Physical significance of different classes of Friedmann–Robertson–Walker spacetime

In this research, Friedmann–Robertson–Walker (FRW) spacetime is classified completely according to Noether symmetries. Different classes are discussed for flat, open and closed universes. According to this classification, we have various forms of cosmic scale factor [Formula: see text]. Different sets of Noether symmetries are reported for different classes of Friedmann–Lemaitre–Robertson–Walker (FLRW) universe. We obtained different classes of the said spacetime along with their Noether symmetries and the corresponding conservation laws. The main objective of this research is to find all possible forms of the scale factor [Formula: see text] and discuss their physical significance.