Throughout the program, the PI has made significant key developments in constraining massive gravity and other effective field theories that describe different periods of our Universe (inflation, pre big bang, dark energy, physics beyond the standard model, etc…) and has been exported to a wide range of physical systems:
* The PI and her collaborators have unleashed an infinite number of new low-energy constraints that severally constrain any low-energy field theory applicable to cosmology and physics beyond the standard model. In addition, these constraints have been generalized to theories with arbitrary field content, both bosonic and fermionic, including massive gravity using a newly uncovered transversity formalism.
Throughout this program, these newly uncovered bounds were further applied to gravitational effective field theories, massive Galileons and massive gravity, which was shown to satisfy a set of improved positivity bounds while remaining weakly coupled.
* In parallel, the program developed a new class of Proca effective field theory which shown to be relevant for cosmology and potentially providing a new model of dark energy consistent with cosmological history which alleviating the Hubble tension and naturalness issues. The implications of the positivity bounds were derived for all Proca theories where island of consistent regions of parameter space were identified.
* The connection between positivity bounds and causality bounds was explored throughout this ERC program. Importantly, the program has allowed to establish how constraints from high energy completion can be manifested directly at the level for the low-energy EFT via the statement of `infrared causality' which can be applied with has the great benefit of being directly applicable when gravity is dynamical and in curved spacetime. Interestingly, the program proved an exact connection between infrared causality and positivity bounds in situations where both bounds are known and under control. These criteria were then applied to generic shift symmetric EFTs and will be directly relevant for models of dark energy and cosmology more generally.
* In addition the ERC program has allowed to establish the first fully four-dimensional non-linear numerical code that accounts for the behavior of the Vainshtein mechanism in time-dependent systems, relevant for models of modified gravity such as massive gravity.
* Finally, the program has allowed to established new classes of multi-band gravitational constraints that can be used to test theories that modify gravity at low-energy (including potentially massive gravity) and other dark energy EFTs.
