http://arxiv.org/abs/2203.05606
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.
Z. Xu
Mon, 14 Mar 22
19/67
Comments: 20 pages, 8 figures