§ Quantigicr Solutions LLC

We discuss non-perturbative dynamics of massive gravity in de Sitter space via gravitational Higgs mechanism. We argue that enhanced local symmetry and null (ghost) state at (below) the perturbative Higuchi bound are mere ar-tifacts of not only linearization but also assuming the Fierz-Pauli mass term. We point out that, besides de Sitter, there are vacuum solutions where the space asymptotically is de Sitter both in the past and in the future, the space first contracts, this contraction slows down, and then reverses into expansion, so there is an epoch where the space is (nearly) flat. We confirm this by con-structing a closed-form exact solution to full non-perturbative equations of motion for a “special ” massive de Sitter case. We give a formula for the “crit-ical ” mass above which such solutions apparently do not exist. For the Fierz-Pauli mass term this “critical ” mass coincides with the perturbative Higuchi bound, which serves as the non-perturbative reinterpretation of the latter. We argue that, notwithstanding the perturbative ghost, non-perturbatively there is no “instability”. Instead, there are additional vacuum solutions that may have interesting cosmological implications, which we briefly speculate on. 1Email