Planck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
Abstract
The six parameters of the standard ΛCDM model have bestfit values derived from the Planck temperature power spectrum that are shifted somewhat from the bestfit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmicvariance level precision. We have investigated these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium τ, the baryon density ω_{b}, the matter density ω_{m}, the angular size of the sound horizon θ_{∗}, the spectral index of the primordial power spectrum, n_{s}, and A_{s}e^{ 2τ} (where A_{s} is the amplitude of the primordial power spectrum), we have examined the change in bestfit values between a WMAPlike large angularscale data set (with multipole moment ℓ < 800 in the Planck temperature power spectrum) and an all angularscale data set (ℓ < 2500Planck temperature power spectrum), each with a prior on τ of 0.07 ± 0.02. We find that the shifts, in units of the 1σ expected dispersion for each parameter, are { Δτ,ΔA_{s}e^{ 2τ},Δn_{s},Δω_{m},Δω_{b},Δθ_{∗} } = { 1.7,2.2,1.2,2.0,1.1,0.9 }, with a χ^{2} value of 8.0. We find that this χ^{2} value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2σ in 9% of simulated data sets, meaning that the shifts are not unusually large. Comparing ℓ < 800 instead to ℓ> 800, or splitting at a different multipole, yields similar results. We examined the ℓ < 800 model residuals in the ℓ> 800 power spectrum data and find that the features there that drive these shifts are a set of oscillations across a broad range of angular scales. Although they partly appear similar to the effects of enhanced gravitational lensing, the shifts in ΛCDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to nonlensing effects; the only exception is τ, which, at fixed A_{s}e^{ 2τ}, affects the ℓ> 800 temperature power spectrum solely through the associated change in A_{s} and the impact of that on the lensing potential power spectrum. We also ask, "what is it about the power spectrum at ℓ < 800 that leads to somewhat different bestfit parameters than come from the full ℓ range?" We find that if we discard the data at ℓ < 30, where there is a roughly 2σ downward fluctuation in power relative to the model that best fits the full ℓ range, the ℓ < 800 bestfit parameters shift significantly towards the ℓ < 2500 bestfit parameters. In contrast, including ℓ < 30, this previously noted "lowℓ deficit" drives n_{s} up and impacts parameters correlated with n_{s}, such as ω_{m} and H_{0}. As expected, the ℓ < 30 data have a much greater impact on the ℓ < 800 best fit than on the ℓ < 2500 best fit. So although the shifts are not very significant, we find that they can be understood through the combined effects of an oscillatorylike set of highℓ residuals and the deficit in lowℓ power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between PlanckTT data and two other CMB data sets, namely the Planck lensing reconstruction and the TT power spectrum measured by the South Pole Telescope, again finding a lack of convincing evidence of any significant deviations in parameters, suggesting that current CMB data sets give an internally consistent picture of the ΛCDM model.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 2017
 DOI:
 10.1051/00046361/201629504
 arXiv:
 arXiv:1608.02487
 Bibcode:
 2017A&A...607A..95P
 Keywords:

 cosmology: observations;
 cosmic background radiation;
 cosmological parameters;
 cosmology: theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 22 pages, 17 figures, abstract abridged for Arxiv submission