This paper explores the idea that the accelerated expansion of the universe could result from gravitational leakage into extra dimensions, rather than a non-zero cosmological constant. The authors propose a 5-dimensional brane-world model with an infinite extra dimension, where gravity is confined to a 3-brane. At short distances, gravity behaves like four-dimensional Newtonian gravity, but at larger distances, it spreads into the extra dimensions, making gravity weaker. This effect leads to an accelerated expansion of the universe without the need for a cosmological constant. The model is tested against astrophysical observations and compared with the conventional cosmological constant scenario. The authors argue that this scenario is intrinsically high-dimensional and cannot be mimicked by ordinary 4D gravity with high-derivative terms. They also suggest that such models might help reconcile string theory with the observed accelerated expansion of the universe, as the bulk metric is Minkowskian and there is no infinite future horizon for 4D observers. The paper presents a cosmological solution where the universe accelerates beyond a crossover scale due to the effective curvature term on the brane, which acts as a cosmological constant. The model is compared with dark energy scenarios, and it is shown that the model can mimic the late-time accelerated expansion of a cosmological constant, although with different parameters. The model is also tested against cosmological observations such as supernovae and the cosmic microwave background, showing that it can produce similar results to standard cosmology. The authors also discuss the implications of the model for high-energy processes and the possibility of dissipation due to quantum effects. They conclude that the model is compatible with current observations and that the five-dimensional Planck scale is consistent with the present Hubble size. The paper also addresses the challenges of describing an accelerated universe within string theory, suggesting that models with infinite-volume extra dimensions might provide a solution.This paper explores the idea that the accelerated expansion of the universe could result from gravitational leakage into extra dimensions, rather than a non-zero cosmological constant. The authors propose a 5-dimensional brane-world model with an infinite extra dimension, where gravity is confined to a 3-brane. At short distances, gravity behaves like four-dimensional Newtonian gravity, but at larger distances, it spreads into the extra dimensions, making gravity weaker. This effect leads to an accelerated expansion of the universe without the need for a cosmological constant. The model is tested against astrophysical observations and compared with the conventional cosmological constant scenario. The authors argue that this scenario is intrinsically high-dimensional and cannot be mimicked by ordinary 4D gravity with high-derivative terms. They also suggest that such models might help reconcile string theory with the observed accelerated expansion of the universe, as the bulk metric is Minkowskian and there is no infinite future horizon for 4D observers. The paper presents a cosmological solution where the universe accelerates beyond a crossover scale due to the effective curvature term on the brane, which acts as a cosmological constant. The model is compared with dark energy scenarios, and it is shown that the model can mimic the late-time accelerated expansion of a cosmological constant, although with different parameters. The model is also tested against cosmological observations such as supernovae and the cosmic microwave background, showing that it can produce similar results to standard cosmology. The authors also discuss the implications of the model for high-energy processes and the possibility of dissipation due to quantum effects. They conclude that the model is compatible with current observations and that the five-dimensional Planck scale is consistent with the present Hubble size. The paper also addresses the challenges of describing an accelerated universe within string theory, suggesting that models with infinite-volume extra dimensions might provide a solution.