What is Hubble’s law and the hot beginning?

Every distant galaxy recedes, at speed proportional to distance:

This is not an explosion into space but an expansion of space — run it backwards and everything was once dense and hot: $1/H_0 \approx 14$ billion years ago (Exercise 27.9). The early universe is this book replayed at speed. At one second it is a $\mathrm{MeV}$ particle soup (Chapter 26); in the first minutes, Chapter 25 runs wild and freezes out one quarter helium by mass — predicted by a Boltzmann factor, observed everywhere (Exercise 27.11). At 380 000 years and $3000\,\mathrm{K}$, Saha’s equation (Proposition 18.5) lets electrons finally settle onto protons; the fog clears, and that last-scattered light — stretched a thousandfold by expansion — arrives today as the cosmic microwave background: a $2.725\,\mathrm{K}$ Planck spectrum (Chapter 20), the oldest photograph there is. What the picture also shows: galaxies spin and cluster as if steered by dark matter no detector has caught, and the expansion accelerates under a dark energy nobody has explained — the ninety-five percent of the budget this book cannot yet write.