Principal power of the CMB

We study the physical limitations placed on cosmic microwave background (CMB) temperature and polarization measurements of the initial power spectrum. These limitations include geometric projection, acoustic physics, gravitational lensing and degeneracies with cosmological parameters. Detailed information on the spectrum is greatly assisted by polarization information and localized to the acoustic regime $k=0.02\mathrm{}-0.2{\mathrm{Mpc}}^{-1}$ with a fundamental resolution of $\Delta k/k>\mathrm{}\mathrm{0.05.}\mathrm{}$ From this study we construct principal component based statistics, which are orthogonal to cosmological parameters including the initial amplitude and tilt of the spectrum, that best probe deviations from scale-free initial conditions. These statistics resemble Fourier modes confined to the acoustic regime and ultimately can yield $\sim 50$ independent measurements of the power spectrum features to percent level precision. They are straightforwardly related to more traditional parametrizations, such as the running of the tilt, and in the future can provide many statistically independent measurements of it for consistency checks. Though we mainly consider physical limitations on the measurements, these techniques can be readily adapted to include instrumental limitations or other sources of power spectrum information.