The First Three Minutes
Section 3 of 6
Part 2: The First Three Minutes
By one second after the Big Bang, the universe had cooled to about ten billion kelvin — a plasma of photons, electrons, protons, and neutrons. This is the furnace.
Big Bang nucleosynthesis
The formation of the first light nuclei — deuterium, helium-3, helium-4, and a trace of lithium-7 — in the first few minutes of the hot early universe. It set the primordial composition: about three-quarters hydrogen and one-quarter helium by mass, with everything heavier left for stars.
Why only three minutes? Because the furnace is closing as it burns. The expansion is cooling and thinning the universe the entire time, and that sets a window:
- Reactions need the universe hot and dense enough to drive nuclei together against their electric repulsion.
- But helium is built through deuterium (a proton + a neutron), and deuterium is fragile: at temperatures above about , energetic photons blast it apart as fast as it forms. So helium cannot accumulate until the universe cools below that — roughly three minutes in.
- Once it does, helium builds almost explosively. But within minutes the expansion has thinned and cooled the plasma so far that reactions can no longer proceed. The window slams shut.
This race — reactions versus expansion — is a freeze-out: a reaction runs until the expanding universe dilutes and cools it to a halt, locking in whatever abundances it had reached. The first three minutes are not three minutes of leisurely cooking; they are the brief interval when the furnace is simultaneously hot enough and not yet too thin.
The decisive number is set even earlier. By one second, the neutrons and protons had frozen out at a ratio of about one neutron for every seven protons. Nearly every neutron then ends up bound into helium-4 (two protons, two neutrons), and that ratio fixes the cosmic helium fraction.
Problem
By the time deuterium survives, the neutron-to-proton ratio has frozen at . Essentially every neutron is captured into helium-4 (2 protons + 2 neutrons). Estimate the primordial helium mass fraction — the fraction of ordinary matter’s mass that is helium.
StepCount what each helium-4 takes
Each helium-4 needs 2 neutrons, so the number of helium nuclei is half the number of neutrons. The mass locked in helium is then nucleon masses, while the total baryon mass is nucleon masses.
StepForm the fraction in terms of n/p
Dimensional check
is a mass fraction — helium mass over total baryon mass — so it is a pure number, dimensionless, and must lie between 0 and 1. It does.
Result
About 25% helium by mass — and therefore about 75% hydrogen. This is a genuine prediction of the hot Big Bang, and it matches the helium found in the oldest, most pristine gas in the universe. A single frozen ratio, set in the first second, is why every corner of the cosmos is roughly one-quarter helium before any star burns.
Quick check
Big Bang nucleosynthesis lasted only a few minutes. What opened the window for it, and what closed it?
It opened when the universe cooled below about (~3 minutes), cool enough that deuterium — the stepping stone to helium — could survive instead of being blasted apart by energetic photons. It closed when the ongoing expansion thinned and cooled the plasma so far that nuclear reactions could no longer proceed. The expansion both enabled and ended BBN: a freeze-out.