Cold dark matter particle mass and properties and axion-like dark radiation in $\Lambda$CDM cosmology

Abstract

A theory is presented for the mass, size, lifetime, and other properties of cold dark matter particles within the $\Lambda$CDM cosmology. Using Illustris simulations, we demonstrate the mass and energy cascade in self-gravitating collisionless dark matter that facilitates the hierarchical structure formation of dark matter haloes. A scale-independent rate of energy cascade $\varepsilon_u \approx 10^{-7}m^2/s^3$ can be identified. Energy cascade leads to universal scaling laws on relevant scales $r$, i.e. a two-thirds law for kinetic energy ($v_r^2\propto \varepsilon_u^{2/3}r^{2/3}$) and a four-thirds law for halo density ($\rho_r\propto\varepsilon_u^{2/3}G^{-1}r^{-4/3}$), where $G$ is the gravitational constant. Both scaling laws can be confirmed by simulations and galaxy rotation curves. For cold and collisionless dark matter interacting via gravity only and because of the scale independence of $\varepsilon_u$, these scaling laws can be extended down to the smallest scale where quantum effect is important. Combined with the uncertainty principle and virial theorem on that scale, we estimate a mass $m_X=(\varepsilon_u\hbar^5G^{-4})^{1/9}=10^{12}$GeV, size $l_X=(\varepsilon_u^{-1}\hbar G)^{1/3}=10^{-13}$m, and lifetime $\tau_X=c^2/\varepsilon_u=10^{16}$years for cold dark matter particles. Here $\hbar$ is Planck constant, and $c$ is the speed of light. The energy scale $E_X=(\varepsilon_u^5\hbar^7G^{-2})^{1/9}=10^{-9}$eV strongly suggests a dark radiation to provide a viable mechanism for energy dissipation. The axion-like dark radiation should be produced at an early time $t_X=(\varepsilon_u^{-5}\hbar^2G^2)^{1/9}=10^{-6}$s (quark epoch) with a mass of $10^{-9}$eV, a GUT scale decay constant $10^{16}$GeV, an axion-photon coupling constant $10^{-18}$GeV$^{-1}$, and energy density 1$\%$ of the photon energy in CMB. Potential extension to self-interacting dark matter is also presented.Comment: 9 pages, 10 figure