### 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 be ns = 0.9603 ± 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 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 $\triangle{\chi^2}_{eff}\approx 10$;
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. Planck constrains with
unprecedented accuracy the amplitude and possible
correlation (with the adiabatic mode) of non-decaying
isocurvature fluctuations. The fractional primordial
contributions of cold dark matter (CDM) isocurvature
modes of the types expected in the curvaton and axion
scenarios have upper bounds of 0.25% and 3.9% (95% CL),
respectively. In models with arbitrarily correlated CDM
or neutrino isocurvature modes, an anticorrelated
isocurvature component can improve the ${\chi^2}_{eff}$
by approximately 4 as a result of slightly lowering the
theoretical prediction for the $\ell \lesssim 40$
multipoles relative to the higher multipoles.
Nonetheless, the data are consistent with adiabatic
initial conditions.

Original language | English |
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Article number | A22 |

Number of pages | 42 |

Journal | Astronomy and Astrophysics |

Volume | 571 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- cosmic background radiation
- inflation
- early Universe

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## Cite this

Varis, J., Tuovinen, J., & Planck Collaboration (2014). Planck 2013 results: XXII. Constraints on inflation.

*Astronomy and Astrophysics*,*571*, [A22]. https://doi.org/10.1051/0004-6361/201321569