Planck 2013 results. XXII. Constraints on inflation

TL;DR

Planck 2013 results tighten the inflationary parameter space, finding n_s ≈ 0.9603 and r < 0.11, indicating a red-tilted spectrum with very small tensor contributions and disfavoring exact scale invariance. Concave and smaller-field inflationary potentials fit the data better, while simple monomial m^n with n>2, exponential, and some hybrid models are disfavored; running of the spectral index is not required by the data. The analysis combines slow-roll and beyond-slow-roll approaches, including potential reconstruction, generalized Lagrangians and isocurvature/non-Gaussian constraints, yielding robust bounds on reheating and the post-inflationary epoch. Overall, the ΛCDM+tensor picture remains favored, with Planck imposing strong constraints on inflationary model space and guiding future polarization analyses.

Abstract

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 $σ$. 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 $χ^2$ 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 $χ^2$ 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.