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We show that Solar System tests can place very strong constraints on K-mouflage models of gravity, which are coupled scalar field models with nontrivial kinetic terms that screen the fifth force in regions of large gravitational acceleration. In particular, the bounds on the anomalous perihelion of the Moon imposes stringent restrictions on the K-mouflage Lagrangian density, which can be met when the contributions of higher-order operators in the static regime are sufficiently small. The bound on the rate of change of the gravitational strength in the Solar System constrains the coupling strength β to be smaller than 0.1. These two bounds impose tighter constraints than the results from the Cassini satellite and big bang nucleosynthesis. Despite the Solar System restrictions, we show that it is possible to construct viable models with interesting cosmological predictions. In particular, relative to ΛCDM, such models predict percent-level deviations for the clustering of matter and the number density of dark matter haloes. This makes these models predictive and testable by forthcoming observational missions. [ABSTRACT FROM AUTHOR]

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 νGalileon, when assuming its stable attractor background solution, contains the same set of free parameters as lambda cold dark matter (ΛCDM), although it leads to different expansion dynamics and nontrivial gravitational interactions. The data provide compelling evidence (≳6σ) for nonzero neutrino masses, with σmν≳0.4 eV at the 2σ 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≲40 will be able to discriminate between the νGalileon and ΛCDM models. Unlike ΛCDM, the νGalileon model is consistent with local determinations of the Hubble parameter. The presence of massive neutrinos lowers the value of σ8 substantially, despite of the enhanced gravitational strength on large scales. Unlike ΛCDM, the νGalileon model predicts a negative ISW effect, which is difficult to reconcile with current observational limits. [ABSTRACT FROM AUTHOR]