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We study the implications of Planck data for models of dark energy (DE) andmodified gravity (MG), beyond the cosmological constant scenario. We start withcases where the DE only directly affects the background evolution, consideringTaylor expansions of the equation of state, principal component analysis andparameterizations related to the potential of a minimally coupled DE scalarfield. When estimating the density of DE at early times, we significantlyimprove present constraints. We then move to general parameterizations of theDE or MG perturbations that encompass both effective field theories and thephenomenology of gravitational potentials in MG models. Lastly, we test a rangeof specific models, such as k-essence, f(R) theories and coupled DE. Inaddition to the latest Planck data, for our main analyses we use baryonicacoustic oscillations, type-Ia supernovae and local measurements of the Hubbleconstant. We further show the impact of measurements of the cosmologicalperturbations, such as redshift-space distortions and weak gravitationallensing. These additional probes are important tools for testing MG models andfor breaking degeneracies that are still present in the combination of Planckand background data sets. All results that include only backgroundparameterizations are in agreement with LCDM. When testing models that alsochange perturbations (even when the background is fixed to LCDM), some tensionsappear in a few scenarios: the maximum one found is \sim 2 sigma for PlanckTT+lowP when parameterizing observables related to the gravitational potentialswith a chosen time dependence; the tension increases to at most 3 sigma whenexternal data sets are included. It however disappears when including CMBlensing.

Planck 2015 results. XIV. Dark energy and modified gravity