Minimal dark energy: key to sterile neutrino and Hubble constant
  tensions?
  Minimal dark energy models, described by the same number of free parameters
of the standard cosmological model with cold dark matter plus a cosmological
constant to parameterize the dark energy component, constitute very appealing
scenarios which may solve long-standing, pending tensions. On the one hand,
they alleviate significantly the tension between cosmological observations and
the presence of one sterile neutrino motivated by the short-baseline anomalies:
we obtain a $95\%$ CL cosmological bound on the mass of a fully thermalized
fourth sterile neutrino ($N_{\rm eff}=4$) equal to $m_s<0.65\ (1.3)$~eV within
the PEDE (VM) scenarios under consideration. Interestingly, these limits are in
agreement with the observations at short-baseline experiments, and the PEDE
scenario is favored with respect to the $\Lambda$CDM case when the full data
combination is considered. On the other hand, the Hubble tension is
satisfactorily solved in almost all the minimal dark energy schemes explored
here. These phenomenological scenarios may therefore shed light on differences
arising from near and far universe probes, and also on discrepancies between
cosmological and laboratory sterile neutrino searches.
