Open AccessWeyl invariance in metric f(R) gravity
Author(s) -
Jose Maria Fernandez Cristobal
Publication year - 2018
Publication title -
revista mexicana de física/revista mexicana de física
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.181
H-Index - 25
eISSN - 2683-2224
pISSN - 0035-001X
DOI - 10.31349/revmexfis.64.181
Subject(s) - f(r) gravity , physics , mathematical physics , dilaton , einstein , scalar curvature , weyl transformation , scalar–tensor theory , scalar (mathematics) , cosmological constant , invariant (physics) , theoretical physics , quantum gravity , scalar field , quantum mechanics , quantum , mathematical analysis , mathematics , conformal symmetry , geometry , conformal map , curvature
We aim to derive the most general f(R) gravity theory, including the matter, so that it be Weyl invariant. Making use of the mathematical equivalence of these theories with an type of scalar-tensor theory, and by imposing the Weyl invariance for the pure gravity as well as for the matter sector, we obtain the fundamental equation that restricts the form of V (phi) (and, accordingly, of f(R)) so that the resulting action to be Weyl invariant in the Jordan frame. We show that this action is not other than the so-called dilaton gravity action with one scalar eld,, which eective mass is R and Phi dependent. In the Einstein frame, the action becomes the Einstein-Hilbert action with the Ricci scalar being constant due to that the eective mass of scalar eld in this frame vanish. So, we can assume that the Ricci scalar, in the Einstein frame, is the true Cosmological Constant. Therefore, is not preposterous to guess that, at least mathematically, all Weyl invariant metric f(R) theory in the Jordan frame is equivalent, at classical level, to the Einstein gravity, in the Einstein frame, with a constant Ricci scalar. At quantum level, as it is known, both theories are not equivalent due to the presence of anomalies in one of the frames.