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Published October 2016 | Published + Submitted
Journal Article Open

Planck 2015 results. XIV. Dark energy and modified gravity


We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ~2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories, and coupled DE. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ΛCDM. When testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ~2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3σ when external data sets are included. It however disappears when including CMB lensing.

Additional Information

© 2016 ESO. Received 5 February 2015; Accepted 19 February 2016; Published online 20 September 2016. It is a pleasure to thank Luca Amendola, Emilio Bellini, Diego Blas, Sarah Bridle, Noemi Frusciante, Catherine Heymans, Alireza Hojjati, Bin Hu, Thomas Kitching, Niall MacCrann, Marco Raveri, Ignacy Sawicki, Alessandra Silvestri, Fergus Simpson, Christof Wetterich and Gongbo Zhao for interesting discussions on theories, external data sets and numerical codes. Part of the analysis for this paper was run on the Andromeda and Perseus clusters of the University of Geneva and on WestGrid computers in Canada. We deeply thank Andreas Malaspinas for invaluable help with the Andromeda and Perseus Clusters. This research was partly funded by the DFG TransRegio TRR33 grant on "The Dark Universe" and by the Swiss NSF. The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/planck-collaboration.

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Submitted - 1502.01590v1.pdf

Published - aa25814-15.pdf


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August 20, 2023
August 20, 2023