Among the competing theories of dark matter, the hypothesis that dark matter is composed of extremely light real scalar fields, axions, originally conceived as a solution of the strong CP problem. In a way reminiscent of the WIMP miracle, for a mass and decay constant , the observed density of dark matter arises naturally. For such a small mass, the density and hence occupation numbers of the axions are large, implying that the scalar field should be interpreted as a classical field, quantum fluctuations around which are small.
Working with M. Amin, E. Lim and their students/collaborators, we are currently studying the dynamics of the axion field coupled to gravity. Using very sophisticated numerical codes, the English branch of the collaboration has been able to simulate the merger of quasi-solitonic clumps of dark matter with each other, and with black holes. In the mean time, here at Rice, we attempt to understand analytically the radiation of scalar and gravitational waves of these perturbed oscillaton systems.
Some useful references are:
L. Hui, J. P. Ostriker, S. Tremaine and E. Witten, On the hypothesis that cosmological dark matter is composed of ultra-light bosons, arXiv:1610.08297 [astro-ph.CO].
E. Seidel and W. M. Suen, Oscillating soliton stars, Phys. Rev. Lett. 66, 1659 (1991).