The effects of a varying cosmological constant on the particle horizon

An important question of modern physics is the nature of dark energy associated with Einstein's cosmological constant, A. It is commonly thought the strength of this intergalactic repulsive force is responsible for an accelerating expansion of our Universe and perhaps the value for A may necessarily vary with expansion. Here I adopt three different cases for the dependence of the A and the particle horizon on some macroscopic properties of our Universe: first, the case for proportionality to the inverse-square of the expansion factor; second, proportionality to the square of the Hubble constant; third, proportionality to decreasing matter density. I begin all derivations from the popular Friedmann-Lemare-Robertson-Walker model in 4D space-time. The results are presented in terms of variables allowing tests with time-dependent astronomical data, such as emissions from Type Ia supernovae and H II galaxy (HIIGx) data.