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

TL;DR

This paper examines the conformal equivalence between Jordan and Einstein frames in scalar-tensor theories of gravity, focusing on cosmological solutions, Noether symmetries, and the physical interpretation of cosmological parameters.

Contribution

It analyzes the preservation of Noether symmetries under conformal transformations and discusses implications for the physical interpretation of cosmological models.

Findings

Noether symmetries may not be preserved under conformal transformations.

The choice of time parameter affects the dynamics and interpretation.

Analysis of cosmological parameters  and  informs the physical relevance of the frames.

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 \Omega and \Lambda, it is possible to contribute to the discussion on which is the physical system.