Planck 2013 results. XXIV. Constraints on primordial non-Gaussianity

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 f<SUB>NL</SUB><SUP>local</SUP> = 2.7 5.8, f<SUB>NL</SUB><SUP>equil</SUP> = -42 75, and f<SUB>NL</SUB><SUP>orth</SUP> = -25 39 (68% CL statistical). Non-Gaussianity is detected in the data; using skew-C<SUB>l</SUB> statistics we find a nonzero bispectrum from residual point sources, and the integrated-Sachs-Wolfe-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<SUB>l</SUB>, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, three-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<SUB>s</SUB> >= 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r<SUB>D</SUB> >= 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the four-point function in the local model tau<SUB>NL</SUB>< 2800 (95% CL). Taken together, these constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.