Cosmological fluctuation growth in bimetric MOND

Abstract

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, Λ ∼ (a0/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 TM 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 back reaction on cosmology of BIMOND effects that appear as "phantom matter" (interpreted by some as "dark matter"), resulting from inhomogeneity differences between the two sectors.PACS numbers: 95.35.+d

Testing quasilinear modified Newtonian dynamics in the Solar System

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A novel MOND effect in isolated high-acceleration systems

“…In this theory, the MOND potential for an isolated system is the (unique) solution of the equation (Bekenstein & Milgrom ) with ∇φ → 0 at infinity. This is the non‐relativistic limit of Einstein aether theories (Zlosnik, Ferreira & Starkman ), and it is also part of the non‐relativistic limit of tensor‐vector‐scalar gravity (TeVeS) (Bekenstein ) and of generic formulations of BIMOND (Milgrom , ).…”

Propagation of gravitational waves in multimetric gravity

“…Note that in addition to the recently discussed theories with N ! 3 this also includes bimetric gravity theories such as [4][5][6]; see [7] for an overview of bimetric theories and a discussion of their weak field limits. In particular, we aim to calculate two properties of gravitational waves which are expected to be accessible by the upcoming detector experiments.…”

“…We then employ the Newman-Penrose formalism to show that two to six polarizations of gravitational waves may exist, depending on the parameters entering the field equations. This corresponds to E (2) representations N 2 , N 3 , III 5 and II 6 . We finally apply our general discussion to a recently presented concrete multimetric gravity model and show that it is of class N 2 , i.e., it allows only two tensor polarizations, as it is the case for general relativity.…”