Comment on "Classification of Cosmic Scale Factor via Noether Gauge Symmetries" [Int. J. Theor. Phys. 54, 2343 (2015)]

TL;DR

This paper examines the link between Noether symmetries of geodesic Lagrangians and the Homothetic algebra of the underlying space, highlighting their equivalence in classifying symmetries in cosmological models.

Contribution

It clarifies the relationship between Noether point symmetries and Homothetic algebra, emphasizing their equivalence in the context of Friedmann-Lemaître-Robertson-Walker spacetimes.

Findings

Noether symmetries correspond to elements of the Homothetic algebra.

Classification of symmetries reduces to classifying the Homothetic algebra.

Results align with known classifications in cosmological models.

Abstract

We discuss the relationship between the Noether point symmetries of the geodesic Lagrangian, in a (pseudo)Riemannian manifold, with the elements of the Homothetic algebra of the space. We observe that the classification problem of the Noether symmetries for the geodesic Lagrangian is equivalent with the classification of the Homothetic algebra of the space, which in the case of a Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime is a well-known result in the literature.