Classification of Noether Symmetries for a Specific Exact Solution in String-Motivated Scalar Field Cosmology

In recent years, scalar-field cosmology has received notable attentions. The noticeable fact is that in order to investigate the exact solutions for a minimally coupled scalar field Φ with potential V it is common to consider a Lagrangian density: L=〖(16πG)〗^(-1) R-1/2 g^μν ∂_μ Φ ∂_υ Φ-V(Φ), where R is the curvature scalar. Furthermore, by a suitable selection of the potential, particular models could be specified. In this paper, an exhaustive analysis of the Noether symmetries for a particular exact solution in string-motivated scalar-field cosmology is presented. The mentioned cosmological solution was originally motivated by six-dimensional Einstein-Maxwell theory and is extendable into exact cosmological solutions which are close to the standard cosmology of the radiation era and are free of cosmological problems. For this purpose, the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to our analyzed string inspired FRLW solution s geodesic Lagrangian, namely Noether symmetries are thoroughly determined. Mainly, a complete classification of one-dimensional subalgebras of the Lie algebra of Noether symmetries is presented via the adjoint representation group, which introduces a conjugate relation in the set of all one-dimensional subalgebras.