The importance of investigating particle horizons in order to interpret a cosmological solution of Einstein’s field equations has been described. We have presented the formula and studied the particle horizons in some of the cosmological models presented in our earlier papers. It is well known that the Friedman-Robertson-Walker (F-R-W) models, the energy density of the free gravitational field denoted by ε, equivalently denoted by MacCallum parameter ξ, vanishes but the particle horizons exist and thus the former has no bearing on the latter. However, we have shown in our models presented herein that ε is related with particle horizons. Further, it is shown that as ε grows, the segment of the corresponding particle horizon decreases and thus the radius of the corresponding visible universe decreases.