Vainshtein Mechanism in Certain Tensor-Scalar Theories

We explore the space of spherically symmetric, static solutions of certain nonlinear tensor-scalar theories that are invariant under linear diffeomorphisms and global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological interaction terms which are shown not to renormalize at any order in perturbation theory. Interestingly, such theories naturally emerge in a high energy limit of two parameter ghost-free massive gravity.;In Chapter one, we focus on a sub-class of these theories where the Galileons can be completely decoupled from the tensor Lagrangian. In massive gravity, these Galileons differ from generic ones; they have interrelated coefficients of the cubic and quartic terms, and most importantly, a non-standard coupling to external stress-tensors governed by the same coefficient. We show that unlike the General Galileons, this theory has no static stable spherically symmetric solutions that would interpolate from the Vainshtein region to flat space; these two regions cannot be smoothly matched for the sign of the coefficient for which fluctuations are stable. Instead, for this sign choice, a solution in the Vainshtein domain is matched onto a cosmological background. Small fluctuations above this solution are stable and sub-luminal. We discuss observational constraints on this theory within the quantum effective Lagrangian approach and argue that having a graviton mass of the order of the present-day Hubble parameter is consistent with data.;In Chapter two, we complete our analysis by extending it to cover the whole parameter space of massive gravity. We find that the stability argument renders the asymptotically flat backgrounds unrealizable, forcing upon us the cosmological asymptotics. In the case of pressure-less, sources these backgrounds are stable as well. However, they become destabilized in the presence of positive pressure larger than the critical density. Even on the self-accelerated background on which the longitudinal component of the massive graviton decouples from sources, the region occupied by the source acquires the elliptic equation of motion. Therefore, we conclude that the only parameter space of massive gravity which is not ruled out by the solar system measurements, is the one considered in Chapter one.