Cosmology

The Big Bang theory is the currently accepted scientific model of the universe's evolution. Its main statements:

1. The universe began in an extremely HOT, DENSE state about 13.8 billion years ago.
2. Space, time, energy and matter all began at this point — there is no meaningful 'before'.
3. Since then, the universe has been EXPANDING and COOLING.
4. As it cooled, the fundamental particles formed, then atoms (hydrogen and helium), then stars and galaxies under gravity.

Main arguments in favour (spec 8.13P).

• Red-shift of distant galaxies (spec 8.17P, 8.18P) — almost every distant galaxy is moving away, with the speed increasing with distance. This is exactly what an expanding universe should look like.

• Cosmic microwave background (spec 8.14P) — a uniform 2.7 K microwave radiation from all directions, exactly matching the predicted relic of the hot early universe.

• Element abundances (not on the spec but useful context) — the observed proportions of hydrogen (~75%) and helium (~25%) in the universe match the predictions of Big Bang nucleosynthesis.

• Galaxy evolution — looking at very distant (and therefore older) galaxies shows them in earlier stages of development than nearby ones.

The Big Bang is not a 'theory' in the casual sense of 'guess' — it is a fully developed scientific model with multiple independent lines of evidence.

The cosmic microwave background (CMB) is microwave radiation reaching Earth uniformly from every direction in the sky, with a thermal spectrum corresponding to a temperature of ~2.7 K.

Where does it come from? In the very early universe, conditions were so hot that matter was ionised — electrons could not stay bound to nuclei. Photons constantly scattered off free electrons → the universe was OPAQUE (like the inside of a fog).

When the universe had cooled to about 3000 K (around 380 000 years after the Big Bang), electrons could finally combine with nuclei to form neutral atoms. Photons stopped scattering → the universe became TRANSPARENT.

Those photons have been travelling freely ever since. But because the universe has EXPANDED by a factor of about 1100 in the meantime, the photons have been STRETCHED — their wavelengths increased by the same factor. Originally optical/IR photons, they are now MICROWAVE photons corresponding to a temperature of ~2.7 K.

Why does this support the Big Bang?

• The Big Bang theory PREDICTED the existence of this radiation before it was observed.
• The temperature (2.7 K) and uniformity match the predictions precisely.
• Tiny temperature variations in the CMB (one part in 100 000) match the predicted seeds of structure that grew into galaxies.

No competing model has provided a viable alternative explanation. The CMB is often described as the most powerful single piece of evidence for the Big Bang.

History. Predicted by Gamow, Alpher and Herman in the 1940s. Detected accidentally by Penzias and Wilson in 1964, using a microwave receiver they thought was malfunctioning. They won the Nobel Prize in 1978.

When a source of waves moves relative to an observer, the observed frequency and wavelength DIFFER from the emitted values.

For sound (covered in spec 3.8): a vehicle's siren sounds higher-pitched when it approaches and lower-pitched when it recedes. Familiar from ambulances and racing cars.

For light (spec 8.15P). The same effect — but because $c$ is huge, the wavelength change is tiny for everyday speeds. Observable only for fast-moving sources:

Source motion relative to observer	Wavelength change	Colour shift
Moving TOWARD observer	DECREASES	Shifted to BLUE end (BLUE-shift)
Moving AWAY from observer	INCREASES	Shifted to RED end (RED-shift)
Stationary	unchanged	none

Why this matters for astronomy. Every chemical element produces a specific set of spectral 'lines' (sharp wavelengths) when its atoms emit or absorb light. Astronomers know the reference (laboratory) wavelengths of these lines. By measuring the same lines from a distant galaxy and comparing, they can determine the galaxy's velocity along the line of sight.

If the observed wavelengths are LONGER than expected → the galaxy is receding (RED-shifted).

If they are SHORTER → the galaxy is approaching (BLUE-shifted).

For a source receding (or approaching) with velocity $v$ small compared with the speed of light $c$:

$\frac{\Delta\lambda}{\lambda_0} = \frac{v}{c}$

where:

• $\lambda_0$ = reference / laboratory wavelength (what we'd measure if the source were stationary).
• $\lambda$ = observed wavelength.
• $\Delta\lambda = \lambda - \lambda_0$ — the change. POSITIVE for red-shift; negative for blue-shift.
• $v$ = source velocity along the line of sight (positive = receding).
• $c$ = speed of light = $3.0 \times 10^8$ m/s.

Units cancel. The ratio $\Delta\lambda/\lambda_0$ is DIMENSIONLESS — you don't need to convert nm to m as long as both are in the same unit. $v$ comes out in the same units as $c$ (so use m/s for $c$ to get $v$ in m/s).

Worked example. A laboratory hydrogen line has $\lambda_0 = 656.0$ nm. The same line from a distant galaxy is observed at $\lambda = 656.6$ nm.

$\Delta\lambda = 0.6$ nm.

$v = c \times \Delta\lambda / \lambda_0 = 3.0 \times 10^8 \times 0.6 / 656.0 \approx 2.7 \times 10^5$ m/s.

So that galaxy is receding at about 270 km/s.

Two observations together pin down the expanding universe:

Observation 1. Almost every distant galaxy shows RED-SHIFT (not blue-shift). The Doppler interpretation: nearly every distant galaxy is moving AWAY from Earth.

Observation 2 (spec 8.17P). The amount of red-shift INCREASES WITH DISTANCE. More distant galaxies are receding FASTER.

Together these imply:

(a) Earth is not special. It might seem like every galaxy fleeing Earth makes us the centre of the universe. But actually, observers in any galaxy would see the same pattern — every other galaxy receding, faster ones being more distant. So Earth isn't unique.

(b) Space itself is expanding (spec 8.18P). The only consistent explanation is that SPACE BETWEEN GALAXIES is increasing with time. Galaxies aren't really moving through space — they are being carried apart by the expansion of space itself, like raisins in a rising loaf of bread.

(c) Big Bang inference. If the universe is expanding now, running the expansion BACKWARD in time means that long ago, everything was much closer together. Extrapolating right back leads to the Big Bang — a single hot, dense state from which the universe emerged.

Hubble's law (not on 4PH1 spec, but useful context). The proportionality between recession speed and distance is $v = H_0 d$, where $H_0$ is Hubble's constant. Measuring $H_0$ gives an estimate for the age of the universe.

Key point. Red-shift alone tells you a galaxy is receding. Red-shift PROPORTIONAL TO DISTANCE tells you the universe is EXPANDING and supports the Big Bang.