  In this paper we study a real scalar field as a possible candidate to explain
the dark matter in the universe. In the context of a free scalar field with
quadratic potential, we have used Union 2.1 SN Ia observational data jointly
with a Planck prior over the dark matter density parameter to set a lower limit
on the dark matter mass as $m\geq0.12H_0^{-1}$ eV ($c=\hbar=1$). For the recent
value of the Hubble constant indicated by the Hubble Space Telescope, namely
$H_0=73\pm1.8$ km s$^{-1}$Mpc$^{-1}$, this leads to $m\geq1.56\times10^{-33}$
eV at 99.7\% c.l. Such value is much smaller than $m\sim 10^{-22}$ eV
previously estimated for some models. Nevertheless, it is still in agreement
with them once we have not found evidences for a upper limit on the scalar
field dark matter mass from SN Ia analysis. In practice, it confirms free real
scalar field as a viable candidate for dark matter in agreement with previous
studies in the context of density perturbations, which include scalar field
self interaction.
