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

The Planck collaboration has recently published maps of the cosmic microwave background (CMB) radiation, in good agreement with a Lambda CDM 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 2 beta(2), defining an effective gravitational constant G(eff) = G(1 + 2 beta(2)). We investigate constraints on the strength of the coupling beta in view of Planck data. Interestingly, we show that a nonzero coupling is compatible with data and find a likelihood peak at beta = 0.036 +/- 0.016 [Planck + WMAP polarization (WP) + baryonic acoustic oscillations (BAO)] (compatible with zero at 2.2 sigma). The significance of the peak increases to beta = 0.066 +/- 0.018 [Planck + WP + Hubble Space Telescope (HST)] (around 3.6 sigma from zero coupling) when Planck is combined to HST data by [16]. This peak comes mostly from the small difference between the Hubble parameter determined with CMB measurements and the one coming from astrophysics measurements and is already present in the combination with BAO. Future observations and further tests of current observations are needed to determine whether the discrepancy is due to systematics in any of the data sets. Our aim here is not to claim new physics but rather to show that a clear understanding of such tension has a considerable impact on dark energy models: it can be used to provide information on dynamical dark energy and modified gravity, allowing us to test the strength of an effective fifth force.