Can Dark Matter be a Scalar Field?

Abstract

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 $m\ge 0.12H_0^{-1}$ eV ($c=\hslash =1$). For the recent value of the Hubble constant indicated by the Hubble Space Telescope, namely $H_0=73\pm 1.8$ km s${}^{-1}$Mpc${}^{-1}$, this leads to $m\ge 1.56\times 10^{-33}$ 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.

14 pages, 6 figures. Major revision after proof-reading, changed 2 figures for better visualization, corrected 1 equation and acknowledgments

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