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.
