Generalised Proca Theories
  In this work we will summarise the recent progress made in constructing
consistent theories for a massive vector field with derivative
self-interactions. The construction is such that only the three desired
polarisations of the Proca field propagate. We apply a systematic construction
of the interactions by using the anti-symmetric Levi-Civita tensors. This
finite family of allowed derivative self-interactions can be also obtained from
the decoupling limit by imposing that the St\"uckelberg field only contains
second derivatives both with itself and with the transverse modes. These
interactions can be generalised to curved backgrounds, which relies on the
presence of non-minimal couplings and constitutes a general family of
vector-tensor interactions. We discuss also some extensions of these
interactions by alleviating the restriction of second order nature of the
equations or by imposing global symmetries. We will also comment on their
interesting cosmological applications.
