Some aspects of the cosmological conformal equivalence between the 'Jordan frame' and the 'Einstein frame'

The conformal equivalence between the Jordan and the Einstein frames can be used in order to search for exact solutions in general theories of gravity in which scalar fields are coupled with geometry in a standard or in a nonstandard way. In the cosmological arena a relevant role is played by the time parameter in which dynamics is described. In this paper we discuss the problem of conformal equivalence between a given nonstandard coupled model and the corresponding standard one. We analyse in detail the cosmological case and we see that, together with this, and through a careful analysis of the cosmological parameters Omega and Lambda, it is possible to contribute to the discussion on which is the physical system.