Abstract
This paper explains the dark energy and acceleration of the universe by quantizing the space in hidden dimensions, which provides the basis and background for the gravitational force through the curvature of space-time. Space-time is considered to be made of a four-dimensional elastic grid in a seven-dimensional universe in which matter also expands along with the universe. Each cube of the grid is considered a quantum of hidden three-dimensional space of Planck volume containing Planck charge, which makes the universe seven dimensional. The dark energy is explained by the electrostatic repulsion between Planck charges in each quantum of the hidden space. Mathematically, this electrostatic repulsion is related to the Hubble constant, which explains the accelerated expansion, dark energy, and increase in the cosmological potential energy of the matter. Expansion of space-time is considered not due to the creation of the new space but due to the stretching of the existing space-time itself like an elastic ruler where the proper length and volume remain constant. The relative values of the Planck constant, gravitational constant, permittivity of free space, and Boltzmann constant are shown to vary owing to the expansion or contraction of space-time in the cosmological, gravitational, and relativistic frameworks. This theory also builds a framework for the relativistic Newtonian theory of gravity, the relativistic MONDian (Modified Newtonian dynamics) gravity, identifies a valid reason for the transition of Newtonian gravity to MOND at a0 and explains the dynamics of galaxy clusters without the dark matter.