Cosmology is then not simply an application of a relativistic version of MOND but a unit with it. The key to finding the underlying theory may lie in understanding first how an acceleration of cosmological significance can, at all, enter local dynamics, which I discuss in the last section.

If *a*_{0} is a fingerprint of
cosmology on local dynamics, it is not necessarily the identification
*a*_{0} ~ *a*_{ex}
*cH*_{0}
which is the the right one.
There are other cosmological acceleration scales
[30]
[3]
[31]
such as *a*_{c}
*c*^{2} /
*R*_{c}, where *R*_{c} is the
curvature radius (spatial or space-time), or
*a*_{}
*c*
^{1/2},
where is the
cosmological constant. Today we have only upper limits on
*a*_{c}, which
is of the order of *a*_{ex}. Several pieces of evidence
seem now to imply a non-zero cosmological-constant with
~
*H*_{0}^{2}. If this is true then we also have
*a*_{0} ~
*a*_{}.
Thus *a*_{0} might be a proxy for any of the cosmological
acceleration parameters.
Since these depend differently on cosmic time, *a*_{0} may vary
with cosmic time in a way that is difficult to know without
the correct identification. Such possible variation of
*a*_{0} has
obvious ramifications for the formation and the ensuing evolution
of galactic systems.

Even without a theory we can make out some semi-quantitative aspects by which MOND cosmology must differ greatly from standard cosmology:

1. MOND is based on the phenomenology of galactic systems and hence, in
principle, is not committed on the question of cosmologically
homogeneous component of dark matter. But certainly, it is in the spirit
of MOND that we should not conjecture the existence of any DM component
without first trying to
explain it away with new physics. Recent leanings toward a non-zero
cosmological constant(CC) are a step in this direction. And perhaps
[25]
the same mechanism that produces a
CC-like contribution might also effect MOND (hence the coincidence
*a*_{0} ~ *c*
^{1/2}).
At any event, a MOND-inspired cosmology would start with no dark matter.

2. The MOND Jeans mass-a basic concept in structure formation, which
indicates which masses are likely to collapse from an homogeneous
medium-depends differently on the temperature, *T*,
and density, ,
of the medium[30]:
*M*_{J}(*MOND*)
*T*^{2}
/ *a*_{0}, instead of the Newtonian dependence
*M*_{J}
*T*^{3/2}
^{-1/2}.

3. The acceleration in a collapsing system increases as the collapse
proceeds (after detachment from the Hubble flow). If
*a*_{0} varies
at all, it is expected to decrease with cosmic time. So, the effect of
MOND is expected to decrease with time in a collapsing system.
(The system would behave as if the fraction of
fictitious dark matter it harbors decreases with time.)

In default of a theory one can still
attempt to obtain approximate MOND cosmologies-in order to get a hint
of what is expected-by supplementing nonrelativistic MOND with
extra assumptions. For instance, one might assume that
*a*_{0} does not vary with
cosmic time, identifying it with a veritable cosmological constant
[30].
This is done in ref.
[32]
where some further
tentative assumptions are made. In such a case one is bound to ask
why it is that this constant *a*_{0} is today of the same
order as the variable *c**H*_{0}. The same question
arises in connection with the emerging value of the cosmological constant
~
*H*_{0}^{2}.
In MOND, at any rate, this could find an antropic explanation whereby
structure formation (hence star formation and the eventual development
of mankind) is facilitated when the acceleration within the horizon
(~ *c**H*_{0}) - decreasing as it does with cosmic
time - becomes similar to the crucial dynamical constant
*a*_{0}
[30]
[32].