Cosmological evolution of a complex scalar field with repulsive or attractive self-interaction

Understand

We study the cosmological evolution of a complex scalar field with a self-interaction potential $V(|\varphi|^2)$, possibly describing self-gravitating Bose-Einstein condensates, using a fully general relativistic treatment.

• We generalize the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field approximation developed in our previous paper.
• We establish the general equations governing the evolution of a spatially homogeneous complex scalar field in an expanding background.
• We show how they can be simplified in the fast oscillation regime and derive the equation of state of the scalar field in parametric form for an arbitrary potential.