Updated constraints on Regge-Teitelboim gravity

In the Regge-Teitelboim model, gravity is described by embedding the space-time manifold in a (usually flat) fixed higher-dimensional background, where the embedding coordinates, rather than the metric tensor, are the dynamical degrees of freedom. Stern \& Xu extended the Regge-Teitelboim framework to encompass scenarios where the background embedding space is not flat, noting that when the background is a five-dimensional de Sitter space, the Robertson-Walker manifold undergoes a transition from a decelerating phase to an accelerating one. Previously, we constrained this model using only low-redshift observations. Here we further explore the observational constraints on this scenario, and report significantly more stringent constraints by including high-redshift data, specifically from the cosmic microwave background. Our results are consistent with $\Lambda$CDM, with the putative model-specific energy component responsible for the recent acceleration being constrained to $\Omega_{RT}<0.006$ and the de Sitter curvature radius in units of the Hubble constant being constrained to $LH_0>1.45$, both at the 95 percent confidence level.