| 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 =
0.960 pm 0.0073, ruling out exact scale invariance at over 5 sigma. Planck
establishes an upper bound on the tensor-to-scalar ratio at r < 0.11 (95% CL).
Planck data 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 any 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 investigate whether the primordial power spectrum contains
any features. A penalized likelihood approach suggests a feature near the
smallest scales probed by Planck at an estimated significance of ~3 sigma after
correction for the look elsewhere effect. Models with a parameterized
oscillatory feature can 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_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 ~4
due to a moderate tension between l < 40 and higher multipoles. Nonetheless,
the data are consistent with adiabatic initial conditions. |
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