Fifth forces and discrete symmetry breaking
  Modifications of general relativity often involve coupling additional scalar
fields to the Ricci scalar, leading to scalar-tensor theories of Brans-Dicke
type. If the additional scalar fields are light, they can give rise to
long-range fifth forces, which are subject to stringent constraints from local
tests of gravity. In this talk, we show that Yukawa-like fifth forces only
arise for the Standard Model (SM) due to a mass mixing of the additional scalar
with the Higgs field, and we emphasise the pivotal role played by discrete and
continuous symmetry breaking. Quite remarkably, if one assumes that
sufficiently light, non-minimally coupled scalar fields exist in nature, the
non-observation of fifth forces has the potential to tell us about the
structure of the SM Higgs sector and the origin of its symmetry breaking.
Moreover, with these observations, we argue that certain classes of
scalar-tensor theories are, up to and including their dimension-four operators,
equivalent to Higgs-portal theories. In this way, ultra-light dark matter
models may also exhibit fifth-force phenomenology, and we consider the impact
on the dynamics of disk galaxies as an example.
