  Quadratic gravity is a UV completion of general relativity, which also solves
the hierarchy problem. The presence of 4 derivatives implies via the
Ostrogradsky theorem that the $classical$ Hamiltonian is unbounded from below.
Here we solve this issue by showing that the relevant solutions are not
unstable but metastable. When the energies are much below a threshold (that is
high enough to describe the whole cosmology) runaways are avoided. Remarkably,
the chaotic inflation theory of initial conditions ensures that such bound is
satisfied and we work out testable implications for the early universe. The
possible instability occurring when the bound is violated not only is
compatible with cosmology but would also explain why we live in a homogeneous
and isotropic universe.
