Scalar field dark matter spectator during inflation: the effect of self-interaction

Nowadays cosmological inflation is the most accepted mechanism to explain the primordial seeds that led to the structure formation observed in the Universe. Current observations are in well agreement to initial adiabatic conditions, which imply that single-scalar-field inflation may be enough to describe the early Universe. However, there are several scenarios where the existence of more than a single field could be relevant during this period, for instance, the situation where the so-called spectator is present. Within the spectator scenario we can find the possibility that an ultra-light scalar field dark matter candidate could coexist with the inflaton. In this work we study this possibility where the additional scalar field could be free or self-interacting. We use isocurvature observations to constrain the free parameters of the model.