Gravitational lensing as a contaminant of the gravity wave signal in CMB

TL;DR

The study tackles the challenge of gravitational lensing contaminating primordial $B$-mode signals in the CMB by evaluating delensing strategies. Through simulations, it compares quadratic and iterative maximum-likelihood lensing reconstructions, showing the quadratic method can reduce lensing noise by up to a factor of ~7 while the iterative method achieves far larger gains (at least ~40x) at low detector noise, potentially enabling detection of tensor-to-scalar ratios as small as $r\sim 10^{-6}$ in ideal conditions. The findings imply no fundamental lensing limit within the tested parameter space, though real-world factors like sky cuts and foregrounds will constrain practical sensitivity. These results inform future CMB polarization mission design and the achievable inflationary energy scale probes.

Abstract

Gravity waves (GW) in the early universe generate B-type polarization in the cosmic microwave background (CMB), which can be used as a direct way to measure the energy scale of inflation. Gravitational lensing contaminates the GW signal by converting the dominant E polarization into B polarization. By reconstructing the lensing potential from CMB itself one can decontaminate the B mode induced by lensing. We present results of numerical simulations of B mode delensing using quadratic and iterative maximum-likelihood lensing reconstruction methods as a function of detector noise and beam. In our simulations we find the quadratic method can reduce the lensing B noise power by up to a factor of 7, close to the no noise limit. In contrast, the iterative method shows significant improvements even at the lowest noise levels we tested. We demonstrate explicitly that with this method at least a factor of 40 noise power reduction in lensing induced B power is possible, suggesting that T/S=10^-6 may be achievable in the absence of sky cuts, foregrounds, and instrumental systematics. While we do not find any fundamental lower limit due to lensing, we find that for high-sensitivity detectors residual lensing noise dominates over the detector noise.

Figures (2)

• Figure 1: Simulated extraction of a $B$ mode from CMB data with noise $w_P^{-1/2} = 0.5\mu$K arcmin and beam FWHM 4 arcmin. In each panel we have plotted the scalar quantity $B=\sum_{\bf l} B_{\bf l}e^{i{\bf l}\cdot\hat{\bf n}}$. For clarity, only $l<150$ modes are shown. The widths of the frames are 34 degrees, and the temperature scale runs from $-0.136\mu$K to $+0.136\mu$K. Upper left: The primary $B$ mode. Upper right: The $B$ mode after lensing and addition of 0.5 $\mu$K arcmin noise. Lower left: Recovered $B$ mode after cleaning with the quadratic estimator. Lower right: Recovered $B$ mode after cleaning with the iterative estimator.
• Figure 2: Power spectra of noise for $2'$, $0.25{\mu{\rm K~arcmin}}$ instrument with no lensing cleaning, cleaning with quadratic method and cleaning with iterative maximum-likelihood method. Also shown are two theoretical power spectra for $r=2\times 10^{-5}$ and $r=10^{-6}$. Assuming this instrument specifications and iterative method the former can be detected (at 2-$\sigma$) both in reionization peak ($l<20$) and in recombination peak $l>20$), while the latter is detectable for $l<20$ only. The noise power spectra have been averaged over the $l<150$ range.