Modified gravity with massive neutrinos as a testable alternative cosmological model

Abstract

We show that, in the presence of massive neutrinos, the Galileon gravity model provides a very good fit to the current cosmic microwave background (CMB) temperature, CMB lensing and baryonic acoustic oscillation data. This model, which we dub $\ensuremath{\nu}\text{Galileon}$, when assuming its stable attractor background solution, contains the same set of free parameters as lambda cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$), although it leads to different expansion dynamics and nontrivial gravitational interactions. The data provide compelling evidence ($\ensuremath{\gtrsim}6\ensuremath{\sigma}$) for nonzero neutrino masses, with $\mathrm{\ensuremath{\Sigma}}{m}_{\ensuremath{\nu}}\ensuremath{\gtrsim}0.4\text{ }\text{ }\mathrm{eV}$ at the $2\ensuremath{\sigma}$ 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 $l\ensuremath{\lesssim}40$ will be able to discriminate between the $\ensuremath{\nu}\text{Galileon}$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ models. Unlike $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, the $\ensuremath{\nu}\text{Galileon}$ model is consistent with local determinations of the Hubble parameter. The presence of massive neutrinos lowers the value of ${\ensuremath{\sigma}}_{8}$ substantially, despite of the enhanced gravitational strength on large scales. Unlike $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, the $\ensuremath{\nu}\text{Galileon}$ model predicts a negative ISW effect, which is difficult to reconcile with current observational limits.