Weyl invariance in metric f(R) gravity



Document title: Weyl invariance in metric f(R) gravity
Journal: Revista mexicana de física
Database: PERIÓDICA
System number: 000426081
ISSN: 0035-001X
Authors: 1
Institutions: 1IES Giner de los Ríos, Segovia. España
Year:
Season: Mar-Abr
Volumen: 64
Number: 2
Country: México
Language: Inglés
Document type: Artículo
Approach: Analítico, teórico
English abstract 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 (which includes a scalar degree of freedom, ϕ) and by imposing the Weyl invariance for the pure gravity (under this label, we understand the part that does not involve fields of matter although it could include kinetic terms linked to ϕ) as well as for the matter sector, we obtain the fundamental equation that restricts the form of V = ˙ R ϕ - f ( R ) (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 gravity-dilaton action with one scalar field, Φ, which effective mass is R and Φ dependent. In the Einstein frame, the action becomes the Einstein-Hilbert action with the Ricci scalar being constant due to that the effective mass of scalar field 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
Disciplines: Física y astronomía
Keyword: Física,
Invarianza de Wevyl,
Gravedad métrica,
Fórmula de Jordan,
Fórmula de Einstein
Keyword: Physics,
Weyl invariance,
Metric gravity,
Jordan frame,
Einstein frame
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