Further analysis of a cosmological model with quintessence and scalar dark matter

Abstract

We present the complete solution to a $95%$ scalar field cosmological model in which the dark matter is modeled by a scalar field $\ensuremath{\Phi}$ with the scalar potential $V(\ensuremath{\Phi}{)=V}_{0}[\mathrm{cosh}(\ensuremath{\lambda}\sqrt{{\ensuremath{\kappa}}_{0}}\ensuremath{\Phi})\ensuremath{-}1]$ and the dark energy is modeled by a scalar field \ensuremath{\Psi}, endowed with the scalar potential $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}(\ensuremath{\Psi})={V}_{0}[\mathrm{sinh}(\ensuremath{\alpha}\sqrt{{\ensuremath{\kappa}}_{0}}\ensuremath{\Psi}){]}^{\ensuremath{\beta}}.$ This model has only two free parameters, \ensuremath{\lambda} and the equation of state ${\ensuremath{\omega}}_{\ensuremath{\Psi}}.$ With these potentials, the fine-tuning and cosmic coincidence problems are ameliorated for both dark matter and dark energy and the model agrees with astronomical observations. For the scalar dark matter, we clarify the meaning of a scalar Jeans length and then the model predicts a suppression of the mass power spectrum for small scales having a wave number $k>{k}_{\mathrm{min},\ensuremath{\Phi}},$ where ${k}_{\mathrm{min},\ensuremath{\Phi}}\ensuremath{\simeq}4.5h$ ${\mathrm{Mpc}}^{\ensuremath{-}1}$ for $\ensuremath{\lambda}\ensuremath{\simeq}20.28.$ This last fact could help to explain the death of dwarf galaxies and the smoothness of galaxy core halos. From this, all parameters of the scalar dark matter potential are completely determined. The dark matter consists of an ultralight particle, whose mass is ${m}_{\ensuremath{\Phi}}\ensuremath{\simeq}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ eV and all the success of the standard cold dark matter model is recovered. This implies that a scalar field could also be a good candidate the dark matter of the Universe.