On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy
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2022
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| _version_ | 1866913706809491456 |
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| author | Zhijie Xu |
| author_facet | Zhijie Xu |
| contents | 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 $\varepsilon_{u}\approx -{a_c u_c/[2(3π)^2]}$, where factor $3π$ is from the angle of incidence and $\varepsilon_u\approx -10^{-7}$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 $a_{c0}\equiv a_c(z=0) \approx 10^{-10}$m/s$^2$, suggesting $a_c$ might explain the universal acceleration $a_0\approx 10^{-10}$m/s$^2$ in the empirical Tully-Fisher relation or modified Newtonian dynamics (MOND). Note that dark energy (DE) density $ρ_{DE0}\approx {a_{c0}^{2}/G}=10^{-10}$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 $Λ$CDM. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_05606 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy Zhijie Xu Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies Fluid Dynamics 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 $\varepsilon_{u}\approx -{a_c u_c/[2(3π)^2]}$, where factor $3π$ is from the angle of incidence and $\varepsilon_u\approx -10^{-7}$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 $a_{c0}\equiv a_c(z=0) \approx 10^{-10}$m/s$^2$, suggesting $a_c$ might explain the universal acceleration $a_0\approx 10^{-10}$m/s$^2$ in the empirical Tully-Fisher relation or modified Newtonian dynamics (MOND). Note that dark energy (DE) density $ρ_{DE0}\approx {a_{c0}^{2}/G}=10^{-10}$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 $Λ$CDM. |
| title | On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy |
| topic | Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies Fluid Dynamics |
| url | https://arxiv.org/abs/2203.05606 |