Measuring Dark Matter Power Spectrum from Cosmic Microwave Background

Abstract

We propose a method to extract the projected power spectrum of density perturbations from the distortions in the cosmic microwave background (CMB). The distortions are imprinted onto the CMB by the gravitational lensing effect and can be extracted using a combination of products of CMB derivatives. We show that future CMB experiments such as Planck will be able to extract the power spectrum with high statistical significance over two orders of magnitude in angle. The method proposed here traces dark matter directly to higher redshift (up to $z \sim 1100$) and larger scale (few Gpc) than any other currently known method. It also traces large scale structure in the linear regime, allowing simple interpretation in terms of cosmological models. By providing additional and complementary information to the one from the primary CMB analysis it will strengthen further the scientific return of future CMB experiments.

Figures (2)

• Figure 1: Logarithmic contribution to $C^{\kappa \kappa}_l$ as a function of $k$ for $l=10$, 100, 1000 (the normalization is arbitrary). The models are flat CDM model (dotted), open CDM model with $\Omega_m=0.3$ (dashed) and cosmological constant model with with $\Omega_m=0.3$ (solid). All the models have $\Gamma=\Omega_m h=0.21$.
• Figure 2: Top: power spectra for noise $N^{\cal S \cal S}_l$ (short dashed), $N^{\cal E\cal E}_l$ (dotted), $N^{\cal E \cal S}_l$ (long-dashed) and $N^{\cal BB}_l$ (dash-dotted) for Planck, using cosmological constant model with $\Omega_m=0.3$ and $\sigma_8=1$. Also shown is power spectrum of convergence $4C^{\kappa \kappa}_l$ (solid) for the same model, together with its reconstruction from a Monte Carlo simulation. Bottom: ratio of output to input power spectrum is plotted for the averaged $C^{\kappa \kappa}_l$ reconstruction and for the $C^{\cal BB}_l$ reconstruction. Also shown is the window $W_l$ (dashed) for Planck satellite characteristics.