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Matter and twin matter in bimetric MOND

Bimetric MOND (BIMOND) theories, propounded recently, predict peculiar gravitational interactions between matter and twin matter (TM). Twin matter is hypothetical matter that might couple directly only to the second metric of the theory. 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 nonrelativistic masses 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. To wit, interaction within each sector is attractive MOND gravity, but between matter and TM it is repulsive MOND gravity. In the high-acceleration regime, the interaction depends on a parameter, beta. For the favored 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 CMB. 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 lensing by TM seems the best way to 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 the value of beta. For beta=1 no strong lensing effects of TM are expected. I also discuss briefly asymmetric theories (abridged).