$\nu$Galileon: modified gravity with massive neutrinos as a testable alternative to $\Lambda$CDM

We show that, in the presence of massive neutrinos, the Galileon gravity model provides a very good fit to the current CMB temperature, CMB lensing and BAO data. This model, which we dub ${\nu} \rm{Galileon}$, when assuming its stable attractor background solution, contains the same set of free parameters as $\Lambda\rm{CDM}$, although it leads to different expansion dynamics and nontrivial gravitational interactions. The data provide compelling evidence ($\gtrsim 6\sigma$) for nonzero neutrino masses, with $\Sigma m_\nu \gtrsim 0.4\ {\rm eV}$ at the $2\sigma$ level. Upcoming precision terrestrial measurements of the absolute neutrino mass scale therefore have the potential to test this model. We show that CMB lensing measurements at multipoles $l \lesssim 40$ will be able to discriminate between the ${\nu} \rm{Galileon}$ and $\Lambda\rm{CDM}$ models. Unlike $\Lambda\rm{CDM}$, the ${\nu} \rm{Galileon}$ model is consistent with local determinations of the Hubble parameter. The presence of massive neutrinos lowers the value of $\sigma_8$ substantially, despite of the enhanced gravitational strength on large scales. Unlike $\Lambda\rm{CDM}$, the ${\nu} \rm{Galileon}$ model predicts a negative ISW effect, which is difficult to reconcile with current observational limits.