Poincar\'e, Scale and Conformal Symmetries: Gauge Perspective and
  Cosmological Ramifications
  In the first part of the thesis we focus on local symmetries. We review a
self-consistent framework that we employed in order to discuss the dynamics of
the theories of interest. Its merit lies in that we can make the symmetry group
act internally and thus be effectively separated from coordinate
transformations. We investigate under which conditions it is not needed to
introduce extra compensating fields to make relativistic as well as
nonrelativistic theories invariant under local symmetries and more precisely
under scale transformations. We clarify the role that torsion plays in this
context. We highlight the difference between Weyl and conformal invariance and
we demonstrate that not all conformal theories can be coupled to gravity in a
Weyl invariant way. Once this minimalistic treatment for gauging symmetries is
left aside, new possibilities appear. Namely, if we consider the Poincar\'e
group, the presence of the extra modes leads to nontrivial particle dynamics.
We derive constraints such that the theory is free from pathologies. In the
second part we make clear that even when not gauged, the presence of scale
invariance is appealing. First, it makes possible for the dimensionful
parameters that appear in a theory to be generated dynamically and be sourced
by the vacuum expectation value of the dilaton. If the Standard Model is
embedded into a scale-invariant framework, a number of interesting implications
for cosmology arise. The inflationary stage of our Universe and its present-day
acceleration become linked, a connection that might give us insight into the
dark energy dynamics. We show that in the context of gravitational theories
which are invariant under restricted coordinate transformations, the dilaton
instead of being introduced ad hoc, can emerge from the gravitational part of a
theory. We discuss the consequences of the nontrivial way this field emerges in
the action.
