Considerations of a $k=+1$ Varluminopic Cosmology

Every relativistic particle has 4-speed equal to $c$, since $g_{\mu \nu} \frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\tau} = c^2$\mathrm{.}Withthechoiceof$k = +1$intheFRWmetric,thecosmologicalscalefactor$a(t)$ has the natural interpretation of the radius of the sphere $S^3_a = {x \in $\mathbb{R}$^4 : (x, x) = a^2}$. Thus, a particle at rest in the cosmological frame has 4-speed equal to $\frac{da}{dt}$. This leads us to infer that $\dot{a}=c$, which respresents a simple kinematic constraint linking the speed of light to the cosmological scale factor. This drastically changes the $k=+1$ picture from a closed deaccelerating universe to an open accelerating universe, settles the horizon problem, and provides for a new cosmological model more appealing to our natural intuition. In this paper we shall consider ramifications of this model.