Planck 2013 results. XXII. Constraints on inflation
Publication date: 29 October 2014
Authors: Planck Collaboration
Journal: Astronomy & Astrophysics
Volume: 571, November 2014
Copyright: ESO, 2014
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 be ns = 0.9603 ± 0.0073, ruling out exact scale invariance at over 5σ.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 dns/ dlnk = − 0.0134 ± 0.0090. We verify these conclusions through a numerical analysis, which makes no slow-roll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by Δχ2eff ≈ 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 Planck bounds on fNL.
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