Noether Symmetry analysis for fourth order modified gravity theory: Cosmological Solution and Evolution

A modified fourth-order gravity theory namely the [Formula: see text] theory is considered in flat FLRW model to investigate both classical and quantum cosmology. The field equations are reduced to second-order differential equations by considering the technique of Lagrange multiplier. Noether symmetry analysis has been used both for obtaining classical solution and the wave function of the Universe in quantum cosmology. Finally the cosmological solutions are examined from observational view point.