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Register a new userPlanck 2015 results. XVII. Constraints on primordial non-Gaussianity
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The Planck full mission cosmic microwave background(CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity(NG). Using three classes of optimal bispectrum estimators - separable template-fitting (KSW), binned, and modal - we obtain consistent values for the local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone fNL^local=2.5+-5.7, fNL^equil=-16+-70 and fNL^ortho=-34+-33(68%CL). Combining temperature and polarization data we obtain fNL^local=0.8+-5.0, fNL^equil=-4+-43 and fNL^ortho=-26+-21 (68%CL). The results are based on cross-validation of these estimators on simulations, are stable across component separation techniques, pass an extensive suite of tests, and are consistent with Minkowski functionals based measurements. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch of the noise model in simulations and the data. Beyond fNL estimates, we present model-independent reconstructions of the CMB bispectrum and derive constraints on early universe scenarios that generate NG, including general single-field and axion inflation, initial state modifications, parity-violating tensor bispectra, and directionally dependent vector models. We also present a wide survey of scale-dependent oscillatory bispectra, and we look for isocurvature NG. Our constraint on the local primordial trispectrum amplitude is gNL^local=(-9.0+-7.7)x10^4 (68%CL), and we perform an analysis of additional trispectrum shapes. The global picture is one of consistency with the premises of the LambdaCDM cosmology, namely that the structure we observe today was sourced by adiabatic, passive, Gaussian, and primordial seed perturbations.[abridged]
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The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNL^local= 2.7+/-5.8, fNL^equil= -42+/-75, and fNL^ortho= -25+-39 (68% CL statistical). NG is detected in the data; using skew-C_l statistics we find a nonzero bispectrum from residual point sources, and the ISW-lensing bispectrum at a level expected in the LambdaCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_l, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, 3-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c_s geq 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r_D geq 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the 4-point function in the local model tauNL < 2800 (95% CL). These constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.
We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following results: f_NL^local = -0.9 +- 5.1; f_NL^equil = -26 +- 47; and f_NL^ortho = - 38 +- 24 (68%CL, statistical). These results include the low-multipole (4 <= l < 40) polarization data, not included in our previous analysis, pass an extensive battery of tests, and are stable with respect to our 2015 measurements. Polarization bispectra display a significant improvement in robustness; they can now be used independently to set NG constraints. We consider a large number of additional cases, e.g. scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 sigma. We present model-independent reconstructions and analyses of the CMB bispectrum. Our final constraint on the local trispectrum shape is g_NLl^local = (-5.8 +-6.5) x 10^4 (68%CL, statistical), while constraints for other trispectra are also determined. We constrain the parameter space of different early-Universe scenarios, including general single-field models of inflation, multi-field and axion field parity-breaking models. Our results provide a high-precision test for structure-formation scenarios, in complete agreement with the basic picture of the LambdaCDM cosmology regarding the statistics of the initial conditions (abridged).
We compute and investigate four types of imprint of a stochastic background of primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) anisotropies: the impact of PMFs on the CMB spectra; the effect on CMB polarization induced by Faraday rotation; the impact of PMFs on the ionization history; magnetically-induced non-Gaussianities; and the magnetically-induced breaking of statistical isotropy. Overall, Planck data constrain the amplitude of PMFs to less than a few nanogauss. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are $B_{1,mathrm{Mpc}}< 4.4$ nG (where $B_{1,mathrm{Mpc}}$ is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity, and $B_{1,mathrm{Mpc}}< 5.6$ nG for a maximally helical field.For nearly scale-invariant PMFs we obtain $B_{1,mathrm{Mpc}}<2.0$ nG and $B_{1,mathrm{Mpc}}<0.9$ nG if the impact of PMFs on the ionization history of the Universe is included. From the analysis of magnetically-induced non-Gaussianity we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is $B_{1,mathrm{Mpc}}< 2.8$ nG. A search for preferred directions in the magnetically-induced passive bispectrum yields $B_{1,mathrm{Mpc}}< 4.5$ nG, whereas the the compensated-scalar bispectrum gives $B_{1,mathrm{Mpc}}< 3$ nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in $EE$ and $BB$ at 70 GHz and gives $B_{1,mathrm{Mpc}}< 1380$ nG. In our final analysis, we consider the harmonic-space correlations produced by Alfven waves, finding no significant evidence for the presence of these waves. Together, these results comprise a comprehensive set of constraints on possible PMFs with Planck data.
We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be $n_mathrm{s} = 0.968 pm 0.006$ and tightly constrain its scale dependence to $d n_s/d ln k =-0.003 pm 0.007$ when combined with the Planck lensing likelihood. When the high-$ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(phi) propto phi^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data.
We show that the new precise measurements of Cosmic Microwave Background (CMB) temperature and polarization anisotropies made by the Planck satellite significantly improves previous constraints on the cosmic gravitational waves background (CGWB) at frequencies $f>10^{-15}$ Hz. On scales smaller than the horizon at the time of decoupling, primordial gravitational waves contribute to the total radiation content of the Universe. Considering adiabatic perturbations, CGWB affects temperature and polarization CMB power spectra and matter power spectrum in a manner identical to relativistic particles. Considering the latest Planck results we constrain the CGWB energy density to $Omega_{rm gw} h^2 <1.7times 10^{-6} $ at 95% CL. Combining CMB power spectra with lensing, BAO and primordial Deuterium abundance observations, we obtain $Omega_{rm gw} h^2 <1.2times 10^{-6} $ at 95% CL, improving previous Planck bounds by a factor 3 and the recent direct upper limit from the LIGO and VIRGO experiments a factor 2. A combined analysis of future satellite missions as COrE and EUCLID could improve current bound by more than an order of magnitude.
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