Delensing CMB B-modes using galaxy surveys: the effect of galaxy bias and matter clustering non-linearities

Abstract

The B-mode of polarization of the CMB is a uniquely powerful probe of gravitational waves produced in the very early Universe. But searches for primordial B-mode anisotropies must contend with gravitational lensing, which induces late-time B-modes not associated with gravitational waves. These lensing B-modes can be removed -- i.e., delensed -- using observations of the E-modes and a proxy of the matter fluctuations along the line of sight that caused the deflections. The number density and redshift reach of galaxy surveys such as the upcoming Rubin observatory offer attractive prospects for using them to delens B-mode data from CMB experiments such as the Simons Observatory, LiteBIRD or CMB-S4. However, stochasticity and non-linear galaxy bias may in principle decorrelate the galaxy field from the matter distribution responsible for the lensing effect, thus hindering efforts to delens B-modes. In addition, non-linear gravitational evolution and bias introduce non-Gaussianities in the large-scale structure which further complicate the modelling. We quantify these effects by populating an N-body simulation with a magnitude-limited, photometric sample of galaxies similar to Rubin's gold selection, and using them to delens CMB maps lensed by the same matter distribution. We find that pipelines that treat the galaxy overdensity as a Gaussian field will incur negligible bias on the inferred tensor-to-scalar ratio, r. Moreover, we show that even in a highly conservative scenario where only the linear bias of the galaxies can be determined, the bias on r arising from this simplification is well within statistical uncertainties for a cosmic-variance limited scenario where Rubin-like galaxies are used for delensing.

Figures (8)

• Figure 1: Projection kernels for the galaxy overdensity (solid) and CMB lensing (dashed, rescaled to match the amplitude of the galaxy kernels). The solid, dark blue curve shows the lump-sum of all the galaxies into a single bin, while the solid black curve shows the kernel for the optimal combination of bins at $\ell=500$, computed following equation \ref{['combine_weights']}.
• Figure 2: Fractional residual lensing $B$-mode power spectrum after delensing using our realistic, simulated galaxies. Different curves correspond to different combinations of galaxies with the redshift distributions shown in figure \ref{['fig:kernels']}: galaxies from the lowest redshift bin (blue), the brute-force combination of all galaxies in every redshift bin into a single one (brown), or the optimal weighting of all the individual redshift bins (green).
• Figure 3: Correlation coefficient with CMB lensing of various samples of simulated galaxies. In the top panel, different tomographic bins are combined optimally; in the bottom one, they are simply added together into a single map. The green, dashed curves show our 'ground truth', measured from the non-Gaussian simulation. By construction, this overlaps with the solid, blue curve, though the latter pertains to a Gaussian simulation. The red, dashed curve also corresponds to a Gaussian simulation, albeit one that further assumes linear galaxy bias with a value fit to the large-scale clustering of the non-Gaussian mock. Though the latter is clearly not a good approximation for $\ell$ larger than a few hundred, these scales are relatively uninmportant when delensing low-$\ell$$B$-modes.
• Figure 4: Fractional difference between the residual lensing $B$-mode power spectrum obtained after delensing with our realistic non-Gaussian simulations and either of two approximate treatments: one involving a Gaussian simulation which by construction has the same correlation with CMB lensing as our 'ground truth' simulation (blue), and another where the Gaussian simulation involves the additional assumption that galaxy bias is linear and is measured from the large scale clustering of the non-Gaussian mocks (red). In the top panel, different bins of our tomographic sample are combined optimally; in the bottom one, they are all lumped together into a single bin. The shaded regions denote the $1\,\sigma$ fractional (Gaussian) uncertainty assuming full-sky coverage and various white noise levels for the large-angle polarization measurements.
• Figure 5: Comparison of the inferred and true values of the tensor-to-scalar ratio, $r$, in the presence of two sources of modeling error: blue curves assume the galaxy distribution is Gaussian, while red curves further assume galaxy bias is linear. In each case, the inference is done in presence of a white noise component with amplitude given in the legend. In the top panel, different redshift bins are optimally combined together using the scale-depedent weights of equation \ref{['combine_weights']}; in the lower panel, they are simply lumped together into a single bin.