Appearance
12.6 — The Big Bang, and How Much of It Is Established
Run the expansion backwards and everything gets closer, denser and hotter. Extrapolate far enough and the equations give infinite density at a finite time in the past.
That infinity is not a prediction about reality. It is general relativity announcing that it has left its domain of validity (Chapter 6.8), exactly as it does at a black hole's centre.
So what is actually established, and what is extrapolation? This chapter separates them.
And one clarification first, because the name misleads. The Big Bang was not an explosion in space. It was — as far as the evidence reaches — a hot dense state that everywhere began expanding. There was no centre and no outside. Fred Hoyle coined the term derisively on a radio broadcast in 1949, promoting his own steady-state model, and it stuck.
The timeline
| Time | Temperature | Event | Status |
|---|---|---|---|
| <10^{-43} s | >10^{32} K | Planck era | Unknown physics |
| 10^{-36} s | 10^{28} K | Inflation | Well motivated, not proven |
| 10^{-32} s | 10^{27} K | Reheating | Speculative |
| 10^{-12} s | 10^{15} K | Electroweak breaking | Tested at LHC energies |
| 10^{-6} s | 10^{13} K | Quarks bind into hadrons | Tested at RHIC and LHC |
| 1 s | 10^{10} K | Neutrinos decouple | Solid theory |
| 3 min | 10^{9} K | Nucleosynthesis | Directly confirmed |
| 47,000 y | 9000 K | Matter–radiation equality | Confirmed by CMB |
| 380,000 y | 3000 K | Recombination | Directly observed |
| 100–500 My | First stars | Being observed by JWST | |
| 13.8 Gy | 2.725 K | Now |
The line between speculation and observation falls at about one second. Everything after that involves physics tested in laboratories.
The four pillars
Four independent observations support the hot Big Bang, and each would be difficult to explain otherwise.
1. The expansion
Chapter 12.5. Hubble's law, confirmed over five orders of magnitude in distance.
2. The cosmic microwave background
Predicted by Alpher and Herman in 1948 at about 5 K, from the requirement that a hot early universe must leave residual radiation. The prediction was forgotten.
Found by accident in 1964. Arno Penzias and Robert Wilson at Bell Labs were calibrating a horn antenna and could not eliminate a persistent 3.5 K excess noise, isotropic and constant in time. They evicted a pair of pigeons and cleaned out what Penzias called "a white dielectric material", and the noise remained.
A colleague mentioned that a group at Princeton was building a detector to look for exactly this. The two papers appeared back to back. Penzias and Wilson received the 1978 Nobel Prize.
The spectrum, measured by COBE's FIRAS instrument in 1990, is the most perfect black-body spectrum ever measured — matching Planck's law (Chapter 7.1) to within 50 parts per million.
T = 2.72548 \pm 0.00057\ \text{K}
When the COBE spectrum was shown at a meeting, the audience applauded. No known process other than a hot dense equilibrium can produce a black body that perfect.
Where it comes from. At 380,000 years the universe cooled to about 3000 K, and electrons combined with protons to form neutral hydrogen — recombination, a poor name since they had never been combined before.
Before that, free electrons scattered photons constantly (Chapter 5.5), so the universe was an opaque glowing fog. After it, photons streamed freely.
\boxed{\text{The CMB is the moment the universe became transparent.}}
Why 3000 K and not 13.6 eV / k_B = 158,000 K? Because there are two billion photons per baryon, so even the far tail of the black-body distribution has enough ionising photons to keep hydrogen ionised well below the naive temperature. The delay is a direct consequence of the photon-to-baryon ratio, and it is one of the checks on that number.
And it has cooled by exactly the expansion factor. Emitted at 3000 K, observed at 2.725 K:
1+z = \frac{3000}{2.725} = 1101
The universe has expanded by a factor of 1100 since then.
3. Primordial nucleosynthesis
This is the sharpest quantitative test, because it predicts numbers that can be checked to a few percent.
Between about 3 and 20 minutes, the universe was hot enough for fusion and cool enough for the products to survive.
Step 1: the neutron-to-proton ratio. Above 10^{10} K, weak interactions keep neutrons and protons in equilibrium:
n+\nu_e \rightleftharpoons p+e^-
The ratio follows the Boltzmann factor with the mass difference \Delta mc^2 = 1.293 MeV:
\frac{n}{p} = e^{-\Delta mc^2/k_BT}
At freeze-out, about 10^{10} K where k_BT = 0.86 MeV:
\frac{n}{p} = e^{-1.293/0.86} = e^{-1.503} = 0.222
Step 2: neutron decay. Free neutrons decay with a lifetime of 879 s. About 3 minutes pass before fusion begins:
\frac{n}{p} = 0.222\times e^{-180/879} = 0.222\times0.816 = 0.181 \approx \frac{1}{5.5}
Step 3: essentially all neutrons end up in helium-4. It is the most tightly bound light nucleus (Chapter 6.P), so the reactions funnel everything into it.
For every 2 neutrons, you get one helium-4 using 2 protons. With n/p = 1/5.5, take 2 neutrons and 11 protons:
\text{1 helium-4 (mass 4)} + \text{9 hydrogen (mass 9)}
Y = \frac{4}{13} = 0.25
\boxed{\text{Predicted helium mass fraction: 25 \%}}
Measured: 0.2453 \pm 0.0034 in the most metal-poor gas clouds, which have undergone the least stellar processing.
A prediction from nuclear physics and thermodynamics, with essentially no free parameters, matching to about 2 %.
And the other light elements:
| Nucleus | Predicted | Observed |
|---|---|---|
| $^4$He | 0.247 | 0.245 |
| D/H | 2.5\times10^{-5} | 2.5\times10^{-5} |
| $^3$He/H | 10^{-5} | \sim10^{-5} |
| $^7$Li/H | 5\times10^{-10} | 1.6\times10^{-10} |
Deuterium is the most sensitive. Its abundance depends steeply on the baryon density, so measuring D/H in high-redshift gas clouds gives \Omega_b directly:
\Omega_bh^2 = 0.0224
And the CMB, by a completely independent route, gives 0.0224.
\boxed{\text{Two methods, different physics, different epochs, agreeing to 1 \%.}}
The lithium problem is the exception, and it is real. Observed lithium-7 is about three times less than predicted. Possible explanations include destruction inside stars, an error in a nuclear cross-section, or new physics. It is unresolved and it is a genuine anomaly, not usually publicised alongside the successes.
Why the process stopped. There is no stable nucleus of mass 5 or 8. Helium-5 and beryllium-8 both fall apart immediately, so the chain cannot bridge past helium-4 without the triple-alpha process (Chapter 12.2), which needs stellar densities. By the time densities and temperatures were right for that, the universe had expanded too far.
So the universe emerged from nucleosynthesis as 75 % hydrogen, 25 % helium, and essentially nothing else. Everything heavier came from stars.
4. Structure formation
Chapter 12.4. Simulations starting from the CMB fluctuations and evolving under gravity reproduce the observed cosmic web quantitatively.
The CMB power spectrum
The CMB is uniform to one part in 10^{5}, and the tiny anisotropies are where the information is.
COBE found them in 1992 at the level of \Delta T/T \approx 10^{-5}, and Smoot and Mather received the 2006 Nobel Prize. WMAP and Planck mapped them in fine detail.
What produces them
Before recombination, photons and baryons were a single tightly coupled fluid.
Dark matter, which does not couple to photons, had already begun clumping and had created gravitational wells.
Baryons fell into the wells, compressed, and the radiation pressure pushed back out. Compression, rebound, compression — acoustic oscillations.
\boxed{\text{Sound waves in the plasma of the early universe.}}
Recombination froze the pattern. Modes caught at maximum compression or maximum rarefaction show as temperature extremes; modes caught mid-swing show nothing.
The angular scale of a mode depends on its wavelength, and the fundamental mode is the one that had just enough time to compress once — a wavelength equal to the sound horizon at recombination.
The sound speed in a photon–baryon plasma:
c_s = \frac{c}{\sqrt{3(1+R)}}, \qquad R = \frac{3\rho_b}{4\rho_\gamma}
For a radiation-dominated plasma, R \to 0 and c_s = c/\sqrt{3} = 0.577c.
Sound travelling at 58 % of light speed. The sound horizon at recombination is about 147 Mpc comoving.
Reading the peaks
The power spectrum plots the amplitude of fluctuations against angular scale.
First peak — angular scale about 1°, multipole \ell \approx 220.
Its position measures the curvature of space. The physical size of the sound horizon is known from the physics; the angle it subtends depends on the geometry between then and now.
In a closed universe, light paths converge and the spot looks larger. In an open universe they diverge and it looks smaller.
Measured: exactly the flat prediction.
\Omega_{\text{total}} = 1.000 \pm 0.002
Second peak — its height relative to the first measures the baryon density.
Baryons add inertia to the oscillating fluid, which enhances compressions (odd peaks) relative to rarefactions (even peaks). The suppressed second peak gives:
\Omega_bh^2 = 0.02237 \pm 0.00015
Third peak and beyond — measure the dark matter density, because dark matter's gravity affects how the oscillations decay and how much the potential wells change.
\Omega_ch^2 = 0.1200 \pm 0.0012
Damping tail — small scales are smoothed because recombination was not instantaneous, and photons diffused out of the smallest overdensities. Silk damping, and its scale is another consistency check.
From these features, six parameters determine essentially everything, and every other cosmological measurement then becomes a test.
Baryon acoustic oscillations
The same sound horizon left an imprint in the distribution of galaxies.
The pattern frozen at recombination corresponds to a preferred separation of about 150 Mpc, which appears as a slight excess of galaxy pairs at that separation.
It was detected in 2005 by SDSS and 2dF, and it is used as a standard ruler at many redshifts, tracing the expansion history independently of supernovae.
\boxed{\text{The same sound wave is measured in the CMB at 380,000 years and in galaxies today.}}
Inflation
Three problems with the standard hot Big Bang, and one idea that fixes all three.
The horizon problem
The CMB is at the same temperature to one part in 10^{5} across the whole sky.
But regions more than about 2° apart were never in causal contact. At recombination, the horizon subtended about 2°, so opposite sides of the sky had never exchanged a signal.
\boxed{\text{How did they come to the same temperature?}}
In a hot Big Bang with no inflation, they cannot have. The uniformity is unexplained.
The flatness problem
\Omega_{\text{total}} = 1 is an unstable equilibrium.
From the Friedmann equation:
|\Omega-1| = \frac{|k|c^2}{a^2H^2}
In radiation domination a \propto t^{1/2} and H \propto 1/t, so a^2H^2 \propto 1/t, and:
|\Omega-1| \propto t
Any deviation grows.
Work backwards. For |\Omega-1| < 0.002 today, at the Planck time it must have been:
|\Omega-1| < 10^{-60}
Sixty decimal places of fine tuning, with no reason.
The monopole problem
Grand unified theories (Chapter 8.7) predict magnetic monopoles produced in the phase transition, at roughly one per horizon volume. They are massive and stable, and would dominate the universe's density by many orders of magnitude.
None has ever been found.
Inflation's answer
Alan Guth proposed in 1980 that the very early universe underwent a brief period of exponential expansion.
a(t) \propto e^{Ht}
Driven by a scalar field — the inflaton — sitting in a false vacuum with an energy density that acts like a large cosmological constant (Chapter 6.8).
The numbers: starting at about 10^{-36} s, lasting until about 10^{-32} s, expanding by a factor of at least e^{60} \approx 10^{26}.
How it solves all three:
Horizon. The entire observable universe was inside one causally connected patch before inflation, so it had time to equalise. Inflation then blew that patch up to far larger than the current horizon.
Flatness. Inflating by 10^{26} flattens any curvature the way inflating a balloon to the size of the Earth makes its surface look flat locally. |\Omega-1| is driven towards zero exponentially.
Monopoles. They were produced before or during inflation and diluted to essentially zero density — fewer than one in the observable universe.
The prediction that made it science
Solving three known problems is not impressive on its own; a model can be built to do that.
Inflation made a prediction nobody expected.
Quantum fluctuations in the inflaton field (Chapter 7.9) were stretched to cosmological scales by the expansion. They became the seeds of all structure.
And the prediction is specific: the fluctuations should be nearly scale-invariant, adiabatic and Gaussian, with a spectral index slightly less than 1.
n_s = 0.965 \pm 0.004\ \text{(measured)}
Predicted: slightly below 1, and the deviation from 1 is related to how the inflaton rolled.
Measured to be 0.965, over 8 sigma away from exactly 1.
\boxed{\text{The structure of the universe came from quantum fluctuations during inflation, magnified } 10^{26}\text{-fold.}}
Every galaxy traces back to a quantum fluctuation in a field, 10^{-36} seconds after the beginning.
What is not established
Inflation is a framework, not a specific theory. Hundreds of models exist with different inflaton potentials, and most cannot be distinguished by current data.
The energy scale is unknown, spanning many orders of magnitude.
Eternal inflation — most models predict that inflation never entirely stops, continuing forever in some regions and producing a multiverse (Chapter 12.9). This is a prediction of the models rather than an observation, and its testability is disputed.
And the smoking gun has not been found.
Inflation should produce primordial gravitational waves (Chapter 6.10), which would imprint a distinctive curl pattern — B-mode polarisation — in the CMB.
BICEP2 announced a detection in March 2014, with a claimed 7-sigma significance and enormous publicity. Within a year, Planck data showed the signal was polarised dust in our own galaxy.
It is a cautionary tale of exactly the kind Chapter 8.6 described, and the search continues with better foreground modelling. Current limits give r < 0.032 on the tensor-to-scalar ratio, which already excludes several simple inflation models.
Before the Big Bang
The honest answer: nobody knows, and the question may not be well posed.
The classical singularity is not a prediction. General relativity fails when quantum effects matter, which is at the Planck scale — 10^{-43} s, 10^{32} K, 10^{-35} m.
Proposals:
Time began. Asking what came before is like asking what is north of the North Pole. Hawking's position, and the no-boundary proposal makes it precise: time becomes another spatial dimension near the beginning, so there is no first moment.
A bounce. Loop quantum cosmology (Chapter 8.7) replaces the singularity with a contraction that reverses at Planck density, because the discreteness of space prevents infinite compression.
Eternal inflation. Our universe is a bubble in an eternally inflating background, with no beginning.
Cyclic models. Ekpyrotic and conformal cyclic cosmologies propose repeated cycles.
None is testable at present. They are respectable theoretical work and they are not established science, and it is worth being clear about the difference.
What is established, and how confidently
Very high confidence:
- The universe is expanding and was hotter and denser in the past.
- Nucleosynthesis at 3 minutes produced the observed light element abundances.
- The CMB was released at 380,000 years and encodes a consistent set of parameters.
- Structure grew by gravitational instability from small primordial fluctuations.
- The age is 13.8 billion years.
High confidence:
- The fluctuations were nearly scale-invariant and adiabatic, consistent with inflation.
- Dark matter is cold and non-baryonic.
Moderate confidence:
- Inflation happened in some form.
Unknown:
- What the inflaton is.
- What happened before 10^{-36} s.
- Whether there was a beginning.
Where this shows up in your life
About 1 % of the static on an old analogue television tuned between channels was the cosmic microwave background — photons released 380,000 years after the beginning, being received by a consumer appliance.
The hydrogen in every water molecule in your body was made in the first three minutes and has never been anything else.
GPS, medical imaging and every precision timing system rest on the same physics that describes the early universe, tested at both ends.
And the CMB is the oldest thing anyone can see. Every photon arriving from it has been travelling for 13.8 billion years and has not interacted with anything since the universe became transparent.
What the next chapter fixes
The parameters have been measured and 95 % of them are unexplained. Dark matter is 27 % of the energy content and nobody knows what it is; dark energy is 68 % and nobody knows what it is either. Chapter 12.7 examines both properly: the full evidence, every serious candidate, the experiments running now, what has been ruled out, and an honest assessment of the alternatives including modified gravity.