Cosmic 21-cm Delensing of Microwave Background Polarization and the Minimum Detectable Energy Scale of Inflation

TL;DR

This method could allow CMB experiments to have increased sensitivity to a background of inflationary gravitational waves (IGWs) compared to methods relying on the CMB alone and may constrain models of inflation which were heretofore considered to have undetectable IGW amplitudes.

Abstract

The curl (B) modes of cosmic microwave background (CMB) polarization anisotropies are a unique probe of the primordial background of inflationary gravitational waves (IGWs). Unfortunately, the B-mode polarization anisotropies generated by gravitational waves at recombination are confused with those generated by the mixing of gradient-mode (E-mode) and B-mode polarization anisotropies as CMB photons propagate through the Universe and are gravitationally lensed. We describe here a method for delensing CMB polarization anisotropies using observations of anisotropies in the cosmic 21-cm radiation emitted or absorbed by neutral hydrogen atoms at redshifts 10 to 200. While the detection of cosmic 21-cm anisotropies at high resolution is challenging, a combined study with a relatively low-resolution (but high-sensitivity) CMB polarization experiment could probe inflationary energy scales well below the Grand Unified Theory (GUT) scale of 10^{16} GeV -- constraining models with energy scales below 10^{15} GeV (the detectable limit derived from CMB observations alone). The ultimate theoretical limit to the detectable inflationary energy scale via this method may be as low as 3 \times 10^{14} GeV.

Figures (2)

• Figure 1: Shown is angular power spectrum of the deflection potential as a function of source redshift $z_{s}$. The curves labeled '$l < 5000$' and '$l <10^5$' are the estimated noise levels for quadratic reconstruction using 21-cm anisotropies in 40 0.5 MHz bins centered around $z_{s} \approx 30$. We assume a noise power spectrum with $T_{sys}=3000 K$ at 46 MHz, that $l_{\rm max} f_{\rm cov} \approx 15$, and a year of integration zaldarriaga. The curve labeled shapes shows the residual noise curve in a scenario where shear is directly measured using resolved minihalos in a 1 MHz bandwidth about $z_{s} \approx 30$. Also shown is the noise levels for a CMB reconstruction of deflections with the planned CMBpol mission assuming a 3 arcminute beam, a noise level of 1$\mu$K $\sqrt{\rm sec}$, and a year of integration.
• Figure 2: Shown are power spectra of CMB B-mode polarization. The curve labeled 'IGWs' is the IGW contribution to B-modes assuming a tensor-to-scalar ratio of 0.1 with (solid line; $\tau=0.17$) and without (dashed line) reionization. The curve labeled 'lensing' is the total lensing confusion to B-modes. Thin lines show the residual B-mode lensing contamination for bias-limited delensing out to $z_{s}$. Thick lines show previous estimates of the residual confusion from CMB experiments alone using quadratic estimators with an ideal noise-free experiment (dashed line), and likelihood methods using a high resolution/sensitivity experiment (dot-dashed). The noise curve of latter this experiment, with 2 arcminute beams and a pixel noise of 0.25 $\mu$K-arcminute, is the curve labeled 'High-Res'. Bias-limited lensing information to $z_{s} \gtrsim 10$ improves upon the limit to the IGW amplitude based on quadratic statistics, and the likelihood level can be reached with $z_{s} \sim 30$. If $z_{s} \sim 100$ an additional order-of-magnitude in the IGW amplitude could be probed. The curve labeled 'Low-Res' is the noise curve for a lower resolution CMB polarization experiment with 30 arcminute beams sufficiently sensitive to detect IGWs when paired with a cosmic 21-cm lensing reconstruction. For very efficient delensing other foregrounds, such as patchy reionization Santos:2003jb, might dominate confusion.