1) We have used the effective field theory (EFT) approach to compute the conservative dynamics for binary systems to next-to-next-to-next-to-next-to leading order (NNNNLO) in the Post-Newtonian regime (4PN order). This is the state-of-the-art in PN theory.
2) We have demonstrated the ability of the EFT framework to tackle also the dynamics of large-scale structures, reaching the state-of-the-art at third order in density fluctuations.
3) Following modern tools for the study of scattering processes, we have developed a map, coined the "boundary to bound" (B2B) dictionary, to relate scattering data to observables for bound orbits. This has opened a new path to using powerful tools from scattering amplitudes and novel integration techniques to study the binary problem.
4) We have developed an EFT formalism to tackle the scattering problem in the Post-Minkowskian (PM) regime.
5) We have used this novel PM EFT to reach the state-of-the-art (at the time) at third PM order.
6) We have incorporated quadrupolar and octupolar tidal effects to NLO using the PM EFT, yielding the present state-of-the-art.
7) We have also developed the concept of 'gravitational collider physics' – using gravitational wave precision data to constrain the nature of compact objects.
8) We have extended the B2B dictionary relating scattering data and observables for bound orbits to incorporate radiation effects in the two-body problem.
9) We have used the EFT framework in the PN regime to compute the spin-dependent contribution to the gravitational wave phase evolution to 3PN and 4PN orders, corresponding to the state-of-the-art for spin effects in the literature.
10) Using the EFT formalism in the PM regime we have obtained for the first time the complete dynamics of spinning binaries at 2PM order.
11) We have computed radiative effects (including hereditary contributions) to 3PN orders for hyperbolic orbits.
12) In collaboration with other groups we have computed the radiative moments needed to complete the gravitational wave flux to 4PN order.
13) We have derived the conservative Keplerian solution to 4PN for eccentric orbits.
14) Using the EFT framework in the PM scheme we have computed the conservative dynamics of non-spinning binary systems including potential and radiation-reaction tail effects to 4PM order. This result includes an infinite tower of velocity corrections at all PN orders at O(G^4).
15) We have extended the EFT formalism to incorporate dissipative effects and rederived the total impulse at 3PM order.
16) We have computed for the first time the complete conservative and dissipative dynamics of non-spinning binaries to 4PM order. Our results have been confirmed by independent derivations and used to compute extremely accurate models that match numerical simulations with exquisite precision for hyperbolic-type encounters.
17) We have put forward a fully systematic framework to "bootstrap" the relativistic two-body problem from the knowledge in the regime of small velocities, by using novel integration techniques from collider physics such as the use of differential equations and method of regions.
18) In collaboration with another group we have completed the knowledge of the gravitational-wave phase evolution for non-spinning binaries at 4PN order. Preliminary work has been done to include spin effects at 5PN order.
19) We have shown that the vanishing of tidal response functions (Love numbers) still applies in the non-linear gravitational regime.
20) The local (universal) contribution to the conservative dynamics at O(G^4) – and all orders in velocity – was obtained in our group for the first time, providing the most accurate description of gravitationally-bound two-body systems harnessing information from scattering processes to date.
21) The contributions from all of the (non-linear) hereditary effects needed to complete the 5PN dynamics of binary systems have been obtained, resolving a long-standing discrepancy with previous computations in the literature.
22) We have demonstrated how the existence of ultralight dark matter cloud surrounding black holes in binary systems can leave an imprint in the evolution of the orbital parameters in binary black hole mergers.
