Axion cosmology with post-Newtonian corrections

Abstract

We present first-order post-Newtonian (1PN) approximations of a general imperfect fluid and of an axion as a coherently oscillating massive scalar field, both in the cosmological context. For the axion, using the Klein transformation and Madelung transformation we derive the Schrödinger and Madelung hydrodynamic formulations, respectively, in exact covariant way and to 1PN order. Complete sets of equations for the 1PN formulations are derived without fixing the temporal gauge condition. We study the linear instability in cosmology and a static limit for both fluid and axion; these are presented independently of the gauge condition to 1PN order, thus are naturally gaugeinvariant.

Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

“…40 In that limit, the Lagrangian of the SF is 40 As in Refs [20,287,288] we have neglected anisotropic stresses and assumed that the lapse function Ψ is equal to the Newtonian potential Φ. See [362,363] for a more general treatment.…”