Further theoretical development of self-consistent (stable, absence of various pathologies etc) modified gravity theories, beyond the linear level, screening mechanisms, etc.
Structure formation, EFT approach, N-body simulations
Numerical relativity in the context of modified gravity.
Theoretical studies of GW propagation to connect phenomenology with theories/models of gravity, dark energy, and dark matter
Multiple different possible tests of modified gravity with GWs.
Requires accurate waveforms from inspiral and ringdown phases, as mentioned in
GW section. E.g. in modified gravity theories: asymptotic symmetries to be developed; calculation of quasi-normal modes; system of EMRIs; …
For NS, develop waveform models taking into account tidal effects also in modified gravity theory (possible degeneracies with the unknown equation of state of the NS, and possibly eccentricity).
Testing the propagation of GWs in modified gravity with CBCs (non-trivial dispersion relations, modified gravitational damping etc)
Using GW observations to test the quantum nature of gravity.
BHs and other compact objects in modified gravity and their properties
e.g. For BH, existence or not of a horizon, fuzzballs, no-hair theorems (requires finding stationary metrics solutions of a given modified gravity theory and comparing their characteristics to Kerr),….
For stars, for e.g. further work on the influence of modified gravity on the mass gap between neutron stars and BH. Properties of neutron stars in modified gravity
Other compact objects considered exotic in general relativity (ie demanding exotic presence of matter), e.g. wormholes. Do such objects exist in vacuum of modified gravity theories? How do they differ from black holes? wormhole throat versus horizon, null geodesics and light rings etc.
EHT: using images and of the light-ring together with GRAVITY+ (orbits of stars around Sgr A*), tests of GR and in particular the no-hair theorem.
Impact on astrophysics: EHT+GWs could confirm existence of super-massive BHs, and their abundance and mass distribution. How are they formed? Idem for stellar and intermediate mass black holes.