Rewinding the Universe to the Beginning of Time

Dive into the Friedmann equations

You are probably familiar with the fact that our universe is expanding, and that it used to be a very hot and dense some 13.8 billion years ago in what we generally call the Big Bang. You may also have heard that this expansion appears to be accelerating due to a mysterious repulsive force that we call dark energy. In this post I recapitulate what we know about these and show you quantitatively how this expansion really looks like.

The Friedmann equations

In 1922, Building on Einstein’s theory of General relativity, Friedman published a set of equations describing the expansion of a homogeneous universe. In his model, the universe is described as a “perfect fluid”, meaning it can be characterized only by its mass density ρ, pressure p and global curvature k. Luckily, this description approximates very well our universe when considering it at very large scales. In the case of a homogeneous universe, the spacetime metric is the same everywhere, and can thus be described by a single parameter known as the scale factor a(t), which correlates to the average distance between objects in the universe.