The dynamics of metric-affine gravity

Journal Article · Sun May 15 04:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.02.008· OSTI ID:21579888

Vitagliano, Vincenzo ^[1]; Liberati, Stefano ^[1]

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1. SISSA-International School for Advanced Studies, Via Bonomea 265, 34136 Trieste (Italy)

Highlights: > The role and the dynamics of the connection in metric-affine theories is explored. > The most general second order action does not lead to a dynamical connection. > Including higher order invariants excites new degrees of freedom in the connection. > f(R) actions are also discussed and shown to be a non- representative class. - Abstract: Metric-affine theories of gravity provide an interesting alternative to general relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should include covariant derivatives of the matter fields, with the covariant derivative naturally defined using the independent connection. As a result, in metric-affine theories a direct coupling involving matter and connection is also present. The role and the dynamics of the connection in such theories is explored. We employ power counting in order to construct the action and search for the minimal requirements it should satisfy for the connection to be dynamical. We find that for the most general action containing lower order invariants of the curvature and the torsion the independent connection does not carry any dynamics. It actually reduces to the role of an auxiliary field and can be completely eliminated algebraically in favour of the metric and the matter field, introducing extra interactions with respect to general relativity. However, we also show that including higher order terms in the action radically changes this picture and excites new degrees of freedom in the connection, making it (or parts of it) dynamical. Constructing actions that constitute exceptions to this rule requires significant fine tuned and/or extra a priori constraints on the connection. We also consider f(R) actions as a particular example in order to show that they constitute a distinct class of metric-affine theories with special properties, and as such they cannot be used as representative toy theories to study the properties of metric-affine gravity.

• OSTI ID: 21579888
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 5 Vol. 326; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING
DEGREES OF FREEDOM
FIELD THEORIES
GENERAL RELATIVITY THEORY
GRAVITATION
INTERACTIONS
MATTER
METRICS
RELATIVITY THEORY
SYMMETRY
TORSION