$z-$Weyl gravity in higher dimensions

Abstract

We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the foliation preserving diffeomorphism invariance adapted to the extra dimensions, thus keeping the general covariance only for the four dimensional spacetime. The conformally invariant gravity can be constructed with an extra (Weyl) scalar field and a real parameter $z$ which describes the degree of anisotropy of conformal transformation between the spacetime and extra dimensional metrics. In the zero mode effective 4D action, it reduces to four-dimensional scalar-tensor theory coupled with nonlinear sigma model described by extra dimensional metrics. There are no restrictions on the value of $z$ at the classical level and possible applications to the cosmological constant problem with a specific choice of $z$ is discussed.

19 pages, no figures, typos corrected

References in corpus (14)

• Quantum Gravity at a Lifshitz Point
• Kaluza-Klein Gravity
• (De)Constructing Dimensions
• Gauge Invariant Effective Lagrangian for Kaluza-Klein Modes
• Brane World Models With Bulk Scalar Fields
• Conformal Invariance in Einstein-Cartan-Weyl space
• Multigravity from a discrete extra dimension
• Anisotropic Weyl symmetry and cosmology
• Kaluza-Klein Formalism of General Spacetimes
• Relaxing the cosmological constant in the extreme ultra-infrared
• Branon stabilization from fermion-induced radiative corrections
• Anisotropic Extra Dimensions
• A New Extension of Hořava-Lifshitz Gravity and Curing Pathologies of the Scalar Graviton
• Modified Brans-Dicke theory with space-time anisotropic parameters

Cited by in corpus (3)

• Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
• A Vanishingly Small Vector Mass from Anisotropy of Higher Dimensional Spacetime
• Aspects of $(d+D)$-dimensional Anisotropic Conformal Gravity