A nonparametric analysis of the cosmic microwave background power spectrum

We examine cosmic microwave background (CMB) temperature power spectra from the BOOMERANG, MAXIMA, and DASI experiments. We nonparametrically estimate the true power spectrum with no model assumptions. This is a significant departure from previous research that used either cosmological models or some other parameterized form (e. g., parabolic fits). Our nonparametric estimate is practically indistinguishable from the best-fit cosmological model, thus lending independent support to the underlying physics that governs these models. We also generate a confidence set for the nonparametric fit and extract confidence intervals for the numbers, locations, and heights of peaks and the successive peak-to-peak height ratios. At the 95%, 68%, and 40% confidence levels, we find functions that fit the data with one, two, and three peaks, respectively (0 less than or equal to l less than or equal to 1100). Therefore, the current data prefer two peaks at the 1 sigma level. However, we also rule out a constant temperature function at the greater than 8 sigma level. If we assume that there are three peaks in the data, we find their locations to be within l(1) = (118, 300), l(2) = (377, 650), and l(3) = (597, 900). We find the ratio of the first peak height to the second (DeltaT(1)/DeltaT(2))(2) = (1.06, 4.27) and the second to the third (DeltaT(2)/DeltaT(3))(2) = (0.41, 2.5). All measurements are for 95% confidence. If the standard errors on the temperature measurements were reduced to a third of what they are currently, as we expect to be achieved by the Microwave Anisotropy Probe and Planck CMB experiments, we could eliminate two-peak models at the 95% confidence limit. The nonparametric methodology discussed in this Letter has many astrophysical applications.