A five-dimensional approach to dark matter and dark energy

A naive five-dimensional model simultaneously explains dark energy and the flat rotation curves of galaxies and enhanced gravitational lensing usually attributed to dark matter. An additional (fifth) dimension is invoked which corresponds to the radius of curvature of four-dimensional space-time and does not represent a degree of freedom of motion. The universe so modeled has two modes of expansion: that of three-dimensional space and that of the fifth dimension itself, where the latter has the characteristics partly of space and partly of time. The boundary between four-dimensional space-time and the fifth dimension is modeled by contours along which energy is conserved. The model is able to reproduce: (i) the observed relationship between distance modulus and red shift for Type 1a supernovae; (ii) the Tully-Fisher relationship; and (iii) gravitational lensing effects beyond General Relativity for galaxies and clusters of galaxies.