An intriguing feature of scalar-tensor theories is the emergence of different metrics, e.g. when
matter is minimally coupled to a metric non-trivially related to the Einstein metric g[mu,nu] used
to construct the Ricci scalar. Strong equivalence principle constraints then typically force permissible
“many-metric” scenarios to reduce to a bimetric picture. In this thesis we first aim
to construct the most general bimetric relation, where the two metrics are related by a single
scalar degree of freedom [phi] and its derivatives. This results in the disformal metric relation and
a natural extension which we present.
In the context of primordial structure formation, disformal bimetric theories give rise to “general
single field inflation” models of the P(X, [phi]) type. We investigate the perturbative properties
of such disformally motivated models. The focus is on non-Gaussian phenomenology and we
establish non-Gaussian fingerprints for inflationary single field models and non-inflationary bimetric
setups, also going beyond the slow-roll approximation. Furthermore we show that various
dualities exist between disformally motivated P(X, [phi]) theories and higher-form models. As an
explicit example we use the dual picture to compute non-Gaussian signals for three-form theories.
In the context of dark energy/modified gravity, we show that the conformal subgroup of
the general disformal relation can be used to construct a generalized “derivative” Chameleon
setup. We present and investigate this setup and study its phenomenology. Finally we show
that a natural extension of the disformal relation can generate Galileon solutions from a single
geometrical invariant - the first Lovelock term - in four dimensions.
As such the over-arching theme of this thesis is to show that the disformal bimetric picture and
its extensions present us with a geometrical understanding of scalar-tensor/single field models.
That they provide a unified description of large classes of scenarios linked to accelerated space-time
expansion and also point us towards new physically motivated setups.