Some cosmological models with non-negligible dark energy fractions, in particular windows of the prerecombination epoch, are capable of alleviating the Hubble tension quite efficiently, while keeping the good description of the data that are used to build the cosmic inverse distance ladder. There has been an intensive discussion in the community on whether these models enhance the power of matter fluctuations, leading de facto to a worsening of the tension with the large-scale structure measurements. We address this pivotal question in the context of several early dark energy (EDE) models, considering also in some cases a coupling between dark energy and dark matter, and the effect of massive neutrinos. We fit them using the Planck 2018 likelihoods, the supernovae of Type Ia from the Pantheon compilation, and data on baryon acoustic oscillations. We find that ultralight axion-like (ULA) EDE can actually alleviate the $H_0$ tension without increasing the values of ${\sigma }_{12}$ with respect to those found in the $\mathrm{\Lambda }\mathrm{CDM}$, whereas EDE with an exponential potential does not have any impact on the tensions. A coupling in the dark sector tends to enhance the clustering of matter, and the data limit greatly the influence of massive neutrinos, since the upper bounds on the sum of their masses are too close to those obtained in the standard model. We find that in the best case, namely ULA, the Hubble tension is reduced to $\sim 2\sigma$.

• Received 3 August 2022
• Accepted 18 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.103522