Considerations of a $k=+1$ Varluminopic Cosmology

Abstract

Every relativistic particle has 4-speed equal to $c$, since $g_{\mu \nu }\frac{d{x}^{\mu }}{d\tau }\frac{d{x}^{\nu }}{d\tau }=c^2$. With the choice of $k=+1$ in the FRW metric, the cosmological scale factor $a(t)$ has the natural interpretation of the radius of the sphere $S_a^3=\{x\in {\mathbb{R}}^4:(x,x)=a^2\}$. 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.

24 pages

References in corpus (1)

• Geometrodynamics of Variable-Speed-of-Light Cosmologies