| 1. |
- Ade, P. A. R., et al.
(författare)
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Planck 2015 results XIV. Dark energy and modified gravity
- 2016
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 594
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Tidskriftsartikel (refereegranskat)abstract
- We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below similar to 2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories, and coupled DE. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ACDM. When testing models that also change perturbations (even when the background is fixed to ACDM), some tensions appear in a few scenarios: the maximum one found is similar to 2 sigma for Planck TT + lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3 sigma when external data sets are included. It however disappears when including CMB lensing.
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| 2. |
- Aghanim, N., et al.
(författare)
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Planck 2015 results XI. CMB power spectra, likelihoods, and robustness of parameters
- 2016
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 594
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlation functions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, i.e., a pixel-based likelihood at low multipoles (l < 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy brought by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the Lambda CDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, n(s), is confirmed smaller than unity at more than 5 sigma from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck's wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline Lambda CDM cosmology this requires tau = 0.078 +/- 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the mu K-2 level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the Lambda CDM model, showing consistency with those established independently from temperature information alone.
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| 3. |
- Aghanim, N., et al.
(författare)
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Planck intermediate results LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
- 2017
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 607
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Tidskriftsartikel (refereegranskat)abstract
- The six parameters of the standard Lambda CDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit 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 cosmic-variance 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 tau, the baryon density omega(b), the matter density omega(m), the angular size of the sound horizon theta(*), the spectral index of the primordial power spectrum, n(s), and A(s)e(-2 pi) (where As is the amplitude of the primordial power spectrum), we have examined the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment l < 800 in the Planck temperature power spectrum) and an all angular-scale data set (l < 2500 Planck temperature power spectrum), each with a prior on tau of 0.07 +/- 0.02. We find that the shifts, in units of the 1 sigma expected dispersion for each parameter, are {Delta tau, Delta A(s)e(-2 tau), Delta n(s), Delta omega(m), Delta omega(b), Delta theta(*)} = {-1.7, -2.2, 1.2, 2.0, 1.1, 0.9}, with a chi(2) value of 8.0. We find that this chi(2) value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2 sigma 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 Lambda CDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to non-lensing effects; the only exception is tau, which, at fixed A(s)e(-2 tau), affects the l > 800 temperature power spectrum solely through the associated change in As 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 best-fit parameters than come from the full l range? We find that if we discard the data at l < 30, where there is a roughly 2 sigma downward fluctuation in power relative to the model that best fits the full l range, the l < 800 best-fit parameters shift significantly towards the l < 2500 best-fit parameters. In contrast, including l < 30, this previously noted low-l deficit drives ns up and impacts parameters correlated with ns, such as omega(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 oscillatory-like set of high-l residuals and the deficit in low-l power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between Planck TT 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 Lambda CDM model.
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