Cosmological constraints on the Multi Scalar Field Dark Matter model
  The main aim of this paper is to provide cosmological constraints on the
Multi Scalar Field Dark Matter model (MSFDM), in which we assume the dark
matter is made up of different ultra-light scalar fields. As a first
approximation, we consider they are real and do not interact with each other.
We study the equations for both the background and perturbations for $N$-fields
and present the evolution of the density parameters, the mass power spectrum
and the CMB spectrum. In particular, we focus on two scalar fields with several
combinations for the potentials $V(\phi) = 1/2 m_{\phi}^2 \phi^2$, $V(\phi) =
m_{\phi}^2f^2\left[1+\cos(\phi/f)\right]$ and $V(\phi) =
m_{\phi}^2f^2\left[\cosh(\phi/f)-1\right]$, however the work, along with the
code, can be easily extended to more fields. We use the data from BAO, Big Bang
Nucleosynthesis, Lyman-$\alpha$ forest and Supernovae to find constraints on
the sampling parameters for the cases of a single field and double field, along
with the Bayesian evidence. We found that some combinations of the potentials
get penalized through the evidence, however for others there is a preference as
good as for the cold dark matter.
