Cold dark matter particle mass, size, and properties and axion-like dark radiation in ΛCDM cosmology*

A new theory is presented to estimate the mass, size, lifetime, and other properties of cold dark matter particles (CDM). Using Illustris simulations, we demonstrate the existence of mass and energy cascade that facilitates the formation of hierarchical structures. A scale-independent rate of cascade ε_u≈10^-7m²/s³ can be identified. The energy cascade leads to universal scaling laws on relevant scales r, i.e. a two-thirds law for kinetic energy (v_r² ~ ε_u^2/3r^2/3) and a four-thirds law for DM halo density (ρ_r ~ ε_u^2/3G^-1r^-4/3), where G is the gravitational constant. For cold and collisionless dark matter that interacts via gravity only, these scaling laws can be extended down to the smallest scale, where quantum effects become important. Combined with the uncertainty principle and virial theorem, three constants (ε_u, ћ, and G) dominate the physics on that scale, so that the properties of CDM can be estimated. We estimate a mass m_X=(ε_uћ⁵G^-4)^1/9=10¹²GeV, a size l_X=(ε_u^-1ћG)^1/3=10^-13m, and a lifetime τ_X=c²/ε_u=10¹⁶ years for CDM particles. Here, ћ is the Planck constant and c is the speed of light. The energy on that scale E_X=(ε_u⁵ћ⁷G^-2)^1/9=10^-9eV suggests a “dark radiation” field to provide a viable mechanism for the energy dissipation during gravitational collapsing of CDM. If existing, the “dark radiation" should be produced around t_X=(ε_u^-5ћ²G²)^1/9=10^-6s (quark epoch) with mass of 10^-9 eV, a GUT scale decay constant 10¹⁶ GeV, or an effective axion-photon coupling 10^-18GeV^-1, such that the axion particle can be a very promising candidate. The current energy density of “dark radiation” is estimated to be about 1% of the cosmic microwave background (CMB). This work suggests a heavy dark matter scenario along with a light axion-like dark radiation field. Potential extension to self-interacting dark matter is also presented. More details can be found at arXiv:2202.07240.