Bimetric MOND as a framework for variable-$G$ theories -- local systems and cosmology

Abstract

Bimetric MOND (BIMOND) is used as a platform for variable-$G$ theories that have MOND-specific idiosyncrasies. E.g., MOND premises dictate return to standard dynamics in the high-acceleration limit, predicting the standard value of $G$ for high-acceleration systems. This automatically ensures compliance of such theories with all the constraints on inconstancy of $G$ that emerge from the study of high-acceleration systems: geophysics, solar system, pulsars, supernovae, stellar evolution, emission of gravitational waves, etc. In MOND, constraints deduced from such phenomena have no bearing on possible $G$ variability in cosmology. My guiding motivation is to see if such theories may account for some roles of dark matter in cosmology; e.g., in accounting for the expansion history of the Universe in the matter-dominated era, by having a $G_e\approx 2\pi G$ govern the later stages of the expansion, instead of invoking matter density $\approx 2\pi\times$ baryon density. Without adding degrees of freedom, or new dimensionful constants, BIMOND can be extended to a class of theories that entail what is best described as phenomenon-dependence of Newton's constant, $G$. I cannot yet present a consistent model that complies with all the observations in cosmology, including the expansion history, with all its details. Instead, I describe some examples of theories in the class that predict different values of $G_e$ in different circumstances, including one where $G$ takes its standard value for all subcosmological systems -- even if they are deep in the MOND regime. I also discuss scenarios in which $G_e\approx G$ in the early Universe, as required by constraints from big-bang nucleosynthesis, but with $G_e> G$ setting in at later times, where it can affect the expansion history during the matter-dominated era.