Classification of Cosmic Scale Factor via Noether Gauge Symmetries

TL;DR

This paper classifies Friedmann-Robertson-Walker spacetimes using approximate Noether gauge symmetries, identifying symmetries for flat, open, and closed universes and deriving associated conserved quantities.

Contribution

It provides a comprehensive classification of FRW cosmologies based on Noether gauge symmetries for different universe types, including perturbed Lagrangians and conserved quantities.

Findings

Identified Noether gauge symmetries for flat, open, and closed universes.

Derived energy-type first integrals of motion.

Found symmetry operators independent of specific scale factor forms.

Abstract

In this paper, a complete classification of Friedmann-Robertson-Walker (FRW) spacetime by using approximate Noether approach is presented. Considered spacetime is discussed for three different types of universe i.e. flat, open and closed. Different forms of cosmic scale factor $a$ with respect to the nature of the universe, which posses the nontrivial Noether gauge symmetries (NGS) are reported. The perturbed Lagrangian corresponding to FRW metric in the Noether equation is used to get Noether operators. For different types of universe minimal and maximal set of Noether operators are reported. A list of Noether operators are also computed which is not only independent from the choice of the cosmic scale factor but also the choice type of universe. Further, corresponding energy type first integral of motions are also calculated.