Scalar fields and gravity

In this thesis we discuss scalar field theories, and their applications to gravity. We provide a summary of why there is interest in modifying Einstein’s General Relativity, and discuss why scalar fields make a good candidate for a modification to make. We demonstrate their effects on the dynamics of matter, and discuss the necessity of screening mechanisms in order for these scalar fields to not be ruled out by current observations. We present discussion on two screening mechanisms in particular, the Chameleon and Vainshtein mechanisms. We then present work that aims to study the soft behaviour of scattering amplitudes belonging to single scalar field theories. We generalise current techniques in the literature such that the study of a much wider set of theories is possible. We use this technique to perform a detailed study of a particular family of theories, a so called (1, 2) theory, and demonstrate that the DBI symmetry is the unique way to enhance the soft behaviour of the scattering amplitudes of this family. We also identify the special Galileon as the unique way to maximally enhance the soft behaviour within the (1, 2) class, and verify the validity of recursion techniques to calculate scattering amplitudes. We then move on to studying the Chameleon in more detail. We provide motivation for modifying its high energy behaviour by studying the ‘surfer solution’, and use this to propose the DBI-Chameleon. We demonstrate that this theory avoids the problems the Chameleon suffers in the early Universe and forms a good effective field theory in this regime. Finally we present a UV complete theory describing a massive Galileon, and study its dynamics to verify if it exhibits Vainshtein screening. Theories with Vainshtein screening are usually unable to be UV completed in a Wilsonian way. We present our preliminary findings which suggest screening is possible for at least some parameter values