The evolution of the universe is described as an advancement of time, and only collaterally an expansion of space. An interpretation of time as proceeding at the equivalent of c across space, perpendicular to space, per a reconsideration of Minkowski’s spacetime geometry, supports a description of the cosmos as a four-dimensional (hyper)spherical wavefront. By treating space as the surface of a four-dimensional sphere with a current radius of 13.82 billion years (equivalent to 13.82 billion light-years), a Hubble constant of 70.6 (km/s)/Mpc is derived from the measure of the expansion of a megaparsec arc on the surface, independent of empirical measurement or mathematical inversion. It is argued that a close correlation between the advancing temporal cosmic radius and the expansion of the arc subtending a Mpc suggests at least a remarkable coincidence, worthy of further investigation. The hypothesis also has the scientific virtue of economy of explanation, dispensing with the need for the (revived) cosmological constant, cosmic inflation, dark energy, and dark matter as a gravitational constraint on expansion, as well as questions of the shape of the universe and of the influence of gravitation on the rate of expansion. A reexamination of various cosmological parameters in terms of an advancing time hypothesis is expected to provide further confirmation and confer greater simplicity and general coherence to cosmology.