The paper discusses the idea that the accelerated expansion of the universe could be due to gravitational leakage into extra dimensions on Hubble distances, rather than a non-zero cosmological constant. The authors explore a 5-dimensional brane-world model with an infinite-volume extra dimension, where gravity spreads into this extra space at large distances, leading to a modified force law and an accelerated expansion of the universe. This model predicts a crossover scale \( r_c \) where the four-dimensional Newtonian gravity transitions to a five-dimensional gravity, causing the universe to accelerate beyond this scale. The authors compare this model with conventional cosmological scenarios and show that it cannot be mimicked by ordinary 4D gravity with high-derivative terms, making it intrinsically high-dimensional. They also argue that such models might avoid the difficulties of reconciling String Theory with the observation of an accelerated universe, as the bulk metric is Minkowskian and there is no infinite future horizon for 4D observers. The paper includes a detailed analysis of cosmological tests, such as supernova observations and cosmic microwave background (CMB) data, to compare the predictions of the model with observations. Finally, the authors discuss the constraints on the five-dimensional Planck scale and the potential for dissipation mechanisms that could modify the asymptotic form of the 4D metric.The paper discusses the idea that the accelerated expansion of the universe could be due to gravitational leakage into extra dimensions on Hubble distances, rather than a non-zero cosmological constant. The authors explore a 5-dimensional brane-world model with an infinite-volume extra dimension, where gravity spreads into this extra space at large distances, leading to a modified force law and an accelerated expansion of the universe. This model predicts a crossover scale \( r_c \) where the four-dimensional Newtonian gravity transitions to a five-dimensional gravity, causing the universe to accelerate beyond this scale. The authors compare this model with conventional cosmological scenarios and show that it cannot be mimicked by ordinary 4D gravity with high-derivative terms, making it intrinsically high-dimensional. They also argue that such models might avoid the difficulties of reconciling String Theory with the observation of an accelerated universe, as the bulk metric is Minkowskian and there is no infinite future horizon for 4D observers. The paper includes a detailed analysis of cosmological tests, such as supernova observations and cosmic microwave background (CMB) data, to compare the predictions of the model with observations. Finally, the authors discuss the constraints on the five-dimensional Planck scale and the potential for dissipation mechanisms that could modify the asymptotic form of the 4D metric.