Anisotropy in constraint 4D Gauss–Bonnet gravity

Recently a new 4D Einstein–Gauss–Bonnet theory has been introduced (Glavan and Lin in Phys Rev Lett 124: 081301, 2020) 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