Wavelet Band Powers of the Primordial Power Spectrum from CMB Data

Measuring the primordial matter power spectrum is our primary means of probing unknown physics in the very early universe. We allow the primordial power spectrum to be an arbitrary function, and parametrize it in terms of wavelet band powers. Current cosmological data correspond to 11 such wavelet bands. We derive constraints on these band powers as well as $H_0$, $\Omega_b h^2$ and $\Omega_m h^2$ from current Cosmic Microwave Background Anisotropy (CMB) data using the Markov Chain Monte Carlo (MCMC) technique. Our results indicate a feature in the primordial power spectrum at $0.008 \la k/(h {Mpc}^{-1}) \la 0.1$. MAP and Planck data should allow us to put tighter constraints on the primordial power spectrum.