Soliton model of dark matter and natural inflation

Axion-like scalar fields with their periodic potential are analyzed as a toy model of dark matter halos. Here, solitons collison of the well-known kinks in (1 + 1) spacetime dimensions are mapped to the localized lumps of the Lane-Emden (LE) truncation. Recent attempts to generalize this mapping to (2 + 1)D or even (3 + 1)D collision are related to an intrinsic inelastic effect during relativistic soliton collisions.

An indirect method of determining the stability of (3 + 1)D soliton or boson stars (BSs) is displayed without resorting to explicit solutions. Instead, the scalar part of the Lagrangian is mapped into a function L(R) of the scalar curvature, such that a BS is effectively described by by a higher order gravity model. This higher order Lagrangian exhibits minima which are correlated with the transition point from stable to unstable configurations. In the case of an axion BS, the function L(R) exhibits a combination of swallow tail cusps well-known from catastrophe theory.