Planck 2013 results. XV. CMB power spectra and likelihood

Jussi Varis, Jussi Tuovinen, Planck Collaboration

    Research output: Contribution to journalArticleScientificpeer-review

    202 Citations (Scopus)

    Abstract

    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 22500. 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 K2 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM 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 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510% at 40, with a statistical significance of 2.53. 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.
    Original languageEnglish
    Article numberA15
    Number of pages62
    JournalAstronomy and Astrophysics
    Volume571
    DOIs
    Publication statusPublished - 2014
    MoE publication typeA1 Journal article-refereed

    Fingerprint

    power spectra
    multipoles
    cosmology
    budgets
    invariance
    astrophysics
    indication
    coverings
    templates
    scalars
    moments
    deviation
    perturbation
    polarization
    detectors
    estimates
    calibration
    approximation
    modeling
    parameter

    Keywords

    • cosmic background radiation
    • cosmological parameters
    • cosmology
    • data analysis

    Cite this

    Varis, Jussi ; Tuovinen, Jussi ; Planck Collaboration. / Planck 2013 results. XV. CMB power spectra and likelihood. In: Astronomy and Astrophysics. 2014 ; Vol. 571.
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    abstract = "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 22500. 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 K2 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM 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 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510{\%} at 40, with a statistical significance of 2.53. 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.",
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    Planck 2013 results. XV. CMB power spectra and likelihood. / Varis, Jussi; Tuovinen, Jussi; Planck Collaboration.

    In: Astronomy and Astrophysics, Vol. 571, A15, 2014.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

    T1 - Planck 2013 results.

    T2 - XV. CMB power spectra and likelihood

    AU - Varis, Jussi

    AU - Tuovinen, Jussi

    AU - Planck Collaboration

    N1 - Project code: 18080

    PY - 2014

    Y1 - 2014

    N2 - 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 22500. 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 K2 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM 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 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510% at 40, with a statistical significance of 2.53. 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.

    AB - 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 22500. 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 K2 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM 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 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510% at 40, with a statistical significance of 2.53. 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.

    KW - cosmic background radiation

    KW - cosmological parameters

    KW - cosmology

    KW - data analysis

    U2 - 10.1051/0004-6361/201321573

    DO - 10.1051/0004-6361/201321573

    M3 - Article

    VL - 571

    JO - Astronomy and Astrophysics

    JF - Astronomy and Astrophysics

    SN - 0004-6361

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