Modified gravity with massive neutrinos as a testable alternative cosmological model

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 Galileon, when assuming its stable attractor background solution, contains the same set of free parameters as lambda cold dark matter (ACDM), although it leads to different expansion dynamics and nontrivial gravitational interactions. The data provide compelling evidence (greater than or similar to 6 sigma) for nonzero neutrino masses, with Sigma m greater than or similar to 0.4 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 less than or similar to 40 will be able to discriminate between the Galileon and ACDM models. Unlike ACDM, the 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 ACDM, the Galileon model predicts a negative ISW effect, which is difficult to reconcile with current observational limits.