Cosmological Information from Lensed CMB Power Spectra

TL;DR

The paper quantifies the non-Gaussian covariance induced by gravitational lensing on lensed CMB power spectra and introduces two lensing observables that capture essentially all information about intermediate-redshift geometry and growth. Using a Fisher-matrix framework and principal-component analysis of the lensing potential, it shows non-Gaussianity is negligible for TT/TE/EE up to $l_{ m max}=2000$ but can strongly degrade BB information, guiding survey design toward broader sky coverage for $B$-modes. The authors demonstrate how the two observables forecast constraints on neutrino mass, curvature, and dark energy evolution, and illustrate significant gains from deep, modest-area surveys when external priors are available. They also discuss survey optimization under non-Gaussian errors and acknowledge limitations such as parameter degeneracies and the potential gains from lens reconstruction and delensing.

Abstract

Gravitational lensing distorts the cosmic microwave background (CMB) temperature and polarization fields and encodes valuable information on distances and growth rates at intermediate redshifts into the lensed power spectra. The non-Gaussian bandpower covariance induced by the lenses is negligible to l=2000 for all but the B polarization field where it increases the net variance by up to a factor of 10 and favors an observing strategy with 3 times more area than if it were Gaussian. To quantify the cosmological information, we introduce two lensing observables, characterizing nearly all of the information, which simplify the study of non-Gaussian impact, parameter degeneracies, dark energy models, and complementarity with other cosmological probes. Information on the intermediate redshift parameters rapidly becomes limited by constraints on the cold dark matter density and initial amplitude of fluctuations as observations improve. Extraction of this information requires deep polarization measurements on only 5-10% of the sky, and can improve Planck lensing constraints by a factor of ~2-3 on any one of the parameters w_0, w_a, Omega_K, sum(m_nu) with the others fixed. Sensitivity to the curvature and neutrino mass are the highest due to the high redshift weight of CMB lensing but degeneracies between the parameters must be broken externally.

Figures (16)

• Figure 1: First three KL eigenmodes, defined by Eq. (\ref{['eq:lambdadef']}), for the $BB$ power spectrum. These represent modes in $BB$ whose true variance is larger than the variance estimated from Gaussian statistics; the eigenvalue $\lambda$ is the ratio of the two.
• Figure 2: Principal components $K_1(l)$, $K_2(l)$ of the lensing potential $C_\ell^{\phi\phi}$ obtained from CMB measurements to $l_{\rm max}=2000$, as described in §\ref{['sec:pcomp']}. These represent modes in the lensing potential which are constrained by measuring either lensed {$T$,$E$} or lensed $B$-modes respectively.
• Figure 3: Redshift sensitivity of the lensing observables $\Theta_i$ near the fiducial model. To good approximation the observables constrain the amplitude of $C_{l_i}^{\phi\phi}$ around multipoles near the median of the eignmodes of Fig. \ref{['fig:eigpp']}, $l_{K1}=114$, $l_{K2}=440$. The redshift sensitivities $Z_i$ at these multipoles (see Eq. (\ref{['eq:redshiftkernel']})) are plotted for the fiducial model.
• Figure 4: Derivatives of $C_l^{\phi\phi}$ with respect to the parameters $\sum m_\nu$, $w_0$, $w_a$, and $\Omega_K$, illustrating the different $l$ dependence. As in Tab. \ref{['tab:theta']}, the derivatives are taken adjusting $\Omega_{\rm DE}$ to hold $l_A$ fixed.
• Figure 5: Uncertainty on $\Theta_1$ from lensed $T$ alone (top) and lensed {$T,E$} (middle), and uncertainty on $\Theta_2$ from lensed $B$ (bottom), for varying beam size and noise level $\Delta_P$. We assume $\Delta_T$ is given by $\Delta_P/\sqrt{2}$ throughout, including the top panel. Only multipoles below $l_{\rm max}=2000$ are included. For the zero beam cases, we also show the uncertainties that would be obtained if Gaussian statistics were falsely assumed (dashed). The impact of non-Gaussian contributions is negligible in {$T,E$} but significant for $B$. The horizontal lines are sample variance limits given by Eq. (\ref{['eq:svlimit']}).