Considerations of a $k=+1$ Varluminopic Cosmology

TL;DR

This paper proposes a novel cosmological model with positive curvature where the scale factor's rate of change equals the speed of light, leading to an open accelerating universe that addresses the horizon problem.

Contribution

It introduces a $k=+1$ cosmology with a kinematic constraint linking the scale factor's derivative to the speed of light, altering the universe's dynamics.

Findings

Reinterprets $k=+1$ cosmology as an open accelerating universe.

Provides a solution to the horizon problem.

Suggests a new cosmological model aligned with natural intuition.

Abstract

Every relativistic particle has 4-speed equal to $c$, since $g_{\mu \nu} \frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\tau} = c^2$. 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 $S^3_a = \{x \in \mathbb{R}^4 : (x, x) = a^2\}$. 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.