Beecroft Institute for Particle Astrophysics and Cosmology

Abstract:

Optimal extraction of cosmological information from observations of the cosmic microwave background (CMB) critically relies on our ability to accurately undo the distortions caused by weak gravitational lensing. In this work, we demonstrate the use of denoising diffusion models in performing Bayesian lensing reconstruction. We show that score-based generative models can produce accurate, uncorrelated samples from the CMB lensing convergence map posterior, given noisy CMB observations. To validate our approach, we compare the samples of our model to those obtained using established Hamiltonian Monte Carlo methods, which assume a Gaussian lensing potential. We then go beyond this assumption of Gaussianity, and train and validate our model on non-Gaussian lensing data, obtained by ray-tracing N-body simulations. We demonstrate that in this case, samples from our model have accurate non-Gaussian statistics beyond the power spectrum. The method provides an avenue towards more efficient and accurate lensing reconstruction, which does not rely on an approximate analytical description of the posterior probability. The reconstructed lensing maps can be used as an unbiased tracer of the matter distribution, and to improve delensing of the CMB, resulting in more precise cosmological parameter inference.

Abstract:

The Simons Observatory (SO), due to start full science operations in early 2025, aims to set tight constraints on inflationary physics by inferring the tensor-to-scalar ratio 𝑟 from measurements of cosmic microwave background (CMB) polarization 𝐵-modes. Its nominal design including three small-aperture telescopes (SATs) targets a precision 𝜎⁡(𝑟=0)≤0.003 without delensing. Achieving this goal and further reducing uncertainties requires a thorough understanding and mitigation of other large-scale 𝐵-mode sources such as Galactic foregrounds and weak gravitational lensing. We present an analysis pipeline aiming to estimate 𝑟 by including delensing within a cross-spectral likelihood, and demonstrate it for the first time on SO-like simulations accounting for various levels of foreground complexity, inhomogeneous noise and partial sky coverage. As introduced in an earlier SO delensing paper, lensing 𝐵-modes are synthesized using internal CMB lensing reconstructions as well as Planck-like cosmic infrared background maps and LSST-like galaxy density maps. We then extend SO’s power-spectrum-based foreground-cleaning algorithm to include all auto- and cross-spectra between the lensing template and the SAT 𝐵-modes in the likelihood function. This allows us to constrain 𝑟 and the parameters of our foreground model simultaneously. Within this framework, we demonstrate the equivalence of map-based and cross-spectral delensing and use it to motivate an optimized pixel-weighting scheme for power spectrum estimation. We start by validating our pipeline in the simplistic case of uniform foreground spectral energy distributions. In the absence of primordial 𝐵-modes, we find that the 1⁢𝜎 statistical uncertainty on 𝑟, 𝜎⁡(𝑟), decreases by 37% as a result of delensing. Tensor modes at the level of 𝑟=0.01 are successfully detected by our pipeline. Even when using more realistic foreground models including spatial variations in the dust and synchrotron spectral properties, we obtain unbiased estimates of 𝑟 both with and without delensing by employing the moment-expansion method. In this case, uncertainties are increased due to the higher number of model parameters, and delensing-related improvements range between 27% and 31%. These results constitute the first realistic assessment of the delensing performance at SO’s nominal sensitivity level.