A scalar field dark energy model: Noether symmetry approach

Scalar field dark energy cosmology has been investigated in the present paper in the frame work of Einstein gravity. In the context of Friedmann–Lemaitre–Robertson–Walker space time minimally coupled scalar field with self interacting potential and non-interacting perfect fluid with barotropic equation of state (dark matter) is chosen as the matter context. By imposing Noether symmetry on the Lagrangian of the system the symmetry vector is obtained and the self interacting potential for the scalar field is determined. Then we choose a point transformation (a,ϕ)→(u,v)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(a, \phi )\rightarrow (u, v)$$\end{document} such that one of the transformation variable (say u) is cyclic for the Lagrangian. Subsequently, using conserved charge (corresponding to the cyclic co-ordinate) and the constant of motion, solutions are obtained. Finally, the cosmological implication of the solutions in the perspective of recent observation has been examined.