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Modified theories of gravity yield an effective dark energy in the backgrounddynamics that achieves an accelerated expansion of the universe. In addition,they present a fifth force that induces gravitational signatures in structureformation, and therefore in the matter power spectrum and related statistics.On the other hand, massive neutrinos suppress the power spectrum at scales thatalso modified gravity enhances it, so a degeneration of these effects has beenrecognized for some gravity models. In the present work, we study both effectsusing kinetic gravity braiding (nKGB) models to find that in spite of somedegeneracies, the role of the fifth force at very large scales imprints a bumpin the matter power spectrum as a distinctive signature of this model and,therefore, acts as a smoking gun that seems difficult to match within thepresent knowledge of power spectra. These models result interesting, however,since the n=1 presents no H0 tension, and all nKGB studied here present nosigma8 tension and, in addition, a null neutrino mass is excluded.

Neutrino mass and kinetic gravity braiding degeneracies