Orateur
Description
We study the cosmological phenomenology of quadratic scalar field dark matter (SFDM) using an implementation in the Boltzmann code CLASS, in which dark matter is modeled as a single ultra-light scalar field with potential V (ϕ) = 12 m2ϕ ϕ2 . Adopting a dynamical-systems approach, we analyze the expansion of the homogeneous scalar field together with its linear perturbations, enabling stable numerical predictions for the relevant cosmological observables. We derive the CMB temperature anisotropy spectrum and the linear matter power spectrum, verifying the numerical stability of our implementation across the parameter space. We constrain the model with Planck 2018 CMB data, DESI DR2 BAO measurements, the three-dimensional Lyman-α forest matter power spectrum, and the Pantheon+ supernova compilation. We find that the standard cosmological parameters remain close to their ΛCDM counterparts, with no clear departures from the concordance scenario. For the scalar-field mass, the baseline dataset combination yields an essentially flat posterior over the explored range. The inclusion of Lyman-α information introduces non-trivial structure in the marginalized posterior, which becomes broad and non-unimodal and allows us to derive a one-sided 95% C.L. lower bound of log10 (mϕ /eV) > −22.15. These results show that the quadratic single-field SFDM scenario remains observationally viable and motivate further discussion of the phenomenological implications associated with the allowed ultra-light mass range.