Accelerated Universe from Gravity Leaking to Extra Dimensions

TL;DR

The paper presents a brane-world scenario in which the observed cosmic acceleration arises from gravity leaking into an infinite-volume extra dimension, controlled by a crossover scale $r_c$ set near the Hubble radius. Gravity is effectively four-dimensional at short distances due to an induced curvature term on the brane, but becomes five-dimensional on cosmological scales, yielding late-time acceleration without a brane cosmological constant. The cosmology is governed by a modified Friedmann equation with a self-accelerating branch, producing expansion histories that mimic dark energy (with $w_{ m eff}>-1$) yet remain distinct in precise distance and CMB tests. The framework addresses theoretical consistency with gravity, constraints on the 5D scale, and potential compatibility with string theory by leveraging an infinite-volume bulk and Minkowski-like bulk geometry. Overall, it offers a high-dimensional mechanism for acceleration that remains testable with upcoming cosmological observations while avoiding certain de Sitter-related issues in quantum gravity.

Abstract

We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant.

Figures (6)

• Figure 1: Different possibilities for the expansion as a function of $\Omega_M$ and $\Omega_{r_c}$. The solid line denotes a flat universe ($k=0$), with $\Omega_{r_c}$ obtained through equation (\ref{['flat5']}). The Universes above the solid line are closed ($k=1$), the universes below are open ($k=-1$). The Universes above the dashed line avoid the big bang singularity by bouncing in the past.
• Figure 2: Luminosity distance as a function of red-shift for ordinary cosmology with $\Omega_\Lambda=0.7, \Omega_M=0.3,k=0$ (dashed line), $\Omega_\Lambda=0, \Omega_M=1,k=0$ (solid line), and dark energy with $\Omega_X=0.7,w_X=-0.6, \Omega_M=0.3, k=0$ (dotted-dashed line) and in our model (dotted line) with $\Omega_M = 0.3$ and a flat universe (for which one gets from equation (\ref{['flat5']}) $\Omega_{r_c} = 0.12$ and $r_c =1.4 H_0^{-1}$).
• Figure 3: Plot of $d_L(z)/d_L^{ref}(z)$ for various models of dark energy with constant equation of state parameters $w_X$ in standard cosmology (solid lines) as compared with the outcome of the model consider in this paper (dashed and dotted lines). All plots correspond to flat universes with $\Omega_M =0.3$ (solid lines, and dotted line), and $\Omega_M =0.27$ (dashed line).
• Figure 4: Plot of $H(z) d_C(z)/H^{ref}(z) d_C^{ref}(z)$ (Alcock-Paczynski test) for various models of dark energy with constant equation of state parameters $w_X$ in standard cosmology (solid lines) as compared with the outcome of the model considered in this paper (dashed and dotted lines). All plots correspond to flat universes, with $\Omega_M =0.3$ (solid lines, and dotted line), and $\Omega_M =0.27$ (dashed line).
• Figure 5: The Solid lines are lines of equal luminosity distance (in our model), $\tilde{d}_L(z=1)/d^{ref}_L(z=1)$, at red-shift $z=1$, the contours are drawn at every 5% level. The dashed line corresponds to a flat universe. The dotted line are line of equal $\sqrt{\Omega_M}\tilde{d}_A(z)$ for $z=1100$, the contours are drawn at every 5% level.