Cosmology & The Big Bang

The universe had a beginning - and we can still see its glow!

Junior level — plain language, no maths

Everything you've ever seen - every star, galaxy, planet and atom - was once packed into a space unimaginably smaller than the full stop ending this sentence. About 13.8 billion years ago that impossibly hot, dense point began to expand in an event we call the Big Bang. And here's the subtlety: it wasn't matter flying out into empty space - space itself was expanding, and it has been ever since.

For the first few minutes the universe was hot enough to fuse protons and neutrons into hydrogen and helium, but far too hot for whole atoms to hold together - it was a glowing fog of plasma, as opaque as the inside of a star. Then, 380,000 years in, it cooled just enough for electrons to settle onto nuclei, and the fog lifted. Light poured freely across the cosmos for the very first time - and, remarkably, we can still catch that ancient light today. It bathes the whole sky as a faint hiss of microwaves, the Cosmic Microwave Background.

The CMB is nothing less than a baby photo of the universe at 380,000 years old. It's almost perfectly smooth in every direction - but not quite. Faint temperature ripples, just one part in 100,000, are the seeds of everything: gravity spent billions of years amplifying those tiny lumps into stars, galaxies and the vast cosmic web we live in. In the simulation below, watch the universe expand from the Big Bang to today.

The Friedmann equations, inflation, and dark energy

Student level — the core equations

The universe's expansion is written into the Friedmann equations, which drop out of general relativity the moment you assume the cosmos looks the same everywhere and in every direction. The first of them, \(H^2 = \dfrac{8\pi G}{3}\rho - \dfrac{kc^2}{a^2} + \dfrac{\Lambda c^2}{3}\), ties the expansion rate \(H\) to what the universe holds: matter and radiation \(\rho\), its curvature \(k\), and the cosmological constant \(\Lambda\). Reading the sky returns a startling inventory - space is flat (\(k \approx 0\)) and made of just ~5% ordinary matter, ~27% dark matter and ~68% dark energy.

Cosmic inflation (Guth, 1981) proposes that in the first sliver of a second the universe ballooned exponentially, \(a \propto e^{Ht}\), swelling by a factor of \(10^{26}\) in about \(10^{-32}\) s. That one wild growth spurt fixes three nagging puzzles at once: why the CMB is uniform across regions that could never have exchanged a signal (the horizon problem), why space is so exquisitely flat (the flatness problem), and why we see no exotic relics. Best of all, quantum jitters stretched during inflation became the density ripples in the CMB - the origin of all cosmic structure, planted by quantum mechanics.

The most disquieting discovery is that the expansion is accelerating, uncovered in 1998 from the surprising dimness of distant supernovae (Nobel 2011). Something with negative pressure - dark energy, equation of state \(w = p/\rho c^2 \approx -1\) - is prising the universe apart ever faster. And a genuine crack has appeared: the expansion rate \(H_0\) measured from the early CMB (67 km/s/Mpc) stubbornly refuses to match the value read off nearby supernovae (73), a five-sigma Hubble tension that may be the first sign of physics beyond the standard model of cosmology.

CMB anisotropies, large-scale structure, and quantum gravity

Scholar level — full mathematical depth

01Reading the oldest light

The CMB's tiny temperature ripples \(\delta T/T \sim 10^{-5}\) are the richest dataset in cosmology, and the way to mine them is to expand the whole sky in spherical harmonics, \(\delta T/T(\hat{n}) = \sum_{\ell m} a_{\ell m} Y_{\ell m}(\hat{n})\). Averaging gives the angular power spectrum \(C_\ell = \langle |a_{\ell m}|^2\rangle\) - a plot of how much structure exists at each angular scale, and effectively a fingerprint of the entire early universe compressed into one curve.

02The acoustic peaks

Before the fog cleared, photons and baryons were a single fluid ringing with sound waves, and those oscillations are frozen into the power spectrum as a series of acoustic peaks. Their positions and heights are pure gold: the first peak's angular scale, near \(\ell \approx 220\), pins the geometry of space (confirming flatness), the peak heights weigh the ordinary matter, and their spacing helps set the expansion rate. A handful of bumps in one graph fixes nearly every cosmological parameter at once.

03Polarisation and the echo of inflation

The CMB is also faintly polarised, and the polarisation splits into two patterns. E-modes come from ordinary density waves and are firmly seen. The prize is the B-modes: a curl pattern that only primordial gravitational waves from inflation could have made, whose strength - the tensor-to-scalar ratio \(r\) - would read out the energy scale of inflation itself. Detecting them would be a direct glimpse of physics at \(10^{16}\) GeV, and the hunt is one of cosmology's great races.

04The cosmic web and its standard ruler

The same primordial ripples grew, under gravity, into the cosmic web of galaxies, and its statistics carry their own fossil of the early sound waves: baryon acoustic oscillations, a preferred galaxy separation of about 150 Mpc imprinted on the whole sky. Because that length is known from first principles, it acts as a cosmic ruler - measure its apparent size at different distances and you chart the expansion across billions of years. Surveys like DESI now do exactly this, tracking whether dark energy has stayed truly constant.

05The quantum-gravity frontier

Rewind far enough and the theory itself fails: at the Big Bang singularity, general relativity predicts infinite density and hands the problem to a quantum theory of gravity we don't yet have. Candidate ideas replace the bang with something gentler - loop quantum cosmology swaps it for a bounce off a maximum density, while string theory pictures our universe as one bubble in an eternally inflating multiverse, which could make the eerie fine-tuning of the physical constants a selection effect rather than a mystery.

06A warning from the swampland

Not every seemingly reasonable universe can be built from a consistent quantum-gravity theory - the ones that can't are said to lie in the swampland. Provocatively, some swampland conjectures hint that a stable, positively accelerating universe like ours may be hard or impossible to realise in string theory, putting the theory in direct tension with the dark energy we actually observe. Whether that tension breaks string theory, our understanding of dark energy, or the conjectures themselves is wide open - and it's where fundamental physics and cosmology now meet head-on.