This fourth part compares the present theory with mainline and Einstein's theory and gives a summary of the present theory. I discuss the mainline and Einstein's theories, instantaneous and retarded action theories, Brillouin's field mass theory and the present theory in two parts, the non-linear and linear universes. The non-linear and linear expansion versions of the present theory are discussed respectively as infinite and finite size eternal existence steady state universes. Brillouin's field mass theory predicts 11 orders unseen cosmic mass above cosmic rest mass Mo and requires that all distance estimates must be revised if the effects of negative field mass is accounted for. While negative field mass makes the observation of galaxies difficult, its suggestion for the conservation of mass, and thus a finite cosmic sphere, puts a serious question on a theory of non-linear expansion of the universe which predicts an eternal existence infinite universe. The non-linear expansion theory, based on the doppler relativistic formula, is an infinite size eternal existence steady state. I define the Radition universe beyond 3.96 bly the high end of Hubble's linear law. The source of the Microwave background is the Radiation Universe. The present linear expansion theory, based on Hubble's linear law no longer assumed valid at all distances, is a finite size eternal existence steady state universe. It is a spherical cavity in which energy flows simultaneously inwards from hot to cold and outwards from cold to hot, in which man has only observed the incoming redshift part. I assume the cosmic energy and cosmic radius are finite and I speculate that the 2nd Law of Thermodynamics and arrow of time may be reversible. Planck black body spectra are located within the cavity. I characterizes the universe as an eternal existence steady state spherical cavity in which the Radiation region is a Planck blackbody which produces the observed microwave background on Earth. I find that the ideas of distance and time are meaningless in the Radiation Universe.