Broader view of bimetric MOND

TL;DR

The paper broadens BIMOND by showing that relativistic MOND can be achieved with a multivariable interaction Lagrangian built from several quadratic scalars derived from the relative-acceleration tensor between two metrics. It derives the general field equations, identifies a subclass with a good nonrelativistic limit where NR phenomenology is governed by a single MOND interpolating function, yet retains a richer relativistic structure for cosmology and lensing. The NR analysis reveals that only a subset of the quadratic scalars contribute to NR dynamics, while other scalars influence cosmology and gravitational waves. It also sketches cosmological solutions with small departures from FLRW and discusses the potential for BIMOND to mimic dark matter effects via a phantom-like stress-energy from the interaction terms. This extended framework thereby opens new avenues for modeling galactic dynamics, lensing, and cosmology without dark matter, while highlighting the context-dependent richness of multi-scalar BIMOND theories.

Abstract

All existing treatments of bimetric MOND (BIMOND) -- a class of relativistic versions of MOND -- have dealt with a rather restricted sub-class: The Lagrangian of the interaction between the gravitational degrees of freedom -- the two metrics -- is a function of a certain {\it 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, {\it 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 {\it a single} acceleration variable -- representing the NR MOND "interpolating function", whose form is largely dictated by the observed NR galactic dynamics. However, these scalars behave differently, in different relativistic contexts. So, the full richness of the multi-variable Lagrangian, as it enters cosmology, for example, is hardly informed by what we learn 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 Friedman-Lemaitre-Robertson-Walker metric. This may offer a framework for describing cosmology within the extended BIMOND.