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Galaxy clustering, CMB and supernova data constraints on $ϕ$CDM model with massive neutrinos

We investigate a scalar field dark energy model (i.e., $ϕ$CDM model) with massive neutrinos, where the scalar field possesses an inverse power-law potential, i.e., $V(ϕ)\propto ϕ^{-α}$ ($α>0$). We find that the sum of neutrino masses $Σm_ν$ has significant impacts on the CMB temperature power spectrum and on the matter power spectrum. In addition, the parameter $α$ also has slight impacts on the spectra. A joint sample, including CMB data from Planck 2013 and WMAP9, galaxy clustering data from WiggleZ and BOSS DR11, and JLA compilation of Type Ia supernova observations, is adopted to confine the parameters. Within the context of the $ϕ$CDM model under consideration, the joint sample determines the cosmological parameters to high precision. It turns out that $α<4.995$ at 95% CL for the $ϕ$CDM model. And yet, the $Λ$CDM scenario corresponding to $α= 0$ is not ruled out at 95% CL. Moreover, we get $Σm_ν< 0.262$ eV at 95% CL for the $ϕ$CDM model, while the corresponding one for the $Λ$CDM model is $Σm_ν < 0.293$ eV. The allowed scale of $Σm_ν$ in the $ϕ$CDM model is a bit smaller than that in the $Λ$CDM model. It is consistent with the qualitative analysis, which reveals that the increases of $α$ and $Σm_ν$ both can result in the suppression of the matter power spectrum. As a consequence, when $α$ is larger, in order to avoid suppressing the matter power spectrum too much, the value of $Σm_ν$ should be smaller.