# Considerations of a $k=+1$ Varluminopic Cosmology

Research paper by **Jared M. Maruskin**

Indexed on: **21 Nov '05**Published on: **21 Nov '05**Published in: **General Relativity and Quantum Cosmology**

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#### 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.