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Register a new userPlanck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
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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.
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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).
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]
We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to $n_s = 0.9603 pm 0.0073$, ruling out exact scale invariance at over 5 $sigma$. Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n > 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining $d n_s/d ln k = -0.0134 pm 0.0090$. Several analyses dropping the slow-roll approximation are carried out, including detailed model comparison and inflationary potential reconstruction. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit $chi^2$ by ~ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with bounds on $f_mathrm{NL}$ measured by Planck. The fractional primordial contribution of CDM isocurvature modes in the curvaton and axion scenarios has upper bounds of 0.25% or 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelation can improve $chi^2$ by approximatively 4 as a result of slightly lowering the theoretical prediction for the $ell<40$ multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.
Any variation of the fundamental physical constants, and more particularly of the fine structure constant, $alpha$, or of the mass of the electron, $m_e$, would affect the recombination history of the Universe and cause an imprint on the cosmic microwave background angular power spectra. We show that the Planck data allow one to improve the constraint on the time variation of the fine structure constant at redshift $zsim 10^3$ by about a factor of 5 compared to WMAP data, as well as to break the degeneracy with the Hubble constant, $H_0$. In addition to $alpha$, we can set a constraint on the variation of the mass of the electron, $m_{rm e}$, and on the simultaneous variation of the two constants. We examine in detail the degeneracies between fundamental constants and the cosmological parameters, in order to compare the limits obtained from Planck and WMAP and to determine the constraining power gained by including other cosmological probes. We conclude that independent time variations of the fine structure constant and of the mass of the electron are constrained by Planck to ${Deltaalpha}/{alpha}= (3.6pm 3.7)times10^{-3}$ and ${Delta m_{rm e}}/{m_{rm e}}= (4 pm 11)times10^{-3}$ at the 68% confidence level. We also investigate the possibility of a spatial variation of the fine structure constant. The relative amplitude of a dipolar spatial variation of $alpha$ (corresponding to a gradient across our Hubble volume) is constrained to be $deltaalpha/alpha=(-2.4pm 3.7)times 10^{-2}$.
We derive robust constraints on primordial non-Gaussianity (PNG) using the clustering of 800,000 photometric quasars from the Sloan Digital Sky Survey in the redshift range $0.5<z<3.5$. These measurements rely on the novel technique of {it extended mode projection} to control the impact of spatially-varying systematics in a robust fashion, making use of blind analysis techniques. This allows the accurate measurement of quasar halo bias at the largest scales, while discarding as little as possible of the data. The standard local-type PNG parameters $f_mathrm{NL}$ and $g_mathrm{NL}$ both imprint a $k^{-2}$ scale-dependent effect in the bias. Constraining these individually, we obtain $-49<f_mathrm{NL}<31$ and $-2.7times10^5<g_mathrm{NL}<1.9times10^5$, while their joint constraints lead to $-105<f_mathrm{NL}<72$ and $-4.0times10^5<g_mathrm{NL}<4.9times10^5$ (all at 95% CL) . Introducing a running parameter $n_{f_mathrm{NL}}$ to constrain $b(k) propto k^{-2+n_{f_mathrm{NL}}}$ and a generalised PNG amplitude $tilde{f}_mathrm{NL}$, we obtain $-45.5 exp({3.7, n_{f_mathrm{NL}}}) < tilde{f}_mathrm{NL} < 34.4 exp({3.3, n_{f_mathrm{NL}}})$ at 95% CL. These results incorporate uncertainties in the cosmological parameters, redshift distributions, shot noise, and the bias prescription used to relate the quasar clustering to the underlying dark matter. These are the strongest constraints obtained to date on PNG using a single population of large-scale structure tracers, and are already at the level of pre-{it Planck} constraints from the cosmic microwave background. A conservative forecast for a {it Large Synoptic Survey Telescope}-like survey incorporating mode projection yields $sigma(f_mathrm{NL}) sim 5$ -- competitive with the {it Planck} result -- highlighting the power of upcoming large scale structure surveys to probe the initial conditions of the universe.
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