Cosmological variation of the MOND constant: secular effects on galactic   systems
  The proximity of the MOND acceleration constant with cosmological accelerations -- for example, a0 cH0/2pi -- points to its possibly decreasing with cosmic time. I begin to consider the secular changes induced in galactic systems by such presumed variations, assumed adiabatic. It is important to understand these effects, in isolation from other evolutionary influences, in order to identify or constrain a0 variations by detection of induced effects, or lack thereof. I find that as long as the system is fully in the deep-MOND regime -- as applies to many galactic systems -- the adiabatic response of the system obeys simple scaling laws. For example, in a system that would be stationary for fixed a0, the system expands homologously as a0^{-1/4}, while internal velocities decrease uniformly as a0^{1/4}. If a0 is proportional to cH at all relevant times, this change amounts to a factor of ~ 2.5 since redshift 10. For a system stationary in a rotating frame, the angular frequency decreases as a0^{1/2}. The accelerations increase relative to a0 as a0^{-1/4}, pushing the system towards the Newtonian regime. All this follows from the appearance of a0 in MOND and the scale invariance of the deep-MOND limit -- two basic tenets of MOND. More complicated evolution ensues when parts of the system become Newtonian, or are so from inception. For example, these parts may become unstable, not being protected by MOND's stabilizing effects. The existence of such regions also modifies the MONDian regime, since they affect the potential everywhere, and since constituents might migrate between the Newtonian and MONDian regimes. Studying these last effects would require detailed numerical calculations. 
Mordehai Milgrom (Weizmann Institute)
astro-ph.GA astro-ph.CO gr-qc hep-ph