Speaker
Description
We present a new theory to predict dark matter (DM) particle mass, size, lifetime, and properties of possible dark radiation from DM particle decay. In self-gravitating collisionless dark matter, the existence of inverse mass and energy cascade from small to large scales facilitates the hierarchical structure formation. A scale-independent constant rate of energy cascade $\varepsilon_u\approx-4.6\times10^{-7}m^2/s^3$ can be identified. The energy cascade leads to a two-thirds law for pairwise velocity and a four-thirds law for halo density profile. Both scaling laws can be directly confirmed by N-body simulations and galaxy rotation curves. For collisionless dark matter with only gravity involved, scaling laws can be extended down to the smallest scale, where quantum effects become important. Combining $\varepsilon_u$, Planck constant $\hbar$, and gravitational constant $G$ on that scale, we predict DM particles have a mass $m_X=(\varepsilon_u\hbar^5G^{-4})^{1/9}=0.9\times10^{12}$GeV, a size $l_X=(\varepsilon_u^{-1}\hbar G)^{1/3}=3\times10^{-13}$m, and a lifetime $\tau_X=c^2/\varepsilon_u=10^{16}$yrs, where $c$ 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" field to provide a viable energy dissipation mechanism. If existing, the dark "radiation" should be produced by DM decay at early time $t_X=(\varepsilon_u^{-5}\hbar^2G^2)^{1/9}=10^{-6}$s (quark epoch) with a mass of $10^{-9}$eV such that axion can be a very promising candidate. If axion is the dark "radiation" responsible for the energy dissipation, it should have a mass around $10^{-9}$eV with a GUT scale decay constant $10^{16}$GeV and an effective axion-photon coupling constant $10^{-18}$GeV$^{-1}$. The dark radiation energy density is around $\Omega_ah^2\approx 2.6\times 10^{-7}$, which is about 1 percent of the photon energy in CMB. Parameterized by the increase in the effective number of neutrino, $\Delta N_{eff}=0.02$ can be obtained. Since the DM particle mass $m_X$ is only weakly dependent on $\varepsilon_u$ as $m_X\propto\varepsilon_u^{1/9}$, the estimation of $m_X$ should be pretty robust for a wide range of possible values of $\varepsilon_u$. If gravity is the only interaction and dark matter is fully collisionless, mass of $10^{12}$GeV seems required to produce the given rate of energy cascade $\varepsilon_u$. In other words, if DM particle mass has a different value, there must be some new interactions beyond gravity. This work suggests a heavy dark matter scenario with a mass much greater than WIMPs. Potential extension to self-interacting dark matter is also presented. More details can be found at arXiv:2202.07240.
