Cosmological effects of the Galileon term in scalar-tensor theories

We study the cosmological effects of a Galileon term in scalar-tensor theories of gravity. The subset of scalar-tensor theories considered are characterized by a nonminimal coupling FðσÞR, a kinetic term with arbitrary sign Zð∂σÞ2 with Z ¼ 1, a potential VðσÞ, and a Galileon term G3ðσ;ð∂σÞ2Þ□σ. In addition to the modified dynamics, the Galileon term provides a screening mechanism to potentially reconcile the models with general relativity predictions inside a Vainshtein radius. Thanks to the Galileon term, the stability conditions, namely, ghost and Laplacian instabilities, in the branch with a negative kinetic term (Z ¼ −1) are fulfilled for a large volume of the parameter space. Solving numerically the background evolution and linear perturbations, we derive the constraints on the cosmological parameters in the presence of a Galileon term for different combination of the cosmic microwave background data from Planck, baryon acoustic oscillations measurements from BOSS, and supernovae from the Pantheon compilation. We find that the Galileon term alters the dynamics of all the studied cases. For a standard kinetic term (Z ¼ 1), we find that Planck data and a compilation of baryon acoustic oscillations data constrain the Galileon term to small values that allow screening very inefficiently. For a negative kinetic term (Z ¼ −1), a Galileon term and a nonzero potential lead to an efficient screening in a physically viable regime of the theory, with a value for the Hubble constant today which alleviates the tension between its cosmic microwave background and local determinations. For a vanishing potential, the case with Z ¼ −1 and the Galileon term driving the late acceleration of the Universe is ruled out by Planck data.