Planck 2013 results. XV. CMB power spectra and likelihood
Battaner López, Eduardo
Cosmic background radiation
Cosmological parameters
Cosmology: observations
Methods: data analysis
The development of Planck has been supported by:
ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF
(Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN,
JA and RES (Spain); Tekes, AoF and CSC (Finland); DLR and MPG
(Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland);
RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE (EU).
A description of the Planck Collaboration and a list of its members with the technical or scientific activities they have been involved
into, can be found at http://www.sciops.esa.int/index.php?project=
planck&page=Planck_Collaboration. We acknowledge the use of the
CLASS Boltzmann code (Lesgourgues 2011) and the Monte Python package
(Audren et al. 2013) in earlier stages of this work. The likelihood code and some
of the validation work was built on the library pmclib from the CosmoPMC package (Kilbinger et al. 2011). This research used resources of the IN2P3 Computer
Center (http://cc.in2p3.fr) as well as of the Planck-HFI data processing
centre infrastructures hosted at the Institut d’Astrophysique de Paris (France)
and financially supported by CNES.
This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations that
accounts for all known relevant uncertainties, both instrumental and astrophysical in nature. We use this likelihood to derive our best estimate of the CMB angular
power spectrum from Planck over three decades in multipole moment, `, covering 2 ≤ ` ≤ 2500. The main source of uncertainty at ` <∼ 1500 is cosmic variance.
Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher `s. For ` < 50, our likelihood exploits all Planck
frequency channels from 30 to 353 GHz, separating the cosmological CMB signal from diffuse Galactic foregrounds through a physically motivated Bayesian
component separation technique. At ` ≥ 50, we employ a correlated Gaussian likelihood approximation based on a fine-grained set of angular cross-spectra
derived from multiple detector combinations between the 100, 143, and 217 GHz frequency channels, marginalising over power spectrum foreground templates.
We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on the final
cosmological parameters. We find good internal agreement among the high-` cross-spectra with residuals below a few µK
2
at ` <∼ 1000, in agreement with estimated
calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from
the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit ΛCDM cosmology
is in excellent agreement with preliminary Planck EE and T E polarisation spectra. We find that the standard ΛCDM cosmology is well constrained by Planck from
the measurements at ` <∼ 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4σ deviation from scale invariance, ns = 1.
Increasing the multipole range beyond ` ' 1500 does not increase our accuracy for the ΛCDM parameters, but instead allows us to study extensions beyond the
standard model. We find no indication of significant departures from the ΛCDM framework. Finally, we report a tension between the Planck best-fit ΛCDM model
and the low-` spectrum in the form of a power deficit of 5–10% at ` <∼ 40, with a statistical significance of 2.5–3σ. Without a theoretically motivated model for
this power deficit, we do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent
data set.
2020-06-18T11:46:01Z
2020-06-18T11:46:01Z
2014-05
info:eu-repo/semantics/article
Ade, P. A., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., ... & Bartlett, J. G. (2014). Planck 2013 results. XV. CMB power spectra and likelihood. Astronomy & Astrophysics, 571, A15. [doi:10.1051/0004-6361/201321573]
http://hdl.handle.net/10481/62545
10.1051/0004-6361/201321573
eng
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
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