Anisotropy in constraint 4D Gauss-Bonnet gravity

Abstract

Recently a new 4D Einstein-Gauss-Bonnet theory has been introduced \textbf{[Phys. Rev. Lett. 124 (2020) 081301]} with a serious debate that it does not possess a covariant equation of motion in $4D$. This feature, makes impossible to consider non-symetric space-times in this model, such as anisotropic cosmology. In this note, we will present a new proposal to make this happen, by introducing a Lagrange multiplier to the action which eliminates the higher dimensional term from the equation of motion. The theory has then a covariant $4D$ equation of motion which is useful to study the less symmetric metrics. On top of FRW universe, the constraint theory is equivalent to the original $4D$ Einstein-Gauss-Bonnet gravity. We will then consider the anisotropic cosmology of the model and compare the theory with observational data. We will see that the theory becomes non-conservative and the matter density abundance falls more rapidly at larger redshifts compared to the conservative matter sources.

arXiv comment9 pages, 4 figures

References in corpus (70)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Massive Gravity
• Theoretical Aspects of Massive Gravity
• Brane-World Gravity
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Horndeski theory and beyond: a review
• $f(Q,T)$ gravity
• Generalization of the Proca Action
• Cosmology and Brane Worlds: A Review
• General Gauss-Bonnet brane cosmology
• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• Rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity and its shadow
• Black holes in three dimensional higher spin gravity: A review
• Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• A consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity
• A formal introduction to Horndeski and Galileon theories and their generalizations
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• A note on the novel 4D Einstein-Gauss-Bonnet gravity
• Beyond generalized Proca theories
• Gravitational lensing by charged black hole in regularized $4D$ Einstein-Gauss-Bonnet gravity
• Wormholes in 4D Einstein-Gauss-Bonnet Gravity
• Black holes in the four-dimensional Einstein-Lovelock gravity
• On the cosmological constant problem
• Extended vector-tensor theories
• Selected topics in scalar-tensor theories and beyond
• A note on the total action of $4D$ Gauss-Bonnet theory
• Amplitudes and 4D Gauss-Bonnet Theory
• Born-Infeld Black Holes in 4D Einstein-Gauss-Bonnet Gravity
• (In)stability of black holes in the 4D Einstein-Gauss-Bonnet and Einstein-Lovelock gravities
• Weak cosmic censorship conjecture for the novel $4D$ charged Einstein-Gauss-Bonnet black hole with test scalar field and particle
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Observational Constraints on the Regularized 4D Einstein-Gauss-Bonnet Theory of Gravity
• Weyl-Cartan-Weitzenböck gravity as a generalization of teleparallel gravity
• Thin Accretion Disk around a four-dimensional Einstein-Gauss-Bonnet Black Hole
• Comment on "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime"
• Quark Stars in 4D Einstein-Gauss-Bonnet gravity with an Interacting Quark Equation of State
• Dust collapse in 4D Einstein-Gauss-Bonnet gravity
• Weyl-Cartan-Weitzenböck gravity through Lagrange multiplier
• Vacua and Exact Solutions in Lower-$D$ Limits of EGB
• Strange Quark Stars in 4D Einstein-Gauss-Bonnet Gravity
• Counterterms, Kounterterms, and the variational problem in AdS gravity
• Nonlinear magnetically charged black holes in 4D Einstein-Gauss-Bonnet gravity
• Cosmological evolution and dark energy in osculating Barthel-Randers geometry
• Inflationary gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Limits on stellar structures in Lovelock theories of gravity
• 4D Einstein-Lovelock black holes: Hierarchy of orders in curvature
• Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime
• Theoretical and observational constraints on regularized 4$D$ Einstein-Gauss-Bonnet gravity
• The Einstein dark energy model
• The Weyl-Cartan Gauss-Bonnet gravity
• $D\to 4$ Einstein-Gauss-Bonnet Gravity and Beyond
• Isotropic compact stars in 4D Einstein-Gauss-Bonnet gravity
• Weyl gravity and Cartan geometry
• Growth of Matter Perturbations in the Bi-Galileons Field Model
• One-loop corrections to vector Galileon theory
• Vector dark energy models with quadratic terms in the Maxwell tensor derivatives
• Quantum corrections to the generalized Proca theory via a matter field
• On cosmic acceleration in four dimensional Einstein-Gauss-Bonnet gravity
• Growth of matter density perturbations in 4D Einstein-Gauss-Bonnet gravity
• Asymptotic structure of Einstein-Gauss-Bonnet theory in lower dimensions
• Stability of asymptotically de Sitter and anti-de Sitter black holes in $4D$ regularized Einstein-Gauss-Bonnet theory
• Simply rotating higher dimensional black holes in Einstein-Gauss-Bonnet theory
• Kundt spacetimes in the Einstein-Gauss-Bonnet theory
• Cosmology of a higher derivative scalar theory with non-minimal Maxwell coupling
• Axionic extension of the Proca action

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