Scalar Field as Dark Energy Accelerating Expansion of the Universe

The features of a homogeneous scalar field $\phi$ with classical Lagrangian $L=\phi_{;i}\phi^{;i}/2-V(\phi)$ and tachyon field Lagrangian $L=-V(\phi)\sqrt{1-\phi_{;i}\phi^{;i}}$ causing the observable accelerated expansion of the Universe are analyzed. The models with constant equation-of-state parameter $w_{de}=p_{de}/\rho_{de}<-1/3$ are studied. For both cases the fields $\phi(a)$ and potentials $V(a)$ are reconstucted for the parameters of cosmological model of the Universe derived from the observations. The effect of rolling down of the potential $V(\phi)$ to minimum is shown.