A Further Analysis of a Cosmological Model of Quintessence and Scalar Dark Matter

We present the complete solution to a 95% scalar field cosmological model in which the dark matter is modeled by a scalar field $\Phi $ with the scalar potential $V(\Phi)=V_{o}[ \cosh {(\lambda \sqrt{\kappa_{o}}\Phi)}-1]$ and the dark energy is modeled by a scalar field $\Psi$, endowed with the scalar potential $\tilde{V}(\Psi)=\tilde{V_{o}}[ \sinh {(\alpha \sqrt{\kappa_{o}}\Psi)}] ^{\beta}$. This model has only two free parameters, $\lambda$ and the equation of state $\omega_{\Psi}$. With this solution, the fine tuning and the cosmic coincidence problems are ameliorated. The dark matter consists of an ultra-light particle, whose mass could be $m_{\Phi}\geq 10^{-26}eV$. All the success of the standard cold dark matter model is recovered. In addition, we clarify the meaning of a scalar Jeans lenght. The model predicts a suppression of the Mass Power Spectrum for small scales having a wave number $k > k_{min,\Phi}$, where $k_{min,\Phi} \geq 0.3 Mpc^{-1}$, that could help to explain the dearth of dwarf galaxies and the smoothness of galaxy core halos. In fact, the suppression scale depends on the parameter $\lambda$ mentioned above. This implies that a scalar field could be a good candidate to be the dark matter of the Universe.