Orateur
Description
We present our work towards a field-level inference (FLI) pipeline for the joint analysis of galaxy clustering and CMB lensing. We demonstrate an end-to-end Bayesian framework that jointly samples the posterior of the initial density field, galaxy bias and cosmological parameters ($\Omega_m$, $\sigma_8$). Our differentiable forward model propagates initial conditions through Lagrangian Perturbation Theory (2LPT), applies a Lagrangian bias expansion, and computes the CMB lensing convergence along the line of sight via the Born approximation. The joint likelihood combines galaxy number counts with the convergence map, incorporating the lensing reconstruction noise and analytically accounting, as a Gaussian variance that follows the cosmology, for the convergence the model does not generate (beyond the simulation volume and below its resolution). The high-dimensional posterior is explored efficiently with gradient-based sampling. Validated externally on a high-resolution N-body simulation, with $\Omega_m$ and $\sigma_8$ free, the joint posterior is consistent with the truth, and CMB lensing tightens the cosmological constraints relative to galaxies alone by breaking the degeneracy between the galaxy bias and $\sigma_8$, as expected from standard analyses. This work is a step towards a field level analysis of real data, combining DESI galaxies with CMB-lensing maps from Planck, ACT and the Simons Observatory.