An Auto-Differentiable Likelihood Pipeline for the Cross-Correlation of CMB and Large-Scale Structure due to the Kinetic Sunyaev-Zeldovich Effect

We develop an optimization-based maximum likelihood approach to analyze the cross-correlation of the Cosmic Microwave Background (CMB) and large-scale structure induced by the kinetic Sunyaev-Zeldovich (kSZ) effect. Our main goal is to reconstruct the radial velocity field of the universe. While the existing quadratic estimator (QE) is statistically optimal for current and near-term experiments, the likelihood can extract more signal-to-noise in the future. Our likelihood formulation has further advantages over the QE, such as the possibility of jointly fitting cosmological and astrophysical parameters and the possibility of unifying several different kSZ analyses. We implement an auto-differentiable likelihood pipeline in JAX, which is computationally tractable for a realistic survey size and resolution, and evaluate it on the Agora simulation. We also implement a machine learning-based estimate of the electron density given an observed galaxy distribution, which can increase the signal-to-noise for both the QE and the likelihood method.