Cosmological instability of scalar-Gauss-Bonnet theories exhibiting
  scalarization
  In a subclass of scalar-tensor theories, it has been shown that standard
general relativity solutions of neutron stars and black holes with trivial
scalar field profiles are unstable. Such an instability leads to solutions
which are different from those of general relativity and have non-trivial
scalar field profiles, in a process called scalarization. In the present work
we focus on scalarization due to a non-minimal coupling of the scalar field to
the Gauss-Bonnet curvature invariant. The coupling acts as a tachyonic mass for
the scalar mode, thus leading to the instability of general relativity
solutions. We point out that a similar effect may occur for the scalar modes in
a cosmological background, resulting in the instability of cosmological
solutions. In particular, we show that a catastrophic instability develops
during inflation within a period of time much shorter than the minimum required
duration of inflation. As a result, the standard cosmological dynamics is not
recovered. This raises the question of the viability of scalar-Gauss-Bonnet
theories exhibiting scalarization.
