Testing modified gravity with Planck: the case of coupled dark energy

Abstract: The Planck collaboration has recently published maps of the Cosmic Microwave Background (CMB) radiation, in good agreement with a LCDM model, a fit especially valid for multipoles l > 40. We explore here the possibility that dark energy is dynamical and gravitational attraction between dark matter particles is effectively different from the standard one in General Relativity: this is the case of coupled dark energy models, where dark matter particles feel the presence of a fifth force, larger than gravity by a factor beta^2. We investigate constraints on the strength of the coupling beta in view of Planck data. Interestingly, we show that a non-zero coupling is compatible with data and find a likelihood peak at beta = 0.036 \pm 0.016 (Planck + WP + BAO) (compatible with zero at 2sigma). The significance of the peak increases to beta = 0.066 \pm 0.018 (Planck + WP + HST) (around 3.6sigma) when Planck is combined to Hubble Space Telescope data. This peak comes mostly from the small difference between the Hubble parameter determined with CMB measurements and the one coming from astrophysics measurements. In this sense, future observations and further tests of current observations are needed to determine whether the discrepancy is due to systematics in any of the datasets. Our aim here is not to claim new physics but rather to show how Planck data can be used to provide information on dynamical dark energy and modified gravity, allowing us to test the strength of an effective fifth force between dark matter particles with precision smaller than 2%.