Aether Scalar Tensor (AeST) theory: Quasistatic spherical solutions and their phenomenology

There have been many efforts in the last three decades to embed the empirical MOND program into a robust theoretical framework. While many such theories can explain the profile of galactic rotation curves, they usually cannot explain the evolution 15 the primordial fluctuations and the formation of large-scale-structures in the Universe. The Aether Scalar Tensor (AeST) theory seems to have overcome this difficulty, thereby providing the first compelling example of an extension of general relativity able to successfully challenge the particle dark matter hypothesis. Here we study the phenomenology of this theory in the quasistatic weak-field regime and specifically for the idealised case of spherical isolated sources. We find the existence of three distinct gravitational regimes, that is, Newtonian, MOND and a third regime characterised by the presence of oscillations in the gravitational potential which do not exist in the traditional MOND paradigm. We identify the transition scales between these three regimes and discuss their dependence on the boundary conditions and other parameters in the theory. Aided by analytical and numerical solutions, we explore the dependence of these solutions on the theory parameters. Our results could help in searching for interesting observable phenomena at low redshift pertaining to galaxy dynamics as well as lensing observations, however, this may warrant proper N-body simulations that go beyond the idealised case of spherical isolated sources.