Matter and twin matter in bimetric MOND

Bimetric MOND (BIMOND) theories, propounded recently, predict peculiar gravitational interactions between matter and twin matter (TM). TM is the hypothetical matter that might couple directly only to the second metric of the theory, as standard matter couples only to the first. Considerations of cosmology in the BIMOND framework suggest that such TM might exist and copy matter in its attributes. Here, I investigate the indirect interactions that BIMOND theories predict between local, non-relativistic mass concentrations of matter and TM. The most salient result is that in the deep-MOND regime of the matter-TM symmetric theories, TM behaves as if it has a negative gravitational mass relative to matter (active and passive, with the inertial mass still positive). To wit, interaction within each sector is attractive MOND gravity, but between matter and TM it is repulsive MOND gravity. Using the space-conformal invariance of the theory in the deep-MOND regime, I derive various exact results; e. g. the repulsive force between a matter and TM point masses (space-conformal theories are a natural framework for masses of opposite signs). In the high-acceleration regime, the interaction depends on a parameter, beta (the strength of the Einstein-Hilbert action for matter). For the favoured value beta = 1, matter and TM do not interact in this regime, for beta < 1 they attract and for beta > 1 they repel each other. Such interactions may have substantial ramifications for all aspects of structure formation, such as matter distribution, peculiar velocities and effects on the cosmic microwave background. The repulsive interactions probably lead to segregation of matter and TM structures, leading, in turn, to intermeshing of the respective cosmic webs, with high-density nodes of one sector residing in the voids of the other (possibly conducing to efficient evacuation of the voids). Weak gravitational lensing by TM seems the best way to detect it or constrain its attributes. In the MOND regime, a TM body acts on matter photons as a diverging lens. Strong lensing occurs in the high-acceleration regime and thus depends on beta. For beta = 1, a TM mass does not bend (matter) light in the high-acceleration regime: no strong lensing effects of TM are expected in this case. I also discuss briefly asymmetric theories.