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Spatially covariant theories of a transverse, traceless graviton: Formalism

Justin Khoury1, Godfrey E. J. Miller1, and Andrew J. Tolley2

  • 1Center for Particle Cosmology, Department of Physics & Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA
  • 2Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA

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Phys. Rev. D 85, 084002 – Published 2 April, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.084002

Abstract

General relativity is a generally covariant, locally Lorentz covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchař, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of local Lorentz covariance. In this paper, we explore modifications of general relativity that retain the same graviton degrees of freedom, and therefore explicitly break Lorentz covariance. Motivated by cosmology, the modifications of interest maintain explicit spatial covariance. In spatially covariant theories of the graviton, the physical Hamiltonian density obeys an analogue of the renormalization group equation which encodes invariance under flow through the space of conformally equivalent spatial metrics. This paper is dedicated to setting up the formalism of our approach and applying it to a realistic class of theories. Forthcoming work will apply the formalism more generally.

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Phys. Rev. D 85, 084002– Published 2 April, 2012
  • Received 12 August 2011
Article part of CHORUS

© 2012 American Physical Society

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