An Alternative Approach for General Covariant Horava-Lifshitz Gravity and Matter Coupling

Abstract

Recently, Horava and Melby-Thompson proposed in arXiv:1007.2410 a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduce the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of $\lambda$ to be $\lambda =1$ as originally claimed. However, the spin-0 graviton is eliminated even for general $\lambda$.

revtex4, 5 pages, typos corrected, references added, matches version published in Class. Quantum Grav

References in corpus (4)

• Quantum Gravity at a Lifshitz Point
• Horava-Lifshitz Cosmology: A Review
• Phenomenologically viable Lorentz-violating quantum gravity
• Lorentz symmetry breaking as a quantum field theory regulator

Cited by in corpus (7)

• Horava-Lifshitz gravity: a status report
• General Covariance in Gravity at a Lifshitz Point
• Stability, ghost, and strong coupling in nonrelativistic general covariant theory of gravity with $\lambda \ne 1$
• Hamiltonian Analysis of Non-Relativistic Covariant RFDiff Horava-Lifshitz Gravity
• Detailed balance condition and ultraviolet stability of scalar field in Horava-Lifshitz gravity
• Spherically symmetric solutions in Covariant Horava-Lifshitz Gravity
• On Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in non-standard gravity