Hubble's law and the Big Bang

Hubble's law, and what it implies

Measure the red shifts of galaxies and a clear pattern appears. Apart from a handful of close neighbours, every galaxy is receding, and the further away it is, the faster it moves. Speed is proportional to distance:

with H the Hubble constant, taken throughout as 65 km s⁻¹ Mpc⁻¹, the value the AQA booklet adopts for calculations; published measurements sit nearer 70. On the adopted value, every megaparsec of extra distance adds 65 kilometres per second of recession. The law reads naturally as evidence that the universe is expanding, and here the shrapnel picture needs dismantling carefully. The galaxies are not flying through space away from one privileged spot. Space-time itself is stretching, carrying the galaxies apart, and an observer in any galaxy sees the same law with themselves at the apparent centre. The expansion has no centre and no edge.

Describe the drawing

The same eight galaxies, at the same fixed separations, drawn twice. In the left panel galaxy A is the observer, and every other galaxy carries an arrow pointing away from A whose length is its recession speed, from about 5900 km per second for the nearest to 24 900 for the most distant. In the right panel the array has not moved at all and galaxy B is the observer, so the arrows now fan out from B instead and a different galaxy carries the longest one; only the arrow joining A and B keeps its length, since the two galaxies must agree about each other. Space is stretching everywhere, so each observer measures the same law with themselves apparently at the middle, and neither panel has a crater the galaxies flew out of.

That last claim has a name, and OCR asks for it by name while the other boards only lean on it. The Cosmological principle is an assumption in three parts. Viewed on a large enough scale, the universe is homogeneous, of the same composition and density everywhere, so no place is special. It is also isotropic, looking the same in every direction, so no direction is special. And the laws of physics are universal, the same here as anywhere else. Learn those three together.

Two clauses in that are worth pressing on. The scale clause is the fine print, since close up the universe is plainly lumpy, all stars and voids, and the principle only claims smoothness once you average over hundreds of megaparsecs. Every measurement in this topic depends on the third part, because reading a galaxy's red shift means assuming that hydrogen ten billion light years away absorbs at the same wavelengths as hydrogen in a laboratory here.

What the expansion will do next depends on what the universe is made of, and most of that mass and energy is not directly observed. Galaxies rotate as though they hold far more mass than shines, and the unseen extra is dark matter. The expansion, measured through distant supernovae, is also accelerating where gravity alone would demand a slowdown, driven by something labelled dark energy.

Between them they determine the universe's fate, but only within a model. Feed a cosmological model enough matter and little dark energy and it predicts an expansion that slows and one day reverses. Feed it the mix the current measurements favour, with dark energy dominant, and the standard model predicts an expansion that runs away, ending cold, dark and dilute. These are outputs of a model fitted to data; nobody has watched them happen, and an answer that says so is the stronger answer.

Run the expansion backwards and everything was once together, in the Big Bang. Read that carefully: it was not an explosion at some address in space. Run the model back and it reaches an early state of space-time that was extremely hot and dense everywhere at once. The expansion measured today is that same space-time still stretching. What, if anything, came before that state is beyond what present physics can establish.

Two further observations support the Big Bang, and both are wanted by name. The cosmic microwave background is a faint glow arriving from every direction, a black-body spectrum at 2.7 K, the cooled and red-shifted afterglow of the hot early universe. Feed 2.7 K into Wien's law and the peak lands near one millimetre. Second, the universe's relative abundance of hydrogen and helium, about three to one by mass, matches what fusion in the first few minutes of a hot dense universe would cook up. No ordinary stellar history accounts for that much helium.

Describe the drawing

Two black-body curves on a logarithmic wavelength axis running from a micrometre to ten millimetres, each drawn to its own peak. The 3000 K curve of the early universe peaks near a micrometre, just past the red end of the visible; the 2.7 kelvin curve measured from the sky today peaks near one millimetre, in the microwave. The two peaks are about eleven hundred times apart in wavelength, which is the same factor by which the temperature has fallen.

What happened next, an OCR section

No other board sets this section, so read it only if OCR A is your specification. OCR A also requires a chronological account of the universe. In order, light nuclei formed first, during nucleosynthesis in the first few minutes. Atoms formed after about 380 000 years, which let the cosmic microwave background travel freely. The first stars and galaxies formed after that. Today the universe is about 13.8 billion years old and its expansion is accelerating. Link each stage to the fall in temperature and density.

One process drives all of it. The universe expands, expansion cools it, and each stage below happens at the moment the temperature falls far enough to permit it. Learn the chapters in order and the reasons come with them.

The first two rows are quick. For a fraction of the first second nothing composite can hold together, and matter is a soup of quarks, leptons and photons; by about a microsecond the quarks have bound into protons and neutrons.

The third row sets a number that has survived ever since. Primordial nucleosynthesis runs from roughly one second to twenty minutes, fusing those protons and neutrons into helium nuclei. That window is short because the expansion is cooling the universe out of the fusion range, and what it leaves behind is the three to one hydrogen to helium ratio by mass quoted above. Stars have processed only a small share of the universe's matter since, which is why the ratio is still close to what those twenty minutes set.

The universe is nonetheless still opaque, because free electrons scatter photons before they can cross. At about 380 000 years the temperature has fallen to some 3000 K, cool enough for nuclei to hold on to electrons. Neutral atoms form, the scattering stops, and light travels freely for the first time. That released light is the microwave background, and the sum ties the two facts together: expansion has stretched its wavelengths by a factor of about 1100 since, and 3000 K divided by 1100 is the 2.7 K measured today.

A long dark age follows. Gravity works on the slight density variations printed on the young universe, pulling matter into clumps that collapse and heat until the first stars ignite, a few hundred million years in. Those stars fuse elements heavier than helium and scatter them when they die, so each generation forms from richer material, and clumps merge into galaxies. The Sun is a late arrival, forming from that enriched debris about 9 billion years in, which is why the Earth has iron in it at all.

For most of its history the expansion was slowing, gravity pulling back on it. The type Ia supernova measurements in The HR diagram and stellar evolution show that over the last few billion years it has instead been accelerating, with dark energy now the dominant term in the budget. The present age is 13.8 billion years, comfortably near the crude 1/H estimate above.