Motivated by the suggestion made by R. H. Dicke in 1957 that the speed of light may be correlated with the gravitational potential of the entire universe, we develop a model for a Machian cosmology in which matter determines the speed of light through a scalar field which has a mathematical form similar to, but distinct from, the gravitational potential. We show that this leads naturally to a cosmology in which the speed of light was higher in the early universe and is decreasing in cosmological time, providing an explanation for the isotropy of the cosmic microwave background (CMB) without the need for inflation. This cosmology results in an apparent amplification of the baryonic mass density (dark matter) and predicts a critical acceleration reproducing that of modified Newtonian dynamics (MOND). We also fit the model to high-redshift supernova data from the Supernova Cosmology Project, showing that an excellent fit is obtained with only baryonic matter. Finally, we derive a geometric relationship between cosmological parameters and the fine structure constant of quantum electrodynamics.