  In this work we explore the possibility of incorporating particle physics
motivated scalar fields to the dark matter cosmological model. In this
landscape, we consider the classical complex scalar field in a certain region
in the parameter space of the model that increases the number of neutrino
species $N_{\mathrm{eff}}$, in order to be consistent with the observed
abundance of light elements produced at Big Bang Nucleosynthesis (BBN). We
perform analyses using one and two scalar fields. We examine the difference
between these models and the priors considered at the edges of the cosmic
ladder, this with the purpose of studying the impact of such models on the
Hubble cosmic flow. In the two scalar field models we explore the possibility
of combining an axion and a Higgs-like field as well as a Higgs-like field and
the classical field, we show that in the first case there is no set of
parameters that allows us to be consistent with $N_\mathrm{eff}$, while in the
second case a strong restriction to the set of parameters is obtained. This
last restriction is given in terms of a maximum bound of the fraction of
Higgs-like field that can be incorporated together with the classical field.
Our results could be relevant in the direct dark matter detection programs.
