations of contemporary analyses based on statistical summaries in order to yield detailed characterizations of individual 3D structures. Presently, apart from our framework, several research groups are developing the technology to perform full 3D characterizations of the cosmic structures probed by galaxy surveys (Wang et al 2014;Modi et al 2018;Kitaura et al 2021;Porqueres et al 2020Porqueres et al , 2021.…”

KaRMMa -- Kappa Reconstruction for Mass Mapping

“…Some of these proposed techniques include Wiener filtering (Jeffrey et al 2018), sparsity priors (Leonard et al 2014;Price et al 2019;Jeffrey et al 2018), null B-mode priors (Jeffrey et al 2021), and others (Pires et al 2020;Starck et al 2021). More advanced Bayesian methods aim to forward model the shear field by modeling the initial density field, which is then non-linearly evolved and integrated along the line of sight (Jasche & Wandelt 2013;Porqueres et al 2021). Lastly, machine learning-based methods have also been demonstrated to effectively recover the convergence field (Shirasaki et al 2019;Jeffrey et al 2020a;Hong et al 2021).…”

“…While we believe that the most physically correct approach to reconstructing the convergence field relies on simulation-based forward modeling (as advocated for instance in Porqueres et al 2021), there is still significant value in the development of fast, approximate reconstruction schemes. Specifically, approximate reconstruction methods can be used to study how to incorporate systematics in the forward modeling approach within a much simplified and significantly more numerically efficient framework.…”