Expansion & the Big Bang | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Trace the expansion backwards

NASA conceptual illustration of cosmic history. An early hot dense region on the left develops into a much larger universe containing separated galaxies on the right. — Read from left to right: tracing today's expansion backwards leads to an earlier, hotter and denser Universe. This is a conceptual timeline, not an explosion from one point into external space. Illustration: NASA / WMAP Science Team.

Spectral lines from distant galaxies are generally redshifted, so the galaxies are receding.
More distant galaxies recede faster. The space between large groups of galaxies is expanding.
Reversing this change means matter was closer together and much denser in the past (9702/42/M/J/22 Q9(b)).
The Big Bang model describes the Universe developing from an earlier hot, dense state.

Common mistake

Do not describe the Big Bang as matter exploding from one central point into empty space. The model describes expansion of the Universe; it does not place Earth at the centre.

One over H₀ is a simple expansion time

In the simplest model, suppose the present separation has built up at a constant recession speed. The characteristic time is then distance divided by speed.

t=\dfrac{d}{v}=\dfrac{d}{H_0d}=\dfrac{1}{H_0}

Worked example

Estimate the age scale

Use $H_0=2.3\times10^{-18}$ s⁻¹.

t=\dfrac{1}{2.3\times10^{-18}}

t=4.35\times10^{17}\ \mathrm{s}

t=\dfrac{4.35\times10^{17}}{3.16\times10^7}

t=1.38\times10^{10}\ \mathrm{years}

Answer

t\approx1.4\times10^{10}\ \mathrm{years}

Your turnrelationship check

If the measured Hubble constant were larger, what would happen to the simple age estimate?

Show worked answer

The estimate would be smaller because the age scale is inversely proportional to the Hubble constant.

Key idea

The relation

1/H_0

is an estimate, not a complete history of the Universe. It assumes a constant expansion rate.

Standard candles give distance. Redshift gives recession speed. Hubble's law links them; tracing that expansion backwards supports an earlier hot, dense Universe.