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When interpreted with the standard theory of cosmology, recent observations of the apparent magnitude vs. redshift of Type Ia supernovae suggest an accelerating expansion of space. The acceleration is justified by assuming the presence of an unknown dark energy working against gravitation at cosmological distances. The assumption of dark energy is equivalent to Einstein's cosmological constant, which he originally proposed to prevent a collapse of spherically closed space which he assumed to be static. If Einstein's spherically closed space, the surface of a 4-sphere, is allowed to expand in a zero energy balance between the energies of motion and gravitation, no cosmological constant or dark energy is needed. In a thorough analysis of such expansion, the apparent magnitude, m, versus redshift, z, obtains the form m = M0 + 5 log(z) + 2.5 log(z+1), which completely agrees with the Type Ia supernovae observations [1,2]. Due to the assumed spherical geometry and the zero energy balance, the obtained magnitude prediction is absolute in its nature; it has no free parameters like omega(m), omega(lamda), or the Hubble constant H(0) that are needed in the corresponding equation derived from the standard cosmology model. In space, described as a dynamic 4-sphere, the fourth dimension is geometrical in its nature, allowing a universal time coordinate. The velocity of light becomes directly linked to the velocity of space in the direction of the 4-radius and the rest energy of mass gets the meaning of the energy of motion mass possesses mass due to the expansion of space. As further consequences of the zero-energy balance, buildup of mass centers in space result in local bending of space allowing solutions of the perihelion advance of planetary orbits, the bending of light and the Shapiro delay in closed mathematical form. The characteristic absorption and emission frequencies of atomic objects become linked to local motion and gravitation, which means that the concept of proper time is replaced by a direct effect of motion and gravitation on the frequencies of atomic oscillators. In dynamic spherical space the well known equality between the total gravitational energy and the rest energy of mass in space reflects the zero energy balance driving the expansion of spherically closed space.
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