Cosmological Simulation for Fuzzy Dark Matter Model

Fuzzy Dark Matter (FDM), motivated by string theory, has recently become a hot candidate for dark matter. The rest mass of FDM is believed to be $\sim 10^{-22}$eV and the corresponding de-Broglie wave length is $\sim 1$kpc. Therefore, the quantum effect of FDM plays an important role in structure formation. In order to study the cosmological structure formation in FDM model, several simulation techniques have been introduced. We review the current status and challenges in the cosmological simulation for the FDM model in this paper.Comment: 10 pages, 2 tables, published on Front. Astron. Space Sci. under the topic: Dark Matter - Where is it? What is it

The Braided Quantum 2-Sphere

In a recent paper the quantum 2-sphere $S^2_q$ was described as a quantum complex manifold. Here we consider several copies of $S^2_q$ and derive their braiding commutation relations. The braiding is extended to the differential and to the integral calculus on the spheres. A quantum analogue of the classical anharmonic ratio of four points on the sphere is given, which is invariant under the coaction of $SU_q(2)$.Comment: 14 page