Cosmological fluctuation growth in bimetric MOND

I begin to look at the growth of weak density inhomogeneities of nonrelativistic matter, in bimetric-MOND (BIMOND) cosmology. Far from making an exhaustive study, I concentrate on one attractive cosmological scenario, which employs matter-twin-matter-symmetric versions of BIMOND, and, furthermore, assumes that, on average, the universe is symmetrically populated in the two sectors. MOND effects are totally absent in an exactly symmetric universe, apart from the significant possible appearance of a cosmological constant, $\Lambda \sim (a_0/c{)}^2$. MOND effects—local and cosmological—do enter when density inhomogeneities that differ in the two sectors appear and develop. MOND later takes its standard form in systems that are islands dominated by pure matter, as are presumably the well scrutinized systems such as galaxies. I derive the nonrelativistic (weak-field-slow-motion) equations governing small-scale fluctuation growth. The equations split into two uncoupled systems, one for the sum, the other for the difference, of the fluctuations in the two sectors. The former is governed strictly by Newtonian dynamics, and describes standard growth of fluctuations. The latter is governed by MOND dynamics, which entails stronger gravity, and nonlinearity even for the smallest of perturbations. These cause the difference to grow faster than the sum, leading to anticorrelated perturbations, conducing to matter-twin-matter segregation (which continues for high overdensities). The nonlinearity also causes interaction between nested perturbations on different scales. Because matter and twin matter (TM) repel each other in the MOND regime, matter inhomogeneities grow not only by their own self-gravity, but also through shepherding by flanking twin matter overdensities (and vice versa). The relative importance of gravity and pressure in the MOND system (analog of the Jeans criterion), depends also on the strength of the perturbation. MOND gravity, which scales as the square root of the difference perturbation, holds sway over pressure for any mass, for weak enough perturbations. The development of structure in the universe, in either sector, thus depends crucially on two initial fluctuation spectra: that of matter alone and that of the matter-TM difference. I also discuss the backreaction on cosmology of BIMOND effects that appear as “phantom matter” (interpreted by some as “dark matter”), resulting from inhomogeneity differences between the two sectors.