Direct Signature of Evolving Gravitational Potential from Cosmic Microwave Background

Abstract

We show that time dependent gravitational potential can be directly detected from the cosmic microwave background (CMB) anisotropies. The signature can be measured by cross-correlating the CMB with the projected density field reconstructed from the weak lensing distortions of the CMB itself. The cross-correlation gives a signal whenever there is a time dependent gravitational potential. This method traces dark matter directly and has a well defined redshift distribution of the window projecting over the density perturbations, thereby avoiding the problems plaguing other proposed cross-correlations. We show that both MAP and Planck will be able to probe this effect for observationally relevant curvature and cosmological constant models, which will provide additional constraints on the cosmological parameters.

Figures (2)

• Figure 1: Square of correlation coefficient $({\rm Corr}^{T\kappa}_l)^2$ as a function of $l$ is shown for open $\Omega_m=0.2$ and $\Omega_m=0.4$ models (upper and lower dashed curve) and for cosmological constant $\Omega_m=0.2$ and $\Omega_m=0.4$ models (upper and lower solid curves).
• Figure 2: Power spectra for noise $N^{\cal S \cal S}_l$ (long dashed), $N^{\cal E\cal E}_l$ (short dashed), $N^{\cal E \cal S}_l$ (dotted) both for Planck (lower curves) and MAP (upper curves) for cosmological constant model with $\Omega_m=0.3$. Also shown is power spectrum of convergence $4C^{\kappa \kappa}_l$ (solid) for the same model, normalized to $\sigma_8=1$.