Scalar modes in extended hybrid metric-Palatini gravity: Weak field phenomenology

We investigate the nature of additional scalar degrees of freedom contained in extended hybrid metric-Palatini gravity, outlining the emergence of two coupled dynamical scalar modes. In particular, we discuss the weak field limit of the theory, both in the static case and from a gravitational waves perspective. In the first case, performing an analysis at the lowest order of the postparametrized Newtonian structure of the model, we stress the settling of Yukawa corrections to the Newtonian potential. In this respect, we show that one scalar field can have long range interactions as used in the principle for mimicking dark matter effects. Concerning the gravitational waves propagation, instead, we demonstrate that it is possible to have well-defined physical degrees of freedom, provided by suitable constraints on model parameters. Moreover, the study of the geodesic deviation points out the presence of breathing and longitudinal polarizations due to these novel scalar waves, which on peculiar assumptions can give rise to beating phenomena during their propagation.