What the Universe Is Made Of

Summary

The Friedmann equation, $H^2 = (8\pi G/3)\rho - kc^2/a^2$, governs the whole universe — and you read it rather than solve it. Dividing by $H^2$ gives the cosmic budget, $1 = \Omega_r + \Omega_m + \Omega_\Lambda + \Omega_k$, each density measured against the critical density of about five hydrogen atoms per cubic meter. The universe is roughly $5\%$ ordinary matter, $26\%$ dark matter, and $69\%$ dark energy, and it is spatially flat ($\Omega_\text{total} = 1$), as the cosmic microwave background shows. Because matter dilutes while dark energy does not, the expansion decelerated under matter’s gravity and now accelerates under dark energy.

We have read the universe’s composition, shape, and fate from one equation. The last question runs the expansion backward: wind the scale factor down and the universe grows hotter and denser, until — in the first three minutes — it was a nuclear furnace. That is the finale.

Glossary

Cosmic microwave background

Relic radiation released at recombination, when the expanding universe first became transparent, now stretched into microwaves at $2.73~\mathrm{K}$. Its near-uniform glow and tiny temperature ripples measure the cosmic budget and the geometry of space.

Critical density

The density $\rho_\text{crit} = 3H_0^2/8\pi G$ that makes the universe spatially flat. About $9\times10^{-30}~\mathrm{g\,cm^{-3}}$ — roughly five hydrogen atoms per cubic meter. Densities are measured against it as $\Omega_i = \rho_i/\rho_\text{crit}$.

Friedmann equation

The equation governing the cosmic expansion rate, $H^2 = (8\pi G/3)\rho - kc^2/a^2$. It ties the expansion rate $H = \dot a/a$ to the total energy density $\rho$ and the spatial curvature $k$. Read, not solved, in this course.

Recombination

The era, about $380{,}000$ years after the Big Bang, when electrons combined with nuclei to form neutral atoms and the universe became transparent. The light freed then is the cosmic microwave background.

Spatial geometry

The curvature of space, fixed by the total density relative to critical: flat ($\Omega_\text{total}=1$), closed ($\gt 1$), or open ($\lt 1$). The cosmic microwave background measures it to be flat to within about a percent.