Investigate the evidence for the Big Bang theory and the early evolution of the universe, including cosmic microwave background radiation, abundance of light elements, and Hubble's law v = H_0 d

What this dot point is asking

NESA wants you to summarise the three primary observational pillars of the Big Bang model: Hubble's law as evidence for the expansion of space, the cosmic microwave background as the cooled relic of the hot early universe, and the abundance of light elements as evidence for primordial nucleosynthesis in the first few minutes. You should be able to use Hubble's law numerically, and to give a coherent timeline of the early universe.

The answer

Hubble's law and the expanding universe

Edwin Hubble (1929) measured distances to galaxies using Cepheid variable stars and found that the redshifts of their spectra (taken to be Doppler shifts of recession) were proportional to those distances:

where $H_0$ is the Hubble constant, today measured at around 70 km/s/Mpc (about $2.3 \times 10^{-18}$ s$^{-1}$).

Two important consequences:

• Uniform expansion. A linear $v$ vs $d$ relation is exactly what every observer in a uniformly expanding space sees. It does not single out our galaxy as the centre; every observer everywhere sees the same law.
• Hubble time as an age estimate. Running the expansion backward at constant rate gives a "Hubble time" $t = 1/H_0 \approx 14$ billion years as a rough age of the universe.

The interpretation is that the galaxies are not flying apart through static space; the space between them is itself expanding, and the redshift is a cosmological redshift (the wavelength stretches with space).

The cosmic microwave background

Penzias and Wilson (1964) discovered an isotropic microwave hiss in their antenna that could not be attributed to instrument noise or known sources. The spectrum measured precisely by the COBE satellite (1989) is the most perfect blackbody known in nature, with $T = 2.725$ K.

This is exactly the prediction of the Big Bang model:

• For the first 380000 years the universe was hot, dense, and opaque (a plasma of nuclei and electrons that scattered photons).
• As the universe expanded and cooled below about 3000 K, electrons combined with nuclei (recombination), the universe became transparent and the photons streamed freely.
• Those photons have been redshifted by the subsequent expansion of space, cooling them from 3000 K to 2.7 K today.

Tiny temperature fluctuations (one part in $10^5$) carry the imprint of the density variations that grew into galaxies. WMAP and Planck measured them precisely; they match simulations of a hot Big Bang universe with about 5% ordinary matter, 27% dark matter and 68% dark energy.

Primordial nucleosynthesis

Between about 1 second and 3 minutes after the Big Bang, the universe was at a temperature comparable to nuclear binding energies. Free protons and neutrons combined to form light nuclei:

• about 75% of the mass remained free protons (hydrogen-1),
• about 25% became helium-4,
• traces of deuterium, helium-3 and lithium-7 formed.

After about 3 minutes the universe had cooled enough that further fusion stopped. No heavier elements were made at this stage; carbon, oxygen, iron and all the rest required stars.

The predicted abundances depend on a single parameter (the baryon-to-photon ratio) and match the observed abundances of these light elements in pristine intergalactic gas. This is independent evidence for a hot dense early universe, complementing the CMB.

Timeline of the early universe

A standard summary:

• **$10^{-43}$ s (Planck time):** the laws of physics as we know them begin to apply. Earlier is outside accepted theory.
• **$10^{-36}$ s to $10^{-32}$ s:** rapid exponential inflation enlarges the universe by a factor of about $10^{26}$, smoothing it and stretching tiny quantum fluctuations into the seeds of structure.
• End of inflation to 10 microseconds: quark-gluon plasma cools into protons and neutrons.
• 1 second to 3 minutes: primordial nucleosynthesis produces hydrogen and helium in roughly the observed ratio.
• 380000 years: recombination releases the photons that we now see as the CMB.
• 100 million to 1 billion years: first stars form. They live and die rapidly, producing the first elements heavier than helium (lithium, carbon, oxygen, iron) by stellar nucleosynthesis and supernovae.
• 13.8 billion years (today): continuing expansion, accelerating under dark energy.

The Big Bang model does not describe "what came before"; it describes the evolution of the universe from a hot dense state of which we have direct evidence (the CMB and primordial element abundances).

Try it: Doppler shift calculator to estimate recession velocities of distant galaxies from observed redshifts of spectral lines.

Worked example: distance to a galaxy

A galaxy shows the H$\alpha$ line at 670 nm instead of its rest wavelength 656.3 nm. Estimate the recession velocity and the distance to the galaxy, using $H_0 = 70$ km/s/Mpc.

Doppler (non-relativistic, valid here):

$v = c \, \Delta \lambda / \lambda_0 = 3.00 \times 10^8 \times (670 - 656.3) / 656.3 = 3.00 \times 10^8 \times 0.0209 = 6.26 \times 10^6$ m/s = 6260 km/s.

Hubble:

$d = v / H_0 = 6260 / 70 = 89$ Mpc, about 290 million light-years.

Common traps

Saying the Big Bang was an explosion in space. It was an expansion of space. There is no centre and no edge; every observer sees galaxies receding from them in all directions.

Treating Hubble's constant as a measure of velocity. $H_0$ has units of 1/time. The product $H_0 d$ has units of velocity.

Confusing the CMB with the hot Big Bang directly. The CMB photons we observe come from the recombination epoch, when the universe was 380000 years old, not from the Big Bang itself. Earlier light cannot reach us because the universe was opaque.

Claiming all elements were made in the Big Bang. Only the lightest elements (mainly H and He, traces of Li) come from primordial nucleosynthesis. Carbon, oxygen, iron and everything heavier require stars and supernovae.

Using the Hubble time as an exact age. $1/H_0$ assumes a constant expansion rate. The actual age (13.8 billion years) accounts for varying expansion under gravity and dark energy, but $1/H_0$ is close enough for HSC estimates.

In one sentence

The Big Bang model is supported by Hubble's law (uniform expansion of space), the cosmic microwave background (cooled blackbody relic of recombination at 380000 years) and the observed abundance of light elements (matching primordial nucleosynthesis), placing the origin of the universe and the lightest elements 13.8 billion years ago.