The origin of MOND acceleration and deep-MOND behavior from mass and
  energy cascade in dark matter flow
  The MOND paradigm is an empirical theory with modified gravity to reproduce
many astronomical observations without invoking the dark matter hypothesis.
Instead of falsifying the existence of dark matter, we propose that MOND is an
effective theory naturally emerging from the long-range and collisionless
nature of dark matter flow. It essentially describes the dynamics of baryonic
mass suspended in fluctuating dark matter fluid. We first review the unique
properties of self-gravitating collisionless dark matter flow (SG-CFD),
followed by their implications in the origin of MOND theory. To maximize system
entropy, the long-range interaction requires a broad size of halos to be
formed. These halos facilitate an inverse mass and energy cascade from small to
large mass scales that involves a constant rate of energy transfer
$\epsilon_u$=$-4.6\times10^{-7}m^2/s^3$. In addition to the velocity
fluctuation with a typical scale $u$, the long-range interaction leads to a
fluctuation in acceleration with a typical scale $a_0$ that matches the value
of critical MOND acceleration. The velocity and acceleration fluctuations in
dark matter flow satisfy the equality $\epsilon_u$=$-a_0u/(3\pi)^2$ such that
$a_0$ can be determined. A notable (unexplained) coincidence of cosmological
constant $\Lambda\propto (a_0/c)^2$ might point to a dark energy density
proportional to acceleration fluctuation, i.e. $\rho_{vac}\propto a_0^2/G$. At
z=0 with $u$=354.61km/s, $a_0$=$1.2\times10^{-10}m/s^2$ can be obtained. For
given particle velocity $v_p$, maximum entropy distributions developed from
mass/energy cascade lead to a particle kinetic energy $\epsilon_k\propto v_p$
at small acceleration $<a_0$ and $\epsilon_k\propto v_p^2$ for large
acceleration $>a_0$. Combining this with the constant rate of energy transfer
$\epsilon_u$, both regular Newtonian dynamics and deep-MOND behavior can be
fully recovered.
