Abstract
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.
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