Noether symmetry analysis in scalar tensor cosmology: a study of classical and quantum cosmology

Abstract The present work deals with a complex scalar field in tensor gravity theory the background of spatially flat Friedmann–Lema $${\hat{i}}$$ i ^ tre–Robertson–Walker (FLRW) geometry. Noether symmetry analysis has been used to determine classical cosmological solution scalar–tensor as nonminimally coupled field. is not only find vector and potential but also it helps finding an appropriate transformation $$(a,~\phi ,~\theta )\rightarrow (u,~v,~\theta )$$ ( a , ϕ θ ) → u v augmented space so that one new variables becomes cyclic. In quantum cosmology, Wheeler–DeWitt (WD) equation formed minisuperspace its i.e. wave function universe evaluated by using operator version conserved (Noether) charge. Finally, nature discussed from observational point view singularity examined both classically mechanically.