The Friedman Robertson Walker Metric is perhaps one of the most useful equations when determining the nature of the universe, dependent of our understanding of the early universe and the ramifications this had on the present. Founded on the work of Einstein in describing relativity and the fabric of space-time, the equation allows for the description of universes with completely different geometries and conceptions of reality, while still preserving some of the discoveries made by the likes of Hubble and Friedman himself (for more on his equations look at posts Cosmology 101 Parts 1 & 2)
\[ds^2 = -c^2 dt^2 + a^2(t) \left[\frac{dr^2}{1-kr^2} + r^2 (d\theta^2 + \sin^2\theta ~ d\phi^2)\right].\]
Previously, we had the chance to see this equation in how it is used (after many steps of simplifying, and integrating, and deriving) to find the radius of the universe’s event horizon, the farthest we can see back in time.
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