Cosmology on a Brane in Minkowski Bulk

TL;DR

This work analyzes a 3-brane cosmology embedded in a 5D Minkowski bulk with an intrinsic curvature term on the brane. By deriving the brane-Friedmann equations under $Z_2$ symmetry, it identifies two asymptotic branches that resemble FLRW at small Hubble radii but diverge at large scales: a transition to a fully 5D regime or a self-inflationary late-time expansion driven by the brane curvature term. The crossover scale $r_0 = M_{(4)}^2/(2 M_{(5)}^3)$ governs when standard 4D gravity holds versus higher-dimensional behavior, and the two embeddings ($\epsilon=\pm1$) correspond to TI and SI branches with distinct geometric interpretations. The analysis also highlights a mismatch between cosmological and Cavendish Newton constants due to an extra scalar polarization, posing challenges for phenomenology, while suggesting that the SI branch offers a mechanism for late-time acceleration without a cosmological constant.

Abstract

We discuss the cosmology of a 3-brane embedded in a 5D bulk space-time with a cosmological constant when an intrinsic curvature Ricci scalar is included in the brane action. After deriving the `brane-Friedmann' equations for a Z_2 symmetrical metric, we focus on the case of a Minkowski bulk. We show that there exist two classes of solutions, close to the usual Friedmann-Lemaitre-Robertson-Walker cosmology for small enough Hubble radii. When the Hubble radius gets larger one either has a transition to a fully 5D regime or to a self-inflationary solution which produces a late accelerated expansion. We also compare our results with a perturbative approach and eventually discuss the embedding of the brane into the Minkowski space-time. This latter part of our discussion also applies when no intrinsic curvature term is included.