4D Einstein-Gauss-Bonnet gravity from non-Einsteinian phase

Abstract We set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions vanishing metrical length [1]. In absence torsion, effective field equations depend only four-metric, reflecting a quadratic curvature nonlinearity but no higher than second order derivatives. contrast proposals to obtain 4dEGB theories through singular rescaling Gauss-Bonnet coupling, this formalism requires (classical) regularization divergences and is inequivalent Horndeski gravity, while being generally covariant independent compactification. Notably, vacuum admit FLRW cosmologies containing nonsingular bounce self-accelerating Universe, spherically symmetric black holes more general Schwarzschild. The emerging here shown be preserved against inclusion Lovelock densities 5+2 n dimensions.