Bimetric MOND as a framework for variable- G theories: Local systems and cosmology

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 Gₑ 2πG govern the later stages of the expansion, instead of invoking matter density 2π 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 Gₑ 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 Gₑ G in the early Universe, as required by constraints from big-bang nucleosynthesis, but with Gₑ> G setting in at later times, where it can affect the expansion history during the matter-dominated era.