Broader view of bimetric MOND

All existing treatments of bimetric MOND (modified Newtonian dynamics) (BIMOND)-a class of relativistic versions of MOND-have dealt with a rather restricted subclass: The Lagrangian of the interaction between the gravitational degrees of freedom-the two metrics-is a function of a certain single scalar argument built from the difference in connections of the two metrics. I show that the scope of BIMOND is much richer: The two metrics can couple through several scalars to give theories that all have a good nonrelativistic (NR) limit-one that accounts correctly, a la MOND, for the dynamics of galactic systems, including gravitational lensing. This extended-BIMOND framework exhibits a qualitative departure from the way we think of MOND at present, as encapsulated, in all its aspects, by one interpolating function of one acceleration variable. After deriving the general field equations, I pinpoint the subclass of theories that satisfy the pivotal requirement of a good NR limit. These involve three independent, quadratic scalar variables. In the NR limit these scalars all reduce to the same acceleration scalar, and the NR theory then does hinge on one function of a single acceleration variable-representing the NR MOND interpolating function, whose form is largely dictated by the observed NR galactic dynamics. However, these scalars take different values and behave differently in different relativistic contexts. So, the full richness of the multivariable Lagrangian, as it enters cosmology, for example, or gravitational-wave dynamics, is hardly informed by what we learn of MOND from observations of galactic dynamics. In this paper, I present the formalism, with some generic examples. I also consider some cosmological solutions where the two metrics are small departures from one Friedmann-Lemaitre-Robertson-Walker metric. This may offer a framework for describing cosmology within the extended BIMOND.

Automated summary

All existing treatments of bimetric MOND (modified Newtonian dynamics) have only considered a restricted subclass, but the scope of BIMOND is much richer. The two metrics can couple through several scalars, giving theories that have a good nonrelativistic limit. These theories can account for the dynamics of galactic systems, including gravitational lensing, and show a departure from the current understanding of MOND.