The Big Bang Theory

OCR H556 mapping. This lesson covers Module 5.5.3 specification points on the Big Bang theory: that the universe began in an extremely hot, dense state and has been expanding ever since; that all distant galaxies are receding (more distant galaxies moving faster) is evidence; that the age of the universe is approximately $1/H_{0} \approx 13.8$1/H0​≈13.8 Gyr; and that the expansion is expansion of space, not motion through space. It builds on Hubble's law (lesson 8) and sets up the three direct lines of evidence (lesson 10).

Hubble's law (lesson 8) showed that galaxies are receding, and the farther away they are, the faster. If we run the film backwards in time, the galaxies must have been closer together; run it far enough backwards, and they must have been extremely close indeed — crammed into an astonishingly hot, dense state. This is the essence of the Big Bang theory: the universe began in a hot, dense state and has been expanding and cooling ever since.

The idea was proposed in 1927 by the Belgian priest and physicist Georges Lemaître, who called it the "hypothesis of the primeval atom". The name "Big Bang" was coined derisively by Fred Hoyle in 1949, but it stuck. Over the following decades, evidence mounted that Lemaître was right. By the 1960s, with the discovery of the cosmic microwave background (lesson 10), the Big Bang had become the standard model of cosmology.

This lesson lays out the Big Bang theory at the level OCR Module 5.5 requires: all galaxies receding, more distant galaxies moving faster, the age of the universe from Hubble's constant, and — crucially — what the Big Bang is not.

---

The Big Bang hypothesis

The Big Bang theory states:

1. The universe began in an extremely hot, dense state — not a point, necessarily, but a configuration so small that the physics of space and time may not apply in a recognisable way. It is often called a "singularity" for want of a better word, but taking this term too literally is misleading.
2. From this initial state, the universe has been expanding ever since. The expansion is not an explosion into some pre-existing space, but an expansion of space itself — every region of space is stretching.
3. As the universe expanded, it cooled. Early on, temperatures were high enough for nuclear reactions to occur; later, atoms could form; later still, stars and galaxies condensed from the primordial gas.
4. The universe has evolved from this hot, dense, uniform beginning into the cold, sparse, structured cosmos we see today.

This is a remarkably simple story. All its complexity comes from applying known physics (general relativity, quantum field theory, nuclear physics) to the expanding universe and seeing what must have happened at each temperature and density.

---

All galaxies are receding

One of the signature predictions of the Big Bang theory — and one of the observations that led to it — is that essentially all galaxies (outside the Local Group) are receding from us. Every direction we look, we see the same story: distant galaxies are red-shifted, and the further the galaxy, the higher the red shift.

graph LR
    subgraph "Spectra of galaxies at increasing distances"
    G1["Near galaxy<br/>small Δλ, small v"] --> G2["Mid-distance<br/>medium Δλ, medium v"]
    G2 --> G3["Far galaxy<br/>large Δλ, large v"]
    end
    subgraph "Hubble's law"
    H["v = H₀ d<br/>all receding<br/>(outside Local Group)"]
    end
    G3 --> H

If only some galaxies were receding, or if recession depended on direction, we would need a different explanation. But it applies uniformly, in every direction, to every sufficiently distant galaxy. This is what we would expect if every point in space is expanding away from every other point — and it is not what we would expect from any other physical mechanism we know of.

---

More distant galaxies move faster

Hubble's law $v = H_{0}d$v=H0​d means that recession velocity is proportional to distance. Doubling the distance doubles the velocity. Tripling it triples the velocity. The most distant galaxies we can see — at distances of $\sim 10$∼10 Gpc — are receding at sizeable fractions of the speed of light.

Why is this pattern exactly what a Big Bang predicts? Consider the balloon analogy from lesson 8. If the balloon is uniformly inflating, the rate at which any two dots move apart is proportional to their current separation. Closer dots move apart slowly; distant dots move apart quickly. There is no preferred centre of expansion — every dot sees the same pattern. This is exactly Hubble's law, and it follows directly from uniform expansion.

Hubble's law also means that, if you extrapolate the expansion backwards, there is a finite time in the past at which all the galaxies were coincident. At that time, the density of matter was enormous. This is the moment of the Big Bang.

In the diagram, the frame (the space) gets larger between $t_{1}$t1​, $t_{2}$t2​, $t_{3}$t3​, but the galaxies (red dots) keep their relative positions in the frame. They are carried apart by the expanding metric, not moving through it.

---

The age of the universe

The simplest estimate of the age of the universe assumes that the expansion rate has been constant: every galaxy has been moving at its current velocity for the entire history of the universe. Under this assumption, a galaxy currently at distance $d$d with velocity $v$v has been travelling for time $t = d/v$t=d/v. By Hubble's law:

$$t = \dfrac{d}{v} = \dfrac{d}{H_{0}\,d} = \dfrac{1}{H_{0}}$$t=vd​=H0​dd​=H0​1​

The reciprocal of the Hubble constant is the Hubble time, and it is our first estimate of the age of the universe.

Numerically, with $H_{0} \approx 2.3 \times 10^{-18}$H0​≈2.3×10−18 s$^{-1}$−1:

$$\begin{aligned} t &= \dfrac{1}{H_{0}} \approx 4.4 \times 10^{17}\,\text{s} \\ &\approx 1.4 \times 10^{10}\,\text{yr} \\ &\approx 14\,\text{Gyr} \end{aligned}$$t​=H0​1​≈4.4×1017s≈1.4×1010yr≈14Gyr​

The modern best value of the age of the universe, from detailed CMB measurements by the Planck satellite, is $\approx 13.8$≈13.8 Gyr. Our simple estimate — 14 Gyr — is correct to within a few per cent. Not bad for an argument that simply runs Hubble's law backwards.

The slight discrepancy ($\approx 14$≈14 Gyr predicted vs $\approx 13.8$≈13.8 Gyr actual) arises because the expansion has not been perfectly constant. For most of the universe's history, gravity has been decelerating the expansion, which would make the true age less than $1/H_{0}$1/H0​. In the past few billion years, dark energy has begun to accelerate the expansion, raising the true age closer to $1/H_{0}$1/H0​. The two effects nearly cancel, and $1/H_{0}$1/H0​ remains an excellent approximation.

---

Worked example 1: estimating the age of the universe

Using $H_{0} = 70$H0​=70 km s$^{-1}$−1 Mpc$^{-1}$−1, calculate the Hubble time.

Step 1. Convert to SI:

$$H_{0} = \dfrac{70 \times 10^{3}\,\text{m s}^{-1}}{3.086 \times 10^{22}\,\text{m}} \approx 2.27 \times 10^{-18}\,\text{s}^{-1}$$H0​=3.086×1022m70×103m s−1​≈2.27×10−18s−1

Step 2. Take reciprocal:

$$\dfrac{1}{H_{0}} \approx \dfrac{1}{2.27 \times 10^{-18}} \approx 4.41 \times 10^{17}\,\text{s}$$H0​1​≈2.27×10−181​≈4.41×1017s

Step 3. Convert to years (1 yr $= 3.156 \times 10^{7}$=3.156×107 s):

$$\dfrac{1}{H_{0}} \approx \dfrac{4.41 \times 10^{17}}{3.156 \times 10^{7}} \approx 1.40 \times 10^{10}\,\text{yr} \approx 14\,\text{Gyr}$$H0​1​≈3.156×1074.41×1017​≈1.40×1010yr≈14Gyr

So in this estimate, the Big Bang happened $\approx 14$≈14 Gyr ago.

---

Worked example 2: a different Hubble constant

Hubble's own 1929 measurements gave $H_{0} \approx 500$H0​≈500 km s$^{-1}$−1 Mpc$^{-1}$−1 — about seven times the modern value. What age of the universe would this have implied?

$$\begin{aligned} H_{0} &= \dfrac{500 \times 10^{3}}{3.086 \times 10^{22}} \approx 1.62 \times 10^{-17}\,\text{s}^{-1} \\ \dfrac{1}{H_{0}} &\approx 6.17 \times 10^{16}\,\text{s} \approx 2 \times 10^{9}\,\text{yr} \end{aligned}$$H0​H0​1​​=3.086×1022500×103​≈1.62×10−17s−1≈6.17×1016s≈2×109yr​

Only 2 Gyr. This is less than the radiometric age of the Earth ($\approx 4.5$≈4.5 Gyr) and less than the age of the oldest stars (estimated from stellar-evolution models). The universe being apparently younger than the objects in it was a major embarrassment for the Big Bang theory in the early decades and was used by steady-state theorists as evidence the Big Bang must be wrong.

The discrepancy was resolved when more accurate distance measurements (using Cepheids and later Type Ia supernovae) revealed that the true Hubble constant is closer to $70$70 km s$^{-1}$−1 Mpc$^{-1}$−1, not $500$500. With the modern value, the universe comfortably contains the stars and planets we observe. The early discrepancy is a beautiful example of how systematic errors — Hubble's distance ladder was contaminated by mistakes about Cepheid metallicities — can mislead even a correct theoretical framework.

---

Worked example 3: a galaxy at half the age of the universe

Light from a galaxy has been travelling for half the age of the universe ($\approx 7$≈7 Gyr). How far away (in light-travel distance) is the galaxy, in light years?

For small fractions of the universe's age the relationship $d \approx ct$d≈ct is reasonable:

$$\begin{aligned} t &= 0.5 \times 1.40 \times 10^{10}\,\text{yr} = 7 \times 10^{9}\,\text{yr} \\ d &\approx ct \\ &= (3.0 \times 10^{8}\,\text{m s}^{-1}) \times (7 \times 10^{9} \times 3.156 \times 10^{7}\,\text{s}) \\ &\approx 6.6 \times 10^{25}\,\text{m} \end{aligned}$$td​=0.5×1.40×1010yr=7×109yr≈ct=(3.0×108m s−1)×(7×109×3.156×107s)≈6.6×1025m​

In light years: $(6.6 \times 10^{25})/(9.46 \times 10^{15}) \approx 7 \times 10^{9}$(6.6×1025)/(9.46×1015)≈7×109 ly — which is what we should expect (light takes 7 Gyr to travel 7 Gly). In practice, in an expanding universe, the relationships between light-travel distance, comoving distance and luminosity distance differ — but the lowest-order estimate $d \approx ct$d≈ct is useful for intuition at modest fractions of the age of the universe.

---

Worked example 4: density of the early universe

The CMB photons were emitted when the universe was $\approx 380\,000$≈380000 yr old (recombination, $T \approx 3000$T≈3000 K). The mass density of matter today is $\rho_{\text{m},0} \approx 3 \times 10^{-27}$ρm,0​≈3×10−27 kg m$^{-3}$−3. Estimate the matter density at recombination.

Distances scale as the scale factor $a(t)$a(t); the universe has expanded by $(1+z) \approx 1100$(1+z)≈1100 since recombination, so $a/a_{0} \approx 1/1100$a/a0​≈1/1100. Volumes scale as $a^{3}$a3, so the density scales as $a^{-3}$a−3:

$$\begin{aligned} \rho_{\text{m,rec}} &= \rho_{\text{m,0}} \times 1100^{3} \\ &\approx (3 \times 10^{-27}) \times 1.33 \times 10^{9} \\ &\approx 4 \times 10^{-18}\,\text{kg m}^{-3} \end{aligned}$$ρm,rec​​=ρm,0​×11003≈(3×10−27)×1.33×109≈4×10−18kg m−3​

At recombination, the universe was about a billion times denser than it is today. Earlier still, at the time of Big Bang nucleosynthesis ($T \approx 10^{9}$T≈109 K, $z \approx 4 \times 10^{8}$z≈4×108), it was $\sim 10^{25}$∼1025 times denser than today — comparable to the density of water. The story of the universe is one of monotonic dilution.

---

The Big Bang and particle physics

In the first microseconds of the universe, temperatures were so high that ordinary matter could not exist in the forms we know today. At $T \approx 10^{13}$T≈1013 K, the universe was a plasma of quarks, leptons and gauge bosons. As it cooled:

• $T \approx 10^{12}$T≈1012 K: quarks combined to form protons and neutrons.
• $T \approx 10^{10}$T≈1010 K, $t \approx 1$t≈1 s: neutrons partially decayed; the surviving ones were captured into deuterium and helium. Big Bang nucleosynthesis — the primordial production of light elements — occurred over the first $\sim 20$∼20 minutes. About 75% of the baryons ended up as hydrogen, 25% as helium-4 by mass.
• $T \approx 3000$T≈3000 K, $t \approx 380\,000$t≈380000 yr: electrons combined with nuclei to form neutral atoms ("recombination"). Photons decoupled from matter and streamed freely — this is the origin of the cosmic microwave background (lesson 10).
• $T \approx 10$T≈10-$100$100 K, $t \approx 10^{8}$t≈108 yr: gravity pulled gas together to form the first stars and galaxies.

graph LR
    A["t = 10⁻⁴³ s<br/>Planck epoch<br/>T = 10³² K"] --> B["t ≈ 10⁻⁶ s<br/>Quarks → hadrons<br/>T ≈ 10¹³ K"]
    B --> C["t ≈ 1-1000 s<br/>BBN<br/>T ≈ 10⁹ K"]
    C --> D["t ≈ 380 000 yr<br/>Recombination<br/>T ≈ 3000 K"]
    D --> E["t ≈ 10⁸ yr<br/>First stars<br/>T ≈ 50 K"]
    E --> F["t ≈ 13.8 Gyr<br/>Today<br/>T ≈ 2.7 K"]

None of this detailed particle physics is on the OCR specification for A-Level, but it is the bedrock of the Big Bang theory, and each of these stages makes observational predictions that have been confirmed. Lesson 10 focuses on the two main direct fingerprints: the cosmic microwave background and the primordial element abundances.

---

What the Big Bang is not

The Big Bang is intuitively misunderstood more often than almost any other idea in modern physics. A few things "Big Bang" does not mean:

1. It is not an explosion at a point. The Big Bang happened everywhere at once. Every point in the current universe was at very high density in the early universe. There is no "centre" in three-dimensional space you could point to.
2. The universe is not expanding into anything. The expansion is of space itself. There is no pre-existing empty space "outside" the universe for it to expand into.
3. It does not require the universe to have been finite in size. The universe may be finite or infinite in spatial extent today; both are consistent with the Big Bang. What matters is that distances have been growing — not that the universe's "size" was ever zero.
4. "Singularity" does not mean a point of literally infinite density. General relativity breaks down at sufficiently high densities, and the earliest instants of the universe need quantum gravity to describe properly — which we do not yet have. Classical extrapolation gives a singularity, but this may be an artefact of applying a theory outside its range of validity.

These subtleties are common exam traps for conceptual questions. If in doubt, stick to the careful statement: the universe was once hot and dense, and has been expanding and cooling ever since.

---

Synoptic Links