paper

On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy

arXiv:2203.05606 · doi:10.3847/1538-4357/adaeb3

Abstract

Universal acceleration $a_{0}$ emerges in various empirical laws, yet its fundamental nature remains unclear. Using Illustris and Virgo N-body simulations, we propose $a_{0}$ is the scale of acceleration fluctuations in collisionless dark matter involving long-range gravity. In contrast, in the kinetic theory of gases, molecules undergo random elastic collisions involving short-range interactions, where only velocity fluctuations are relevant. We identify the redshift evolution $a_{0} \propto (1 + z)^{3/4}$ that is in good agreement with Magneticum and EAGLE simulations and in reasonable agreement with limited observations. This suggests a larger $a_{0}$ at a higher redshift such that galaxies of fixed baryonic mass rotate faster at a higher redshift. The velocity fluctuations involve a critical velocity $u_{c} \propto (1 + z)^{- 3/4}$ . The acceleration fluctuations involve a critical acceleration $a_{c} \propto (1 + z)^{3/4}$ . Two critical quantities are related by the rate of energy cascade $ε_{u} \approx - a_{c} u_{c} / [2 (3 I ¨ )^{2}]$ , where factor $3 I ¨ $ is from the angle of incidence and $ε_{u} \approx - 1 0^{- 7}$ m $^{2}$ /s $^{3}$ . With critical velocity $u_{c}$ on the order of 300 km/s at $z = 0$ , the critical acceleration is determined to be $a_{c 0} \equiv a_{c} (z = 0) \approx 1 0^{- 10}$ m/s $^{2}$ , suggesting $a_{c}$ might explain the universal acceleration $a_{0} \approx 1 0^{- 10}$ m/s $^{2}$ in the empirical Tully-Fisher relation or modified Newtonian dynamics (MOND). Note that dark energy (DE) density $I ¨ _{D E 0} \approx a_{c 0}^{2} / G = 1 0^{- 10}$ J/m $^{3}$ , we postulate an entropic origin of the dark energy from acceleration fluctuations of dark matter, in analogy to the gas pressure from velocity fluctuations. This leads to a dynamical dark energy coupled to the structure evolution involving a relatively constant DE density followed by a slow weakening phase, suggesting possible deviations from the standard $I^$ CDM.

Reformatted with data source provided, 17 pages, 21 figures