Motivated by the observation made by R. H. Dicke in 1957 that the speed of light seems to be correlated with the gravitational potential of the entire universe, we develop a spatially-variable speed of light theory of gravity based on a gravitational wavefunction. The gravitational wavefunction is treated as a fundamental property of matter, while the gravitational potential and resulting forces derived from it are emergent properties which are critically dependent on the distribution of mass on both local and global scales throughout the universe. We then show that the theory leads naturally to an association of gravitation with zero-point fluctuations of the electromagnetic field in the Dirac gauge, with the amplitude and frequency of the fluctuations constrained by the gravitational potential. The theory is free of gravitational singularities. It is capable of reproducing the Schwarzschild metric and is therefore consistent with tests of general relativity. It allows a first-principles calculation of the numerical value of the cosmological constant and the size of the universe using only the speed of light and the average density of ordinary matter in the universe which agrees closely with the observed values. Finally, it numerically predicts the approximate critical acceleration in modified Newtonian dynamics theory (MOND), providing an alternative explanation for dark matter. This shows that the theory may have value in explaining cosmological observations which are currently attributed to dark matter and dark energy.