Cosmological structure formation in complex scalar field dark matter versus real ultralight axions: A comparative study using CLASS

Scalar field dark matter (SFDM) has become a popular alternative to standard collisionless cold dark matter (CDM), because of its potential to resolve the small-scale problems that has plagued the latter for decades. Typically, SFDM consists of a single species of bosons of ultralight mass, m ??? 10???22 eV/c2, in a state of Bose-Einstein condensation, hence also called BEC-DM. In this paper, we continue the study of ASFDM cosmologies, which differ from ACDM in that CDM is replaced by SFDM, by calculating the evolution of the background Universe, as well as the formation of linear perturbations, focusing on scalar modes. We consider models with complex scalar field, where we include a strongly repulsive, quartic selfinteraction (SI), also called SFDM-TF, as well as complex-field models without SI, referred to as fuzzy dark matter (FDM). To this end, we modify the Boltzmann code CLASS, in order to incorporate the physics of complex SFDM which has as one of its characteristics that it leads to a non-standard, early expansion history, where complex SFDM (or FDM) dominates over all the other cosmic components, even over radiation, in the very early Universe, because its equation of state is maximally stiff. We calculate various observables, such as the temperature anisotropies of the cosmic microwave background, the matter power spectra and the unconditional Press-Schechter halo mass function for various models, and thereby expand previous findings in the literature that were limited either to the background, or to a semianalytical approach to SFDM density perturbations neglecting the early stiff phase. We also compare our results of each, SFDM and FDM, with ultralight axion models (ULAs) without SI and modeled as real fields. Thereby, we characterize in detail the differences between ASFDM, AFDM and AULA in terms of their background evolution and their linear structure growth. Our calculations confirm previous results of recent literature, implying that SFDM models with ??? kpc-size halo cores are disfavored, which questions the ability of SFDM to explain the small-scale problems on dwarf-galactic scales. Furthermore, we find that the gain in kinetic energy of SFDM due to the phase of the complex field leads to marked differences between SFDM/FDM versus ULAs. The mild falloff in the SFDM matter power spectrum toward high k is explained by an evolution history of perturbations similar to that of CDM, although based on different physical effects, namely the rapidly shrinking Jeans mass for SFDM as opposed to the Meszaros effect for CDM. In addition, we find that the sharp cutoff in the matter power spectrum of ULAs is also followed by a mild falloff, albeit at very small power.

Automated summary

Scalar field dark matter (SFDM) is an alternative option to address the issues with traditional cold dark matter. This paper studies SFDM cosmologies by calculating the evolution of the background universe and the formation of linear perturbations. The results show differences in the background evolution and structure growth between models with complex scalar field and models with a complex field.