CMB power spectrum parameter degeneracies in the era of precision cosmology

Howlett, Cullan; Lewis, Antony; Hall, Alex; Challinor, A.

doi:10.1088/1475-7516/2012/04/027

Cited by 460 publications

(390 citation statements)

References 48 publications

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“…The code has been publicly available for over a decade and has been very well tested (and improved) by the community. Numerical stability and accuracy of the calculation at the sensitivity of Planck has been explored in detail (Hamann et al 2009;Lesgourgues 2011b;Howlett et al 2012), demonstrating that the raw numerical precision is sufficient for numerical errors on parameter constraints from Planck to be less than 10% of the statistical error around the assumed cosmological model. (For the high multipole CMB data at > 2000 introduced in Sect.…”

Section: Power Spectramentioning

confidence: 99%

“…In addition, we compute Ω m h 3 (a well-determined combination orthogonal to the acoustic scale degeneracy in flat models; see e.g., Percival et al 2002 andHowlett et al 2012), 10 9 A s e −2τ (which determines the small-scale linear CMB anisotropy power), r 0.002 (the ratio of the tensor to primordial curvature power at k = 0.002 Mpc −1 ), Ω ν h 2 (the physical density in massive neutrinos), and the value of Y P from the BBN consistency condition.…”

Section: Derived Parametersmentioning

confidence: 99%

“…It is well known that certain cosmological parameter combinations are highly degenerate using CMB power spectrum measurements alone Efstathiou & Bond 1999;Howlett et al 2012). These degeneracies can be broken by combining with other cosmological data (though the Planck lensing analysis does help to break the principal "geometrical" degeneracy, as discussed in Sect.…”

Section: Introductionmentioning

confidence: 99%

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Planck2013 results. XVI. Cosmological parameters

Ade¹,

Aghanim²,

Armitage-Caplan³

et al. 2014

A&A

5,074

163

2,253

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This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles ( > ∼ 40) are extremely well described by the standard spatiallyflat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ * = (1.04147 ± 0.00062) × 10 −2 , Ω b h 2 = 0.02205 ± 0.00028, Ω c h 2 = 0.1199 ± 0.0027, and n s = 0.9603 ± 0.0073, respectively (note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H 0 = (67.3 ± 1.2) km s −1 Mpc −1 , and a high value of the matter density parameter, Ω m = 0.315 ± 0.017. These values are in tension with recent direct measurements of H 0 and the magnituderedshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r 0.002 < 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find N eff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N eff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = −1.13 +0.13 −0.10 . We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. T...

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Section: Power Spectramentioning

confidence: 99%

Section: Derived Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Planck2013 results. XVI. Cosmological parameters

Ade¹,

Aghanim²,

Armitage-Caplan³

et al. 2014

A&A

5,074

163

2,253

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“…5: the Planck+WP contours are extended along the same line of degeneracy as the CFHTLenS constraint. We explain this as follows (drawing heavily on Section V of Howlett et al (2012)): although increasing neutrino mass does reduce growth of structure, hence driving the Planck+WP contours to lower σ8, light (mν well below 1 eV) neutrinos, are relativistic before/at recombination, so to preserve the position of the CMB acoustic peaks, dA(z * ) must remain constant. However, at late times, the massive neutrinos become non-relativistic, increasing the energy density relative to a model with massless neutrinos, and decreasing dA(z * ), unless h also decreases.…”

Section: Discordance In Mν λCdmmentioning

confidence: 99%

Cosmic discordance: are Planck CMB and CFHTLenS weak lensing measurements out of tune?

MacCrann

Zuntz

Bridle

et al. 2015

Monthly Notices of the Royal Astronomical Society

177

192

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We examine the level of agreement between low redshift weak lensing data and the CMB using measurements from the CFHTLenS and Planck+WMAP polarization. We perform an independent analysis of the CFHTLenS six bin tomography results of Heymans et al. (2013). We extend their systematics treatment and find the cosmological constraints to be relatively robust to the choice of non-linear modeling, extension to the intrinsic alignment model and inclusion of baryons. We find that when marginalised in the Ω m -σ 8 plane, the 95% confidence contours of CFHTLenS and Planck+WP only just touch, but the discrepancy is less significant in the full 6-dimensional parameter space of ΛCDM. Allowing a massive active neutrino or tensor modes does not significantly resolve the tension in the full n-dimensional parameter space. Our results differ from some in the literature because we use the full tomographic information in the weak lensing data and marginalize over systematics. We note that adding a sterile neutrino to ΛCDM brings the 2d marginalised contours into greater overlap, mainly due to the extra effective number of neutrino species, which we find to be 0.88 ± 0.43 (68%) greater than standard on combining the datasets. We discuss why this is not a completely satisfactory resolution, leaving open the possibility of other new physics or observational systematics as contributing factors. We provide updated cosmology fitting functions for the CFHTLenS constraints and discuss the differences from ones used in the literature.

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“…At scales where the matter perturbations are in the linear regime, the power spectrum can be accurately modeled using a Boltzmann code. To this end, we use CAMB 6 (Howlett et al 2012;Lewis et al 2000). In the nonlinear regime, the matter power spectrum is more difficult to model.…”

Section: Bias Modelmentioning

confidence: 99%

Joint measurement of lensing–galaxy correlations using SPT and DES SV data

Baxter

Clampitt

Giannantonio

et al. 2016

Mon. Not. R. Astron. Soc.

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We measure the correlation of galaxy lensing and cosmic microwave background lensing with a set of galaxies expected to trace the matter density field. The measurements are performed using pre-survey Dark Energy Survey (DES) Science Verification optical imaging data and millimeter-wave data from the 2500 square degree South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) survey. The two lensing-galaxy correlations are jointly fit to extract constraints on cosmological parameters, constraints on the redshift distribution of the lens galaxies, and constraints on the absolute shear calibration of DES galaxy lensing measurements. We show that an attractive feature of these fits is that they are fairly insensitive to the clustering bias of the galaxies used as matter tracers. The measurement presented in this work confirms that DES and SPT data are consistent with each other and with the currently favored ΛCDM cosmological model. It also demonstrates that joint lensing-galaxy correlation measurement considered here contains a wealth of information that can be extracted using current and future surveys.

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CMB power spectrum parameter degeneracies in the era of precision cosmology

Cited by 460 publications

References 48 publications

Planck2013 results. XVI. Cosmological parameters

Planck2013 results. XVI. Cosmological parameters

Cosmic discordance: are Planck CMB and CFHTLenS weak lensing measurements out of tune?

Joint measurement of lensing–galaxy correlations using SPT and DES SV data

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