Concept

Matter radiation equality — where it appears

The epoch at which the matter and radiation densities were equal, near redshift 3400. It sets the scale at which the matter power spectrum turns over, and modes that entered the horizon before it were driven and boosted.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

$The same universe, four times, as a fraction of itself. Each bar is the fractional contribution of the four components to the total density at one epoch, computed from the Planck 2018 parameters by scaling each component from today: radiation as (1+z)⁴, both kinds of matter as (1+z)³, and Λ as a constant. The familiar figure — five per cent baryons, twenty-six dark matter, sixty-nine dark energy — is the top bar and only the top bar. At recombination the same universe is three-quarters dark matter and Λ is one part in ten million; before matter–radiation equality it is mostly radiation. A pie chart of the contents of the universe is therefore a statement about a moment, and the moment is the one it happens to be drawn in.$

A budget whose familiar part is five per cent

Five per cent ordinary matter, twenty-six per cent dark matter, sixty-nine per cent dark energy. The figures are quoted everywhere and each one comes from a different measurement, the denominator they are fractions of is itself built out of the expansion rate, and the whole chart is a statement about one instant that was a different chart at every earlier time.

cosmology · Density parameters $A mass measured by the structure it prevents. The fractional suppression of the small-scale matter power spectrum against the sum of the neutrino masses. The relic density follows from the thermal history with no astrophysics in it — the neutrinos’ share of the critical density, times h², is the mass sum divided by 93.14 eV exactly — and the suppression is about eight times the neutrinos' share of the matter, because a particle moving at a large fraction of the speed of light streams out of an overdensity while it is still growing and takes its own gravity with it. The two mass orderings put a floor under the sum at 58 meV and 100 meV; the cosmological upper bound is near 0.12 eV, which is 7.2 per cent of suppression. The floor and the ceiling are within a factor of two of each other, so this is a measurement about to happen or a model about to break, and the quantity it returns is a sum rather than any individual mass.$

A mass measured by what it stopped from forming

Neutrinos were relativistic in the early universe and are not now, so they are the one entry in the cosmic budget that changes category. What cosmology measures is not their density but the hole they leave — they stream out of a growing clump and take their gravity with them, and the missing structure bounds a particle mass more tightly than any laboratory has.

cosmology · Density parameters $The Hubble constant the microwave background implies, with an early component. The Hubble constant that keeps the microwave background's measured angular sound horizon fixed, against the peak fraction of early dark energy at z = 3500, with the baryon density held at its standard value and the matter fraction at the 0.315 that late-time distances measure, so that the dark-matter density rises with the Hubble constant. With none, it is 67.4 km/s/Mpc and the horizon 144.3 Mpc. At 5 per cent it is 68.7; at 10 per cent 70.2, with the horizon at 138.5 Mpc; the local value of 73 is reached at 19 per cent. The shrinkage of the horizon is what raises the constant: a shorter ruler at the same angle must be nearer, and nearer at a fixed matter fraction means faster expansion. The extra dark matter this requires is the cost the published fits also find: at the value that reaches 73, the physical matter density is 18 per cent higher than in the standard model.$

A ruler shortened by something already gone

The microwave background gives the Hubble constant only through a computed length, the distance sound travelled before the universe became transparent. Add a component of energy that exists for a few thousand years before recombination and then vanishes faster than radiation, and the universe expands a little faster while the sound is travelling, the ruler comes out a few per cent shorter, and the inferred expansion rate rises toward the local value. The price is paid in dark matter and in the finest details of the oldest light.

cosmology · Hubble constant

A clump that does not grow until the radiation is outweighed. The amplitude of a dark-matter overdensity inside the horizon against the scale factor in units of its value at matter–radiation equality, both logarithmic, from y = 10⁻⁴ to today near y = 3400. The solution of the growth equation, δ = 1 + 3y/2, stays flat until equality and then rises in proportion to the scale factor; matter domination alone would have grown it in proportion to the scale factor from the start. Over the whole range the true growth is 5.1e+3 against 3.4e+7 — radiation withheld a factor of 6666, which is the interval from y = 10⁻⁴ to about y = 0.67.

A clump that waits for the radiation to thin

Dark matter feels no pressure from light, so nothing should have stopped it clumping in the radiation era. Almost nothing did stop it, and yet a clump inside the horizon at that time barely grows. The radiation does not push on it. It only makes the universe expand too fast for the clump's own gravity to keep up — and the length of that wait is the bend in the spectrum of every structure in the sky.

cosmology · Large-scale structure

Named alongside it

The objects these essays reach for when they reach for this one.

Density parameter Baryon density Coincidence problem Cold dark matter Cosmic inventory Critical density Damping tail Dark energy Dark matter Degeneracy Early dark energy Effective number of species

All concepts