CMBPol Mission Concept Study: Gravitational Lensing

TL;DR

This paper examines the scientific value of CMB polarization lensing for a future mission like CMBPol, focusing on how the lensing signal from $C_\ell^{\phi\phi}$ reveals late-time physics (e.g., neutrino mass $\sum m_\nu$, dark energy equation of state $w$, and curvature $\Omega_k$) and how delensing can improve searches for primordial gravitational waves via the large-scale B-mode. It analyzes lens reconstruction methods (notably the EB quadratic estimator) and delensing strategies using internal small-scale polarization or external data (temperature or LSS), concluding that internal polarization delensing offers the strongest improvement in $\sigma(T/S)$ under low-noise, high-resolution conditions, while external delensing provides limited gains. The work also assesses foregrounds, especially polarized point sources, and beam-systematics, finding that under realistic models these are unlikely to be the limiting factors for lensing- and delensing-based science, though they require careful calibration and data-analysis strategies. Overall, the paper provides quantified forecasts for neutrino mass sensitivity ($\sigma(\sum m_\nu) \sim 0.03$–$0.12$ eV, potentially $\sim 0.05$ eV for ideal cases), dark energy constraints ($\sigma(w) \sim 0.08$–$0.2$), and curvature constraints ($\sigma(\Omega_k) \sim \text{a few} \times 10^{-3}$), and outlines the design implications for resolution-sensitivity trade-offs and the role of delensing in maximizing scientific return. The results highlight the complementary information content of lensing to the unlensed CMB and illustrate the practical considerations in instrument design, foreground treatment, and systematics control for exploiting CMB polarization lensing.

Abstract

Gravitational lensing of the cosmic microwave background by large-scale structure in the late universe is both a source of cosmological information and a potential contaminant of primordial gravity waves. Because lensing imprints growth of structure in the late universe on the CMB, measurements of CMB lensing will constrain parameters to which the CMB would not otherwise be sensitive, such as neutrino mass. If the instrumental noise is sufficiently small (<~ 5 uK-arcmin), the gravitational lensing contribution to the large-scale B-mode will be the limiting source of contamination when constraining a stochastic background of gravity waves in the early universe, one of the most exciting prospects for future CMB polarization experiments. High-sensitivity measurements of small-scale B-modes can reduce this contamination through a lens reconstruction technique that separates the lensing and primordial contributions to the B-mode on large scales. A fundamental design decision for a future CMB polarization experiment such as CMBpol is whether to have coarse angular resolution so that only the large-scale B-mode (and the large-scale E-mode from reionization) is measured, or high resolution to additionally measure CMB lensing. The purpose of this white paper is to evaluate the science case for CMB lensing in polarization: constraints on cosmological parameters, increased sensitivity to the gravity wave B-mode via lens reconstruction, expected level of contamination from non-CMB foregrounds, and required control of beam systematics.

Figures (13)

• Figure 1: Left panel: Signal angular power spectrum for the E (dashed line) and B (solid lines) modes. The black solid dashed line corresponds to the lensing induced B modes for all the models considered. The light to dark red colored curves correspond to different $r$ values, namely 0.43, 0.1, 0.01 and 0.001. The cosmological parameters used for this plot correspond to the WMAP5 $\Lambda$CDM+$r$ best fit model Komatsu:2008hk. Note that $r=0.43$ corresponds to the 95% upper limit on $r$ using this data-set. Obviously, for any allowed value of $r$, the lensing signal will dominate for $\ell\ge 200$. Right panel: Redshift dependence of the two principal components ($Z_1$ and $Z_2$ respectively) of the lensing potential angular power spectrum defined in Eq. (\ref{['eq:clphiphi']}) (from Smith:2006nk). These curves illustrate the CMB polarization lensing sensitivity to moderate redshifts, i.e. up to $z\simeq 5$.
• Figure 2: Signal power spectrum $C_\ell^{\phi\phi}$ for the CMB lens potential, and reconstruction noise power spectra for low-noise (1 $\mu$K-arcmin noise, 1 arcmin beam) and high-noise (10 $\mu$K-arcmin noise, 10 arcmin beam) polarization measurements, and for temperature measurements which are cosmic variance limited to $\ell_{\rm max}=3000$.
• Figure 3: Derivatives of the unlensed$C_\ell^{EE}$ power spectrum with respect to the late universe parameters $\{\Omega_\nu h^2, w, \Omega_K\}$ along the angular diameter distance degeneracy, showing that the power spectra remain constant to a good approximation.
• Figure 4: Derivatives of $C_\ell^{\phi\phi}$ with respect to the same late universe parameters as in Fig. \ref{['fig:unlensed_degeneracy']}, showing a large change in the power spectrum as the parameters are varied: the angular diameter distance degeneracy is broken by lensing.
• Figure 5: Uncertainty $\sigma(m_\nu)$ on the neutrino mass as a function of beam size and noise level for $\ell_{\rm max}=2000$ (left panel) or $\ell_{\rm max}=4000$ (right panel) using CMB lens reconstruction, assuming fixed $w,\Omega_K$.