Evidence For The Big Bang

OCR H556 mapping. This is the closing lesson of Module 5.5.3 and covers the three principal lines of evidence for the Big Bang: (a) the red shift of distant galaxies and Hubble's law (lessons 7-8), (b) the cosmic microwave background (CMB) at $T \approx 2.725$T≈2.725 K (a near-perfect black body), and (c) the primordial abundances of hydrogen and helium ($\approx 75:25$≈75:25 by mass), predicted by Big Bang nucleosynthesis. It also covers the cosmological principle — that the universe is homogeneous and isotropic on large scales — which is the foundational assumption of modern cosmology.

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 $T \approx 2.7$T≈2.7 K filling all of space, the "afterglow" of the hot early universe.
3. The primordial abundances of hydrogen ($\approx 75\%$≈75%) and helium ($\approx 25\%$≈25%) by mass, 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 final lesson describes all three and closes with the cosmological principle, the assumption that underlies all of modern cosmology.

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Evidence 1: red shift of distant galaxies

We covered this in lessons 7-8. To summarise:

• Observation. Galaxies outside the Local Group show red-shifted spectra, indicating that they are receding from us.
• Quantitative law. $v = H_{0}d$v=H0​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 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 $T \approx 3000$T≈3000 K — roughly $380\,000$380000 yr 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 $\approx 1100$≈1100, and the corresponding temperature has dropped from $\approx 3000$≈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, WMAP and Planck satellites — and found to match a black-body spectrum at $T \approx 2.725$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 ≈ 2.725 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 ($\Delta T/T \approx 10^{-5}$ΔT/T≈10−5) encode the seeds of cosmic structure.
2. It is a near-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 $T \approx 5$T≈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 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, and to Smoot and Mather (for COBE) in 2006. 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 $T \approx 10^{9}$T≈109 K (a few minutes after the Big Bang):

• 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:

• $\approx 75\%$≈75% hydrogen by mass.
• $\approx 25\%$≈25% helium-4 by mass.
• Traces of deuterium ($\sim 10^{-5}$∼10−5), helium-3 ($\sim 10^{-5}$∼10−5), and lithium-7 ($\sim 10^{-10}$∼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\%$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\%$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.

These two statements are not identical. A universe can be isotropic without being homogeneous (e.g. onion-layered centred on a special point), and homogeneous without being isotropic (e.g. filled with parallel field lines). But if the universe is isotropic around every point, it must be homogeneous as well — so observational isotropy, combined with the Copernican principle (we are not in a special location), implies both.

The cosmological principle is supported observationally by:

• The near-perfect isotropy of the CMB (temperature fluctuations of only $\sim 10^{-5}$∼10−5).
• The uniform distribution of galaxies on scales larger than $\sim 100$∼100 Mpc. On smaller scales, clusters and superclusters introduce lumpiness, but on the largest scales the universe is smooth.
• The uniformity of Hubble's law, which holds with the same $H_{0}$H0​ in every direction.

The cosmological principle is a simplification, but it is an extraordinarily good one. It allows the Einstein field equations of general relativity to be simplified to a single differential equation — the Friedmann equation — that describes how the scale of the universe evolves with time. Every modern cosmological model is built on this foundation.

Without the cosmological principle, cosmology would be hopeless: if the universe were different in every direction with no pattern, there would be no point trying to describe its global properties with a single theory. With it, cosmology becomes tractable and testable.

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Alternative theories: why not steady-state?

For a long time, the main alternative to the Big Bang was the steady-state theory, proposed in 1948 by Hoyle, Bondi and Gold. In this theory:

• The universe is expanding (as Hubble showed).
• But new matter is continuously created in the gaps, at just the rate needed to keep the density constant.
• The universe therefore has no beginning and no end — it has always existed, and always will, in roughly its present form.
• The perfect cosmological principle is assumed: the universe is homogeneous and isotropic not only in space but also in time.

The steady-state theory was aesthetically attractive and was vigorously defended for twenty years. But it could not account for:

1. The cosmic microwave background. In steady state, there is no hot early phase, so no relic thermal radiation. The CMB is fatal to the theory.
2. The primordial abundance of helium. Steady state has no Big Bang nucleosynthesis. It cannot explain $25\%$25% helium by mass.
3. The observed evolution of galaxies. Distant galaxies (which we see in their past) look different from nearby galaxies. Steady state predicts they should look the same.
4. The age-density relation. Observations show the universe evolves over time — in steady state, it does not.

By the 1970s, even Hoyle was forced to admit that the CMB was hard to reconcile with steady state (though he spent the rest of his life trying). The theory is now of historical interest only.

The Big Bang theory has no serious competitor. Refinements — dark matter, dark energy, inflation — modify and enrich the basic picture, but they build on the Big Bang; they do not replace it.

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Worked example 1: the CMB temperature and expansion

When photons decoupled from matter, the temperature was $T_\text{dec} \approx 3000$Tdec​≈3000 K. Today the CMB has temperature $T_\text{now} \approx 2.725$Tnow​≈2.725 K. By what factor has the universe expanded since decoupling?

In an expanding universe, the wavelengths of free photons stretch in proportion to the scale factor $a(t)$a(t). The peak wavelength of a black-body spectrum is inversely proportional to temperature (Wien's law, $\lambda_\text{max}T =$λmax​T= const), so $T \propto 1/a$T∝1/a:

$$\dfrac{T_\text{dec}}{T_\text{now}} = \dfrac{a_\text{now}}{a_\text{dec}} = \dfrac{3000}{2.725} \approx 1100$$Tnow​Tdec​​=adec​anow​​=2.7253000​≈1100

The universe has expanded by a factor of $\approx 1100$≈1100 since photon decoupling. Distances between distant points are $1100$1100 times larger than they were when the CMB photons last scattered. The corresponding red shift is $z = (a_\text{now}/a_\text{dec}) - 1 \approx 1100$z=(anow​/adec​)−1≈1100. Remarkable — but quantitatively consistent with everything else we know about cosmological evolution.

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Worked example 2: predicting the H:He ratio from BBN

A simplified BBN calculation. Suppose that when the universe cooled to $T \approx 0.7$T≈0.7 MeV ($\sim 1$∼1 s after BB), the neutron-to-proton ratio froze out at $n/p \approx 1/7$n/p≈1/7 — a number set by the neutron-proton mass difference and the weak-interaction freeze-out temperature. Almost every neutron then ended up bound in a helium-4 nucleus. Estimate the helium mass fraction $Y_\text{p}$Yp​.

Each $^{4}\text{He}$4He nucleus contains 2 neutrons + 2 protons, so the number of helium nuclei made is $n/2$n/2, consuming $n$n neutrons and $n$n protons. Remaining free protons (becoming hydrogen): $p - n$p−n. The helium mass fraction is then

$$\begin{aligned} Y_\text{p} &= \dfrac{\text{mass in He}}{\text{total nucleon mass}} = \dfrac{4 \times (n/2)}{n + p} = \dfrac{2n}{n+p} \\ &= \dfrac{2 \times (n/p)}{1 + (n/p)} = \dfrac{2 \times 1/7}{1 + 1/7} = \dfrac{2/7}{8/7} = \dfrac{1}{4} = 0.25 \end{aligned}$$Yp​​=total nucleon massmass in He​=n+p4×(n/2)​=n+p2n​=1+(n/p)2×(n/p)​=1+1/72×1/7​=8/72/7​=41​=0.25​

So $Y_\text{p} \approx 0.25$Yp​≈0.25 — $25\%$25% helium by mass — predicted from a single freeze-out number. The observed primordial helium mass fraction in pristine extragalactic HII regions is $Y_\text{p} \approx 0.245 \pm 0.003$Yp​≈0.245±0.003 — exquisite agreement. This is one of the cleanest quantitative confirmations of the Big Bang theory.

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Synoptic Links

• Hubble's law (lesson 8) + Big Bang theory (lesson 9). Lessons 8-9 establish that the universe is expanding from a hot, dense state. This lesson provides the direct evidence for the hot dense state — the CMB and BBN — that complements the Hubble-law evidence for expansion alone.
• Wien's law (lesson 3). The CMB peak wavelength comes from Wien's law: $\lambda_\text{max} = (2.9 \times 10^{-3}\,\text{m K})/(2.725\,\text{K}) \approx 1.06$λmax​=(2.9×10−3m K)/(2.725K)≈1.06 mm — squarely in the microwave band, as the name suggests. The lesson-3 formula is the basis for naming the CMB.
• Stefan-Boltzmann law (lesson 2). The CMB carries an energy density $u = aT^{4}$u=aT4 with $a = 4\sigma/c \approx 7.6 \times 10^{-16}$a=4σ/c≈7.6×10−16 J m$^{-3}$−3 K$^{-4}$−4. At $T = 2.725$T=2.725 K, this gives $u \approx 4.2 \times 10^{-14}$u≈4.2×10−14 J m$^{-3}$−3 — small today, but the CMB dominated energy density until $z \approx 3400$z≈3400.
• Stellar evolution (lesson 6). Heavier elements (C, O, Fe, etc.) are made in stars; H and He are primordial from BBN. The chemical composition of the present universe is a layered product: primordial H and He (BBN) plus stellar nucleosynthesis (heavier elements).
• Quantum physics (Module 4.4-4.5). The CMB photons trace back to the recombination epoch when electrons combined with nuclei to form neutral atoms. The physics here is Thomson/Compton scattering and the $13.6$13.6 eV binding energy of hydrogen.
• Black-body radiation and thermal physics (Module 5.1). The CMB is the most perfect black body in nature. Its spectrum, measured by COBE-FIRAS to part-in-$10^{4}$104 precision, matches a Planck distribution at $T = 2.725$T=2.725 K. The black-body framework of Module 5.1 is the right description.

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Specimen question modelled on the OCR H556 paper format

Question (10 marks):

(a) State the three principal lines of observational evidence for the Big Bang theory and indicate what each piece of evidence specifically supports. [4]

(b) State the cosmological principle and explain how it is supported by (i) the isotropy of the CMB and (ii) the uniformity of Hubble's law. [3]