A hot, dense past
The radiation that fills the universe cools as space expands — each photon redshifts to lower energy, so the temperature of the cosmic gas falls in inverse proportion to the scale factor. Rewind, and the early universe was blisteringly hot. This single scaling law turns the Big Bang into a chronology you can compute.
Temperature scales as 1/a = (1+z). Today's background is 2.725 K; at z≈1100 it was about 3000 K.
Because temperature is energy, the young universe was its own particle accelerator: hot enough, early enough, to make and unmake every particle we know. As it cooled it passed through a sequence of thresholds — quarks binding into protons and neutrons, nuclei forming, atoms forming — each leaving a fossil we can still detect. This timeline is the backbone of the hot Big Bang.
The first three minutes: nucleosynthesis
When the universe was roughly one second to a few minutes old and near a billion kelvin, protons and neutrons could stick together without being instantly blasted apart. In that brief window, Big Bang nucleosynthesis forged the lightest nuclei — mostly hydrogen and helium, with traces of deuterium and lithium. The theory predicts that about a quarter of all ordinary matter, by mass, should be helium-4, and that is exactly what we observe.
Recombination and the oldest light
For its first 380,000 years the universe was an opaque plasma: free electrons scattered photons so relentlessly that light could travel no distance at all, like sunlight lost inside fog. Then, as the temperature fell to about 3000 K, electrons finally combined with protons into neutral hydrogen atoms — an event confusingly called recombination. Suddenly there were no free electrons to scatter light, and the universe became transparent.
The light set free at that instant has been streaming toward us ever since, stretched by the expansion from a 3000 K glow down to a chilly microwave hiss. This is the cosmic microwave background (CMB): a snapshot of the entire sky as it was at recombination, redshifted by a factor of about 1100 to a temperature of 2.725 K today. It is the oldest light we can ever see with a telescope.
Reading the CMB
The CMB is the most perfect blackbody ever measured — its spectrum matches Planck's radiation law to staggering precision, confirming that it really is thermal radiation from a hot, opaque past. But its true riches are its faint imperfections. The temperature is not perfectly uniform: it varies from point to point by only a few parts in a hundred thousand.
The CMB temperature ripples are tiny — about one part in 100,000 — yet they are the seeds of every galaxy.
Those ripples are the seeds of cosmic structure: slightly denser patches were slightly hotter, and gravity later grew them into galaxies and clusters. The statistics of the ripples — how much power sits at each angular scale — encode the whole recipe of the universe. Fitting that pattern is how cosmologists measure \Omega, H_0, the geometry, and the dark-matter and dark-energy fractions to percent precision.
Inflation: solving two deep puzzles
The hot Big Bang is a triumph, but it leaves two nagging puzzles. The horizon problem: opposite sides of the CMB sky have the same temperature to a part in 10^5, yet in the standard history they were never in causal contact — light could not have crossed between them to equalise anything. The flatness problem from Guide 2: why is \Omega so exquisitely close to 1 today, when that value is unstable? Both smell of impossible fine-tuning.
Cosmic inflation solves both at a stroke. The idea: in the first sliver of a second (around 10^{-34} s), the universe underwent a brief burst of exponential expansion, blowing up by a factor of e^{60} or more. A single tiny patch, small enough to have been causally connected and smoothed out, was stretched to encompass everything we now see — fixing the horizon problem. And any curvature was flattened out like the surface of an inflating balloon — fixing the flatness problem.
Inflation is a phase of near-exponential growth, driven by a temporarily constant, dark-energy-like density.