A small deviation from scale invariance in the form of oscillations in the primordial correlation spectra has been predicted by various cosmological models. In this paper we review a recently developed method to search for these features in the data
in a more effective way. By Taylor expanding the small features around the background cosmology, we have shown we are able to improve the search for these features compared to previous analyses. In this short paper we will extend that work by combining this method with a multi nested sampler. We recover our previous findings and are able to do so in 192 CPU hours. We will also briefly discuss the possibility of a long wavelength feature in the data to alleviate some tension between CMB data and the LCDM+r concordance cosmology.
We apply our recently developed code to search for resonance features in the Planck CMB temperature data. We search both for log spaced oscillations or linear spaced oscillations and compare our findings with results of our WMAP9 analysis and the Pla
nck team analysis. While there are hints of log spaced resonant features present in the WMAP9 data, the significance of these features weaken with more data. With more accurate small scale measurements, we also find that the best fit frequency has shifted and the amplitude has been reduced. We confirm the presence of a several low frequency peaks, earlier identified by the Planck team, but with a better improvement of fit (delta chi^2 ~ 12). We further investigate this improvement by allowing the lensing potential to vary as well, showing mild correlation between the amplitude of the oscillations and the lensing amplitude. We find that the improvement of the fit increases even more (delta chi^2 ~ 14) for the low frequencies that modify the spectrum in a way that mimics the lensing effect. Since these features were not present in the WMAP data, they are primarily due to better measurements of Planck at small angular scales. For linear spaced oscillations we find a maximum delta chi^2 ~ 13 scanning two orders of magnitude in frequency space, and the biggest improvements are at extremely high frequencies. We recover a best fit frequency very close to the one found in WMAP9, which confirms that the fit improvement is driven by low l. Further comparisons with WMAP9 show Planck contains many more features, both for linear and log space oscillations, but with a smaller improvement of fit. We discuss the improvement as a function of the number of modes and study the effect of the 217 GHz map, which appears to drive most of the improvement for log spaced oscillations. We conclude that none of the detected features are statistically significant.
In this first of two papers, we present a new method for searching for oscillatory features in the primordial power spectrum. A wide variety of models predict these features in one of two different flavors: logarithmically spaced oscillations and lin
early spaced oscillations. The proposed method treats the oscillations as perturbations on top of the scale-invariant power spectrum, allowing us to vary all cosmological parameters. This perturbative approach reduces the computational requirements for the search as the transfer functions and their derivatives can be precomputed. We show that the most significant degeneracy in the analysis is between the distance to last scattering and the overall amplitude at low frequencies. For models with logarithmic oscillations, this degeneracy leads to an uncertainty in the phase. For linear spaced oscillations, it affects the frequency of the oscillations. In this first of two papers, we test our code on simulated Planck-like data, and show we are able to recover fiducial input oscillations with an amplitude of a few times order 10^{-2}. We apply the code to WMAP9-year data and confirm the existence of two intriguing resonant frequencies for log spaced oscillations. For linear spaced oscillations we find a single resonance peak. We use numerical simulations to assess the significance of these features and conclude that the data do not provide compelling evidence for the existence of oscillatory features in the primordial spectrum.
