Scalar field dark matter with two components: combined approach from
  particle physics and cosmology
  We explore the possibility of incorporating particle physics motivated scalar
fields to the dark matter cosmological model, along with the successful
modeling performed by the classical complex scalar field and without spoiling
the advantages that this model gives, particularly, the one related to the
existence of certain region in the parameter space, which increases the number
of neutrino species $N_{\text{eff}}$ in the correct amount needed in the early
Universe to be consistent with the observed abundance of light elements
produced at Big Bang Nucleosynthesis (BBN). We also examine the differences
between these models and the priors considered at the edges of the cosmic
ladder obtaining that they have a clearly different behavior depending on the
combination of the two scalar fields taken into account. In such cases we
obtain that depending on the value of the Hubble constant inferred from CMB
Planck 2018 data or considering a local value of this constant we can notice a
different distribution of matter densities at early or late epochs. We take as
a first example, one of the Higgs-like candidates of dark matter and show that
if it is added along with the classical complex scalar field, it will give
consistent results within the BBN constrain if the heavy scalar field composes
less than $58\%$ of the total dark matter. We also use an axion field which has
negative self interaction then we will show that (as long as the symmetry
breaking scale $f_a$ is below the Planck scale) there will be at least a region
for which the two-field system is consistent with the constrains. Finally we
will explore the possibility of combining the axion and Higgs-like scalar
fields and show that there is no set of parameters that allows to be consistent
with $N_{\text{eff}}$ from BBN constraints. Our results could be relevant on
the direct dark matter detection programs.
