Experimental evidence suggests that we live in a spatially flat, accelerating universe composed of roughly one-third of matter (baryonic + dark) and two-thirds of a negative-pressure dark component, generically called dark energy. The presence of such energy not only explains the observed accelerating expansion of the Universe but also provides the remaining piece of information connecting the inflationary flatness prediction with astronomical observations. However, despite of its good observational indications, the nature of the dark energy still remains an open question. In this paper we explore a geometrical explanation for such a component within the context of brane-world theory without mirror symmetry, leading to a geometrical interpretation for dark energy as warp in the universe given by the extrinsic curvature. In particular, we study the phenomenological implications of the extrinsic curvature of a Friedman-Robertson-Walker universe in a five-dimensional constant curvature bulk, with signatures (4,1) or (3,2), as compared with the X-matter (XCDM) model. From the analysis of the geometrically modified Friedman's equations, the deceleration parameter and the Weak Energy Condition, we find a consistent agreement with the presently known observational data on inflation for the deSitter bulk, but not for the anti-deSitter case.

Final form to appear in classical and Quantum Gravity 2005, with updated references, typos corrected, improved introduction and appendices