Explaining the cuspy dark matter halos by the Landau–Ginzburg theory

Abstract The equilibrium cold dark matter halos show the almost universal inner r − 1 {r}^{-1} cusps, whose physical origin is still not completely clear. This work tries to further clarify this problem by the Landau–Ginzburg (LG) theory, which is often used to study the long-range correlation of the fluctuations in the critical phenomenon, and we will first introduce it in detail. The order parameter in this work is the density fluctuation, and the external perturbation is denoted by its gravitational effects on the particles. Then we discuss the availability of the aforementioned method for the cold dark matter halos and show that the universal r − 1 {r}^{-1} cusp may even form at the early age of the halo formation and can be expected for the dark matter halos with all the scales, which is also consistent with recent works. This article suggests that the r − 1 {r}^{-1} cusp may originate from the long-range correlations of the gravitating system. This correlation also exists in the short-range system near the critical point, and the difference is that the correlation length in the gravitating system is much longer than that of the short-range system.