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 $V\left(\Phi {)=V}_0\right[\cosh \left(\lambda \sqrt{{\kappa }_0}\Phi \right)-1]$ and the dark energy is modeled by a scalar field Ψ, endowed with the scalar potential $\tilde{V}\left(\Psi \right)=V_0\left[\sinh \right(\alpha \sqrt{{\kappa }_0}\Psi ){]}^{\beta }.$ This model has only two free parameters, λ and the equation of state ${\omega }_{\Psi }.$ 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 $k>\mathrm{}{k}_{\min ,\Phi },$ where $k_{\min ,\Phi }\simeq 4.5h$ ${\mathrm{Mpc}}^{-1}$ for $\lambda \simeq \mathrm{20.28.}$ 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 $m_{\Phi }\simeq 1.1\times {10}^{-23}$ 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.

Continuing with previous works, we present a cosmological model in which dark matter and dark energy are modeled by scalar fields $\Phi $ and $\Psi$, respectively, endowed with the scalar potentials $V(\Phi)=V_{o}[ \cosh {(\lambda \sqrt{\kappa_{o}}\Phi)}-1] $ and $\tilde{V}(\Psi)=\tilde{V_{o}}[ \sinh {(\alpha \sqrt{\kappa_{o}}\Psi)}] ^{\beta}$. This model contains 95% of scalar field. We obtain that the scalar dark matter mass is $m_{\Phi}\sim 10^{-26}eV.$ The solution obtained allows us to recover the success of the standard CDM. The implications on the formation of structure are reviewed. We obtain that the minimal cutoff radio for this model is $r_{c}\sim 1.2 kpc.$

In this paper we propose a quintessence model with the potential $V\left(\Phi {)=V}_0\right[\sinh \left(\alpha \sqrt{{\kappa }_0}\Delta \Phi \right){]}^{\beta }$ with $\beta <0,$ whose asymptotic behavior corresponds to an inverse power-law potential at early times and to an exponential one at late times. We demonstrate that this is a tracker solution and that it could have driven the Universe into its current inflationary stage. The exact solutions and the description for a complete evolution of the Universe are also given. We compare such a model with current cosmological observations.