$D\to 4$ Einstein-Gauss-Bonnet Gravity and Beyond

Abstract

A `novel' pure theory of Einstein-Gauss-Bonnet gravity in four-spacetime dimensions can be constructed by rescaling the Gauss-Bonnet coupling constant, seemingly eluding Lovelock's theorem. Recently, however, the well-posedness of this model has been called into question. Here we apply a `dimensional regularization' technique, first used by Mann and Ross to write down a $D\to 2$ limit of general relativity, to the case of pure Einstein-Gauss-Bonnet gravity. The resulting four-dimensional action is a particular Horndeski theory of gravity matching the result found via a Kaluza-Klein reduction over a flat internal space. Some cosmological solutions of this four-dimensional theory are examined. We further adapt the technique to higher curvature Lovelock theories of gravity, as well as a low-energy effective string action with an ${\alpha }^{\prime }$ correction. With respect to the $D\to 4$ limit of the ${\alpha }^{\prime }$-corrected string action, we find we must also rescale the dilaton to have a non-singular action in four dimensions. Interestingly, when the conformal rescaling $\Phi$ is interpreted as another dilaton, the regularized string action appears to be a special case of a covariant multi-Galileon theory of gravity.

arXiv comment12 pages, references added, published in JCAP, https://doi.org/10.1088/1475-7516/2020/10/026

References in corpus (30)

• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• G-inflation: inflation driven by the Galileon field
• Galilean Genesis: an alternative to inflation
• G-Bounce
• Charged Black Holes in AdS Spaces in $4D$ Einstein Gauss-Bonnet Gravity
• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• Rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity and its shadow
• Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?
• Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions
• Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space
• Bouncing Galileon Cosmologies
• Swampland Implications of GW170817-compatible Einstein-Gauss-Bonnet Gravity
• A note on the novel 4D Einstein-Gauss-Bonnet gravity
• Galileons from Lovelock actions
• The $D\to 2$ Limit of General Relativity
• Wormholes in 4D Einstein-Gauss-Bonnet Gravity
• Black holes in the four-dimensional Einstein-Lovelock gravity
• Lower-Dimensional Black Hole Chemistry
• Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography
• Covariant multi-galileons and their generalisation
• When Matter Matters
• From Satisfying to Violating the Null Energy Condition
• Multi-field G-inflation
• More about wormholes in generalized Galileon theories
• The Second Law in 4D Einstein-Gauss-Bonnet Gravity
• Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aether
• Novel Aspects of the Extended First Law of Entanglement
• Can Galileons support Lorentzian wormholes?

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• Isotropic compact stars in 4D Einstein-Gauss-Bonnet gravity
• Dynamical analysis in regularized $4D$ Einstein-Gauss-Bonnet gravity with non-minimal coupling
• Stability of asymptotically de Sitter and anti-de Sitter black holes in $4D$ regularized Einstein-Gauss-Bonnet theory
• Holographic Consistency and the Sign of the Gauss-Bonnet Parameter
• Topological Corrections and Conformal Backreaction in the Einstein Gauss-Bonnet/Weyl Theories of Gravity at D=4
• 4D Einstein-Gauss-Bonnet Gravity From Non-Einsteinian Phase
• Anisotropy in constraint 4D Gauss-Bonnet gravity
• Dilaton invading from infinitesimal extra dimension
• The Stringy Origins of Galileons and their Novel Limit
• A Post-Newtonian Analysis of Regularized 4D-EGB Theory: Complete Set of PPN Parameters and Observational Constraints
• Cosmological Time Crystals from Gauss-Bonnet Gravity in Four Dimensions
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity
• Cosmic acceleration from string induced Galileons