Deep Learning for Primordial $B$-mode Extraction

TL;DR

This work tackles the challenge of isolating primordial B-mode polarization by addressing secondary B modes, primarily lensing, through a deep-learning pipeline. It introduces ResUNet-CMB to simultaneously estimate distortion fields responsible for delensing and derotation, integrating these estimates into a likelihood-based r inference. The results show near-optimal, unbiased estimates of the tensor-to-scalar ratio r, with residuals matching an ideal iterative delensing benchmark within about 10% across multipoles, and robustness to different noise levels. Overall, the approach demonstrates a viable ML-driven pathway to significantly tighten constraints on primordial gravitational waves in upcoming CMB surveys.

Abstract

The search for primordial gravitational waves is a central goal of cosmic microwave background (CMB) surveys. Isolating the characteristic $B$-mode polarization signal sourced by primordial gravitational waves is challenging for several reasons: the amplitude of the signal is inherently small; astrophysical foregrounds produce $B$-mode polarization contaminating the signal; and secondary $B$-mode polarization fluctuations are produced via the conversion of $E$ modes. Current and future low-noise, multi-frequency observations enable sufficient precision to address the first two of these challenges such that secondary $B$ modes will become the bottleneck for improved constraints on the amplitude of primordial gravitational waves. The dominant source of secondary $B$-mode polarization is gravitational lensing by large scale structure. Various strategies have been developed to estimate the lensing deflection and to reverse its effects the CMB, thus reducing confusion from lensing $B$ modes in the search for primordial gravitational waves. However, a few complications remain. First, there may be additional sources of secondary $B$-mode polarization, for example from patchy reionization or from cosmic polarization rotation. Second, the statistics of delensed CMB maps can become complicated and non-Gaussian, especially when advanced lensing reconstruction techniques are applied. We previously demonstrated how a deep learning network, ResUNet-CMB, can provide nearly optimal simultaneous estimates of multiple sources of secondary $B$-mode polarization. In this paper, we show how deep learning can be applied to estimate and remove multiple sources of secondary $B$-mode polarization, and we further show how this technique can be used in a likelihood analysis to produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.

Figures (8)

• Figure 1: Modified ResUNet-CMB architecture with residual connections excluded for clarity. The network input tensor has a shape of $(256, 256, 2)$ which consists of the stacked ($Q^{\mathrm{obs}}$, $U^{\mathrm{obs}}$) CMB polarization maps. There are only two outputs in this architecture, ($\alpha^{\mathrm{biased}}$, $\kappa^{\mathrm{biased}}$) which come from the final batch normalization layers in their respective branches. The numbers on the side of each convolutional layer are the number of filters used for that layer. The numbers at the bottom of the front of the output batch normalization layers are the image size. Down-sampling by using a stride of 2.0 is done in the encoder phase instead of using pooling layers. (The graphic was made with publicly available code from https://github.com/HarisIqbal88/PlotNeuralNet.)
• Figure 2: Example $B$-mode polarization maps showing the progression of going from observed to delensed then derotated and delensed CMB maps. Delensing and derotation are performed on $(Q^{\mathrm{obs}}, U^{\mathrm{obs}})$ maps and converted to $B$ polarization for each step in this figure. One can see that the amplitude of the residual $B$-modes are reduced after an application of delensing and even further minimized after derotation. The effect of derotation is more visible in the polarization map with $r=0$.
• Figure 3: Averaged power spectra after three different steps in the secondary removal process (solid lines) and the estimated power from an ideal iterative procedure (dashed). Power spectra (solid lines) are calculated by averaging over 5000.0 simulated CMB maps of the noiseless prediction data set.
• Figure 4: Averaged power spectra of B-mode polarization maps for every stage of secondary anisotropy removal compared against the primordial and null ($r=0$) power spectra. Power spectra are from simulated CMB maps (prediction data set) with a tensor-to-scalar ratio of $r=0.1$. Power spectra are averaged over 5000.0 simulated CMB maps from the noiseless experiment. The $r=0$ spectrum is equivalent to the delensed and derotated spectrum from Fig. \ref{['fig:null_b_ps']} and is included for easing comparisons between the two figures.
• Figure 5: Histogram of all inferred $r$ values ($r=0.1$) from the 5000.0 likelihood predictions obtained from the noiseless data set shown at two stages of secondary removal: after delensing in coral and after delensing and derotation in cyan. Delensing provides significantly tighter constraints and derotation subsequently provides an additional small improvement. The estimates remain unbiased after each step in the procedure.