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Inflationary models are characterized by the form of a potential which is arbitrary and usually parametrized so as to match the observational data. However, making use of the renormalization group methods to a gravity-scalar field system it is possible to find physically nontrivial potentials that might be relevant for cosmology and particle physics as well. I will pinpoint the way this class of potentials may be found as well as discuss their utility for inflationary models. [ABSTRACT FROM AUTHOR]

This paper studies the cosmological equations for a scalar field φ in the framework of a quantum gravity modified Einstein–Hilbert Lagrangian where G and Λ are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Λ = Λ(G) and the potential V = V(φ) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling. [ABSTRACT FROM AUTHOR]