The Big Bang
Cosmology is the study of the universe as a whole: its origin, evolution, and ultimate fate. The hot Big Bang model is the most successful scientific theory of cosmic history, supported by multiple independent lines of evidence. It tells us that the universe was once unimaginably hot, dense, and small, and has been expanding and cooling for approximately 13.8 billion years. This lesson traces that history from the earliest moments to the present day.
What the Big Bang Is (and Is Not)
The Big Bang is not an explosion that happened at a particular point in pre-existing space. Rather, it is the expansion of space itself. Every point in the universe was the "center" of the Big Bang, because the Big Bang happened everywhere simultaneously. The proper description is that the scale factor $a(t)$ of the universe was once very small and has been growing ever since.
Hubble's Discovery: The Expanding Universe
What is the expansion of the universe?
The expansion of the universe means that space itself is stretching over time. It is not that galaxies are moving through space: it is the "fabric" of space between them that is growing. Imagine dots drawn on a balloon that is being inflated: every dot moves away from every other dot, not because they move on the surface, but because the surface itself is expanding. Similarly, the more distant a galaxy is, the faster it recedes from us.
In 1929, Edwin Hubble made one of the most profound discoveries in the history of science. By measuring the redshifts and distances of distant galaxies, he found that galaxies are receding from us with velocities proportional to their distance:
$$v = H_0 \, d$$where $H_0$ is the Hubble constant, currently measured at approximately $H_0 \approx 70 \, \text{km/s/Mpc}$. This is not galaxies flying through space; it is space itself stretching. The redshift of a photon is related to the scale factor at the time of emission:
$$1 + z = \frac{a(t_0)}{a(t_{\text{emit}})}$$Running the expansion backward in time, we conclude that the universe must have been denser and hotter in the past, converging toward an initial state of extraordinary density. The Friedmann equations, derived from general relativity, govern this expansion:
$$H^2 = \left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2}$$where $\rho$ is the total energy density and $k$ describes the spatial curvature.
Thermal History: A Cosmic Timeline
As the universe expands, it cools. The temperature scales inversely with the scale factor: $T \propto 1/a(t)$. This means the early universe was a furnace of extraordinary temperatures, and as it cooled, different physical processes switched on and off. The thermal history of the universe reads like a sequence of phase transitions.
Key Epochs in Cosmic History
Planck era ($t < 10^{-43}$ s, $T > 10^{32}$ K): Quantum gravity dominates. Our current theories break down.
Grand unification ($t \sim 10^{-36}$ s, $T \sim 10^{28}$ K): The strong, weak, and electromagnetic forces may be unified.
Electroweak transition ($t \sim 10^{-12}$ s, $T \sim 10^{15}$ K): The Higgs field acquires a vacuum expectation value; the W and Z bosons gain mass.
QCD transition ($t \sim 10^{-6}$ s, $T \sim 10^{12}$ K): Quarks become confined into protons and neutrons.
Nucleosynthesis ($t \sim 1$-$300$ s, $T \sim 10^{9}$ K): Light nuclei form.
Recombination ($t \sim 380{,}000$ years, $T \sim 3{,}000$ K): Atoms form; photons decouple.
Today ($t \sim 13.8$ billion years, $T = 2.725$ K): The cosmic microwave background fills the universe.
Big Bang Nucleosynthesis
One of the most powerful pieces of evidence for the Big Bang is the prediction of light element abundances. In the first few minutes after the Big Bang, when the temperature was between $10^{10}$ K and $10^{9}$ K, nuclear reactions fused protons and neutrons into light nuclei.
The key reactions began once the temperature dropped below the deuterium binding energy (the "deuterium bottleneck"). The chain proceeds rapidly:
$$p + n \to \text{D} + \gamma$$ $$\text{D} + \text{D} \to {}^3\text{He} + n$$ $${}^3\text{He} + n \to {}^4\text{He} + \gamma$$By the time the universe had cooled below about $10^9$ K (around 3 minutes), nuclear reactions effectively ceased. The predicted abundances are remarkably specific:
| Element | Predicted Abundance | Observed |
|---|---|---|
| ${}^4\text{He}$ | ~25% by mass | ~24-25% |
| Deuterium D | ~$2.5 \times 10^{-5}$ | ~$2.5 \times 10^{-5}$ |
| ${}^3\text{He}$ | ~$10^{-5}$ | ~$10^{-5}$ |
| ${}^7\text{Li}$ | ~$5 \times 10^{-10}$ | ~$1.6 \times 10^{-10}$ |
The agreement for helium-4, deuterium, and helium-3 is spectacular. The slight discrepancy for lithium-7 (the "lithium problem") remains an active area of research. Crucially, the predictions depend sensitively on the baryon-to-photon ratio $\eta = n_b / n_\gamma \approx 6.1 \times 10^{-10}$, which is independently confirmed by CMB measurements.
Radiation-Matter Equality
The energy density of radiation dilutes as $\rho_r \propto a^{-4}$ (the extra factor of $a^{-1}$ compared to matter comes from the cosmological redshift of each photon's energy), while matter dilutes as $\rho_m \propto a^{-3}$. There was therefore a crossover time, about 50,000 years after the Big Bang, when the two densities were equal:
$$\rho_r(t_{\text{eq}}) = \rho_m(t_{\text{eq}})$$Before this time, the universe was radiation-dominated. After it, the universe became matter-dominated. This transition is crucial because density perturbations can only grow significantly under gravity in the matter-dominated era. Without this transition, the gravitational clumping that eventually formed galaxies could not have occurred.
Recombination and the Last Scattering Surface
About 380,000 years after the Big Bang, the temperature dropped to roughly 3,000 K. At this point, electrons could finally be captured by protons to form neutral hydrogen atoms:
$$p + e^- \to \text{H} + \gamma$$Before recombination, photons were tightly coupled to the electron-baryon plasma through Thomson scattering. The universe was opaque: a photon could not travel far before being scattered. Once neutral atoms formed, photons decoupled and streamed freely across the universe. These photons are what we observe today as the cosmic microwave background (CMB), redshifted from 3,000 K to 2.725 K by the expansion of the universe.
Three Pillars of Evidence
The hot Big Bang model rests on three independent, robust pieces of observational evidence:
1. The cosmic microwave background. The CMB is a nearly perfect blackbody spectrum at $T = 2.725$ K, exactly as predicted by a universe that was once in thermal equilibrium and has since expanded by a factor of about 1,100. No other model has naturally explained this radiation.
2. Light element abundances. The observed cosmic abundances of hydrogen, deuterium, helium-3, helium-4, and lithium-7 match the predictions of Big Bang nucleosynthesis with remarkable precision (with the mild exception of lithium-7).
3. The expansion of the universe. Hubble's law, confirmed with increasing precision by modern surveys, demonstrates that the universe is expanding. Combined with general relativity, this implies a hot, dense beginning.
The Initial Singularity and Its Problems
Extrapolating the Friedmann equations backward, we reach $a(t) \to 0$ at a finite time in the past: the initial singularity. But this does not mean the Big Bang model is complete. The singularity signals the breakdown of general relativity at extreme densities ($\rho \to \infty$). Moreover, the standard Big Bang model has several puzzles: Why is the universe so homogeneous (horizon problem)? Why is it so flat (flatness problem)? Where are the magnetic monopoles? These problems motivated the theory of cosmic inflation.
Key Insights
- The Big Bang is the expansion of space itself, not an explosion in pre-existing space
- Hubble's law $v = H_0 d$ reveals that the universe is expanding, implying a hotter, denser past
- The thermal history traces the universe from the Planck era through nucleosynthesis to recombination
- Big Bang nucleosynthesis predicts light element abundances with remarkable accuracy
- Radiation-matter equality marks the transition enabling gravitational structure formation
- Recombination at $t \approx 380{,}000$ years released the CMB photons we observe today
- Three independent pillars support the Big Bang: the CMB, element abundances, and cosmic expansion
- The initial singularity signals the need for new physics (quantum gravity, inflation)
Looking Ahead
The standard Big Bang model is spectacularly successful, but it leaves several deep puzzles unexplained. Why is the universe so uniform on large scales when distant regions have never been in causal contact? Why is the spatial geometry so close to flat? In the next lesson, we explore cosmic inflation: a brief period of exponential expansion in the very early universe that resolves these puzzles and, remarkably, provides the seeds for all the structure we see today.
- The Big Bang is the expansion of space itself, not an explosion in pre-existing space, and Hubble's law $v = H_0 d$ provides direct evidence that the universe is expanding.
- The thermal history of the universe traces a sequence of phase transitions from the Planck era through nucleosynthesis to recombination, with each epoch leaving observable imprints.
- Big Bang nucleosynthesis successfully predicts the cosmic abundances of light elements, and recombination at 380,000 years released the CMB photons we observe today.
- Three independent pillars of evidence support the Big Bang model: the cosmic microwave background, light element abundances, and the observed expansion of the universe.