Evidence For The Big Bang

The Big Bang theory is not a philosophical speculation. It is a precise physical model, and it makes precise predictions that can be tested against observation. Over the past sixty years, three principal lines of evidence have established the Big Bang as the standard model of cosmology:

1. The red shift of distant galaxies — all moving away, with velocity proportional to distance (Hubble's law).
2. The cosmic microwave background (CMB) — a diffuse glow of microwave radiation at `T approx 2.7) K filling all of space, the "afterglow" of the hot early universe.
3. The primordial abundances of hydrogen (approx 75%)) and helium (approx 25%)), predicted by Big Bang nucleosynthesis and confirmed by observation.

Each of these observations, on its own, would be consistent with a handful of alternative cosmologies. Together, they uniquely favour the Big Bang. This lesson — the final in the course — describes all three and closes with a statement of the cosmological principle, the assumption that underlies all of modern cosmology.

This is OCR specification content 5.5.3(m)–(p).

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Evidence 1: Red Shift Of Distant Galaxies

We already covered this in Lessons 8 and 9. To summarise:

• Observation: Galaxies outside the Local Group show red-shifted spectra, indicating that they are receding from us.
• Quantitative law: `v = H_0 d) (Hubble's law). More distant galaxies recede faster.
• Interpretation: The universe is uniformly expanding. Running this back in time leads to a hot, dense initial state.

The red-shift evidence shows that the universe is expanding, and tells us that distances between galaxies have been growing throughout cosmic history. Without additional information, however, it does not distinguish the Big Bang from other expanding-universe scenarios — for instance, the now-discredited steady-state theory of Hoyle, Bondi and Gold, in which the expansion is compensated by the continuous creation of new matter, so that the overall density of the universe remains constant over time. To rule out the steady-state theory and confirm the Big Bang, we need more evidence.

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Evidence 2: The Cosmic Microwave Background

The most direct and dramatic piece of evidence for the Big Bang is the cosmic microwave background (CMB), discovered accidentally by Arno Penzias and Robert Wilson in 1964. They were testing a microwave antenna at Bell Labs and could not get rid of a persistent background hiss that seemed to come from every direction in the sky — with the same intensity day and night, winter and summer. After exhausting every possible source of interference (they famously cleaned pigeon droppings off the antenna), they realised the noise was real: it was a genuine, cosmic signal.

At the same time, a group at Princeton led by Robert Dicke had been predicting the existence of just such a signal. The logic was: in the hot early universe, matter and radiation were in thermal equilibrium. When the universe cooled to about 3000 K — roughly 380 000 years after the Big Bang — electrons and protons combined to form neutral hydrogen, and photons were no longer scattered by free electrons. The photons began to stream freely through space. Those photons have been travelling ever since, cooling as the universe expanded. By now, the expansion has stretched their wavelength by a factor of about 1100, and the corresponding temperature has dropped from 3000 K to about 2.7 K.

Penzias and Wilson's hiss was exactly this cooled radiation. Its spectrum was subsequently measured — first from ground-based telescopes, then by the COBE and WMAP and Planck satellites — and found to match a black body spectrum at `T = 2.725) K to exquisite precision. This is the most perfect black body spectrum ever observed in nature.

graph LR
    A[Hot plasma<br/>T ≈ 3000 K<br/>380 000 yr after BB] --> B[Photons decouple<br/>universe becomes transparent]
    B --> C[Photons stream freely<br/>through expanding space]
    C --> D[Wavelength stretched<br/>by factor ~1100]
    D --> E[CMB today<br/>T ≈ 2.7 K<br/>peak in microwave]

Why The CMB Is Such Strong Evidence

The CMB is overwhelming evidence for the Big Bang because:

1. It is isotropic. It comes from every direction in the sky with essentially the same temperature, as expected from a uniform early universe. Tiny anisotropies (`Delta T/T approx 10⁻⁵)) encode the seeds of cosmic structure.
2. It is a perfect black body. A thermal spectrum is the signature of a gas in thermal equilibrium at a definite temperature. This is exactly what the primordial plasma was. No alternative theory predicts such a precise black body spectrum at such a precise temperature.
3. Its temperature was predicted in advance. Gamow, Alpher and Herman predicted `T approx 5) K in the late 1940s — roughly a decade before Penzias and Wilson's discovery. This is a genuine prediction, not a post-hoc fit.
4. Its anisotropies match structure formation. The tiny temperature fluctuations in the CMB (mapped precisely by COBE, WMAP and Planck) correspond exactly to what we expect as the seeds of today's galaxies, clusters and large-scale structure.

The CMB is, more than any other observation, the "smoking gun" of the Big Bang. Its existence is essentially inexplicable in any steady-state or non-expanding cosmology. The Nobel Prize was awarded to Penzias and Wilson in 1978, to Smoot and Mather (for COBE) in 2006, and cosmic-microwave-background science has remained one of the most productive areas of observational cosmology ever since.

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Evidence 3: Primordial Abundances Of Hydrogen And Helium

The third piece of evidence comes from the observed abundances of the lightest elements. In stars, heavier elements are built up by fusion from lighter ones. But the lightest elements — hydrogen and helium — were mostly produced not in stars but in the first few minutes after the Big Bang, when temperatures and densities were high enough for nuclear fusion to occur throughout the universe. This process is called Big Bang nucleosynthesis (BBN).

BBN predicts that when the universe cooled to about `10⁹) K (a few minutes after the Big Bang), the following happened:

• Protons and neutrons combined into deuterium.
• Deuterium rapidly captured further protons and neutrons to form helium-4.
• A small fraction of nuclei formed helium-3, lithium-7 and (much less) heavier isotopes.

The predicted end result is:

• ~75% hydrogen by mass.
• ~25% helium-4 by mass.
• Traces of deuterium ((sim 10⁻⁵)), helium-3 ((sim 10⁻⁵)), and lithium-7 ((sim 10⁻¹⁰)).

These fractions depend on the baryon-to-photon ratio in the early universe, which is a single free parameter. Once that is fixed, all the predicted abundances are determined. The observed abundances — measured from spectra of pristine gas clouds, low-metallicity stars and the interstellar medium — match the predictions with remarkable accuracy.

graph LR
    A[First few minutes<br/>T ≈ 10⁹ K] --> B[p + n → D]
    B --> C[D + p → He³<br/>D + n → H³]
    C --> D[H³ + p → He⁴<br/>He³ + n → He⁴]
    D --> E[End of BBN<br/>~75% H<br/>~25% He]

No process in the current universe can easily produce 25% helium by mass. Stars do produce helium — from the proton–proton chain — but even over the entire age of the universe, stars have not had time to synthesise anything like 25% of the baryonic mass. The only natural explanation is that most of the helium was made before stars existed, in the first few minutes of the Big Bang.

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The Three Pieces Together

Each piece of evidence rules out different alternatives:

• Red shift alone is consistent with any expanding-universe scenario, including the steady-state theory.
• CMB rules out the steady-state theory: the universe must have passed through a hot, dense phase.
• Primordial abundances confirm a specific prediction about nuclear processes in the first few minutes, pinning down the conditions of that hot phase.

Combined, these three observations uniquely favour a hot, dense, expanding early universe — the Big Bang. The theory has stood every observational test for sixty years.

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The Cosmological Principle

Underlying all of modern cosmology is a single assumption known as the cosmological principle:

The universe, on sufficiently large scales, is homogeneous and isotropic.

This means:

• Homogeneous: the density of matter is the same everywhere (averaged over large enough volumes). No part of the universe is "special"; the Milky Way is in no privileged location.
• Isotropic: the universe looks the same in every direction. There is no preferred direction in space.