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Precision Gravity: From the LHC to LISA

Periodic Reporting for period 2 - LHCtoLISA (Precision Gravity: From the LHC to LISA)

Reporting period: 2020-12-01 to 2022-05-31

The observation of gravitational waves by LIGO/VIRGO started a new era for astronomy. The discovery potential of this nascent field largely hinges upon the ability to make precise theoretical predictions. Reliable templates are critical for successful data analysis and interpretation of the signals. The goal of LHCtoLISA project is to push forward the frontiers of analytic understanding in gravitational dynamics through the Effective Field Theory framework. The novel formalism, that the PI and collaborators have developed, has been instrumental for the construction of the state-of-the-art gravitational wave template bank. The high-accuracy calculations the project will undertake will have enormous implications, from probing strongly interacting matter to enabling the discovery of exotic compact objects and putative ultralight particles in nature.
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 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 reached the state-of-the-art for the 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 state-of-the-art at 3PM order.
We have opened a completely new direction to tackle the two-body dynamics of compact objects borrowing ideas from particle physics and the theory of scattering amplitudes. Our EFT framework endowed with novel computational techniques has demonstrated its ability to push forward our understanding of binary dynamics, providing the present state-of-the-art both in the Post-Newtonian and Post-Minkowskian regime at 4PN and 4PM orders, respectively. We are now progressing smoothly towards the benchmark at 5PN.