Abstract

How much can we learn about Dark Energy and its equation of state from weak gravitational lensing surveys ? Two-point functions offer some insight but miss non-Gaussian information. Simulation-based inference (SBI) offers a way to combine and learn higher-order statistics via neural compression, but does not always a) leverage or b) exceed human domain knowledge in physical inference problems in terms of bits extracted from data, especially when simulations are large and limited in number. I will present an information-theoretic approach to illustrate SBI , which can be naturally extended to derive hybrid statistics, an optimal framework for combining domain knowledge and learned neural summaries. These statistics improve information extraction from the field-level compared to neural summaries alone or their concatenation to existing summaries and makes inference robust in settings with low training data. I will show an application of hybrid statistics for constraining wCDM from DES Y3 data. By changing the optimisation objective alone, the method is forecast to provide the most competitive Dark Energy and weak lensing parameter constraints to date. Furthermore, the modular nature of hybrid statistics may shed light on where non-Gaussian signatures of Dark Energy information might lie in weak lensing maps, to be exploited in upcoming Stage IV analyses.