Bootstrapping gravity: A consistent approach to energy-momentum self-coupling

Journal Article · Thu Oct 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.084014· OSTI ID:21325358

Butcher, Luke M; Hobson, Michael; Lasenby, Anthony ^[1]

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1. Astrophysics Group, Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom)

It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity of this idea has recently been brought into doubt [T. Padmanabhan, Int. J. Mod. Phys. D 17, 367 (2008).]. Motivated by this, we present a graviton action for which energy-momentum self-coupling is indeed consistent with the Einstein field equations. The Hilbert energy-momentum tensor for this graviton is calculated explicitly and shown to supply the correct second-order term in the field equations; in contrast, the Fierz-Pauli action fails to supply the correct term. A formalism for perturbative expansions of metric-based gravitational theories is then developed, and these techniques employed to demonstrate that our graviton action is a starting point for a straightforward energy-momentum self-coupling procedure that, order by order, generates the Einstein-Hilbert action (up to a classically irrelevant surface term). The perturbative formalism is extended to include matter and a cosmological constant, and interactions between perturbations of a free matter field and the gravitational field are studied in a vacuum background. Finally, the effect of a nonvacuum background is examined, and the graviton is found to develop a nonvanishing 'mass-term' in the action.

• OSTI ID: 21325358
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTRONOMY AND ASTROPHYSICS
AVAILABILITY
COSMOLOGICAL CONSTANT
COUPLING
DISTURBANCES
EINSTEIN FIELD EQUATIONS
ENERGY-MOMENTUM TENSOR
EXPANSION
GRAVITATION
GRAVITATIONAL FIELDS
INTERACTIONS
MASS
MATTER
PERTURBATION THEORY
SPIN
SURFACES