No abstract

No abstract

The conformal equivalence between Jordan frame and Einstein frame can be used in order to search for exact solutions in general theories of gravity in which scalar fields are minimally or nonminimally coupled with geometry. In the cosmological arena a relevant role is played by the time parameter in which dynamics is described. In this paper we discuss such issues considering also if cosmological Noether symmetries in the "point-like" Lagrangian are conformally preserved.Through this analysis and through also a careful analysis of the cosmological parameters Ω and Λ, it is possible to contribute to the discussion on which is the physical system.

In this paper, we discuss a possible method of finding cosmological exact solutions in the context of nonstandard coupled gravity theories. We consider whether Noether symmetries, present in the cosmological `point-like' Lagrangian, are preserved under the conformal transformation which reduces a given nonstandard coupled model to the corresponding standard coupled one. We see that Noether symmetries are conformally preserved in a general way.

Adopting the method described in previous papers, we search for Nöther's symmetries in point-like Friedman--Robertson--Walker (FRW) Lagrangians derived for general non-minimally coupled gravitational theories. We obtain exact solutions for flat models capable of producing inflation and recovering the Einstein regime at the present time (i.e. the scalar field and the coupling become constants directly related to the Newton constant ).