Inhomogeneous brane models

The existence of a set of 10 Intrinsic Conformal Symmetries, which acts on three-dimensional hypersurfaces (spacelike or timelike), leads to the existence of two distinct families of 5D geometries. These models represent the general solutions of the bulk field equations where their energy-momentum tensor, includes only two components: a negative cosmological constant and a parallel pressure \(p_{\parallel }\) aligned with the extra spatial dimension. Significantly, these models offer a novel perspective for investigating the impacts of spatial inhomogeneity and anisotropy on the cosmological evolution of the Universe, particularly within the context of the braneworld scenarios. It is shown that one of these families reduces to a fully inhomogeneous, anisotropic and conformally flat brane model with a perfect fluid equation of state and corresponds to the Stephani Universe (i.e. a Stephani brane) which implies that our model can be matched smoothly with the standard FRW model. We provide the generalized Friedmann and Raychaudhuri equations and we present how the additional quantities could affect the cosmological evolution. In particular we show that the new constituents are the terms \(p_{\parallel }\), \(\sigma ^{2}\) and the four acceleration of the brane observers that could affect the observational measurement of the Hubble parameter depending on which term dominates therefore provide us a potential answer to the Hubble tension and cosmic acceleration problems due to local inhomogeneities and anisotropies.