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

TL;DR

This work tests whether a coupling between dark energy and dark matter, producing an effective fifth force with strength $β^2$, can be constrained by Planck CMB data. By implementing coupled dark energy in the CAMB code via the IDEA framework and performing a COSMOMC Monte Carlo analysis, the authors compare Planck data with external probes (BAO or HST) to break the degeneracy with the distance to last scattering. They find a small preference for non-zero coupling, with $β \approx 0.036 \pm 0.016$ (PlanckWP+BAO) and $β \approx 0.066 \pm 0.018$ (PlanckWP+HST), the latter driven by $H_0$ tension and corresponding to a Brans–Dicke parameter $ω_{BD} \approx 56$–$191$. While not claiming new physics, the paper demonstrates that Planck data can yield informative constraints on dynamical dark energy and modified gravity, highlighting potential degeneracies with $H_0$ and emphasizing the need for future datasets to clarify systematics and the true nature of any observed deviations.

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%.

Figures (4)

• Figure 1: CMB temperature spectra for three values of $\beta$ (in agreement with pettorino_etal_2012, inserted here for reference).
• Figure 2: Confidence contours for the cosmological parameters for coupled quintessence models. We compare runs PlanckWP + BAO (green) and PlanckWP + HST (blue). 1 $\sigma$ and 2 $\sigma$ contours are shown.
• Figure 3: 1D likelihoods for the cosmological parameters for coupled quintessence models. We compare runs from Planck WP + BAO (green) and Planck WP + HST (blue). As expected, in coupled quintessence models, no dependence is seen on the value of $\sigma$ and $w$, which are arbitrary and related to each other, as illustrated in the text.
• Figure 4: This figure (based on Fig.3 of hou_etal_2012) investigates the consistency between CMB and BAO$_{BOSS}$ and $H_0$ datasets for a coupled dark energy model. We compare runs Planck WP + BAO (green) and Planck WP + HST (blue). 1$\sigma$ and 2$\sigma$ contours are shown. The grey ellipses correspond to the 1$\sigma$ and 2$\sigma$ region ellipses drawn in Fig.3 of hou_etal_2012, which refer to the combination $BAO_{BOSS}$ + $H_0$ (with $H_0$ from riess_etal_2011). The horizontal (vertical) solid and dashed lines mark the central value and 1$\sigma$ region.