The Big Bang Theory

Hubble's law (Lesson 8) told us that galaxies are receding, and the further away they are, the faster. If we run the film backwards in time, we find that all the galaxies used to be closer together. Run it far enough backwards, and they must all have been extremely close indeed — perhaps 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, and an estimate of the age of the universe from Hubble's constant.

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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 idea 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.

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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<br/>small v] --> G2[Mid-distance<br/>medium Δλ<br/>medium v]
    G2 --> G3[Far galaxy<br/>large Δλ<br/>large v]
    end
    subgraph "Hubble's law"
    H[v = H₀ d<br/>all receding]
    end
    G3 --> H

If only some galaxies were receding, or if recession depended on direction, we would look for 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.

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More Distant Galaxies Move Faster

Hubble's law `v = H_0 d) means that recession velocity is proportional to distance. Doubling the distance doubles the velocity. Tripling it triples the velocity. The furthest galaxies we can see — at distances of 10 Gpc or more — 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.

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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) with velocity v) has been travelling for time `t = d/v). By Hubble's law:

t = d / v = d / (H_0 d) = 1/H_0

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

Numerically, with `H_0 = 2.27 × 10⁻¹⁸) s⁻¹:

t = 1/H_0 = 1/(2.27 × 10⁻¹⁸) = 4.40 × 10¹⁷ s
          ≈ 1.39 × 10¹⁰ years
          ≈ 14 billion years

The modern best value of the age of the universe, from detailed cosmic microwave background measurements by the Planck satellite, is `13.787 × 10⁹) years. Our simple estimate — 14 billion years — is correct to within a few per cent. Not bad for an argument that simply runs Hubble's law backwards!

The slight discrepancy (14 Gyr predicted vs. 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). In the past few billion years, however, dark energy has begun to *accelerate* the expansion, which would raise the true age closer to 1/H_0). The two effects nearly cancel, and `1/H_0) remains an excellent approximation.

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Worked Example 1: Estimating The Age Of The Universe

Using `H_0 = 70) km s⁻¹ Mpc⁻¹, calculate the Hubble time.

Step 1. Convert to SI:

H_0 = (70 × 10³ m/s) / (3.086 × 10²² m)
    = 2.268 × 10⁻¹⁸ s⁻¹

Step 2. Take reciprocal:

1/H_0 = 1 / (2.268 × 10⁻¹⁸ s⁻¹)
      = 4.41 × 10¹⁷ s

Step 3. Convert to years:

1 year = 365.25 × 24 × 3600 = 3.156 × 10⁷ s

1/H_0 = (4.41 × 10¹⁷) / (3.156 × 10⁷)
      = 1.40 × 10¹⁰ years
      ≈ 14 billion years

The Big Bang, in this estimate, happened about 14 billion years ago.

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Worked Example 2: A Different Hubble Constant

Some early measurements gave `H_0 approx 500) km s⁻¹ Mpc⁻¹. What age of the universe would this imply?

H_0 = (500 × 10³) / (3.086 × 10²²)
    = 1.62 × 10⁻¹⁷ s⁻¹
1/H_0 = 6.17 × 10¹⁶ s
      ≈ 2 × 10⁹ years