Astronomy & Celestial Mechanics
the sky, computed
Concept

Cosmological principle — where it appears

The assumption that matter is arranged alike everywhere and in every direction, which is a claim about a scale rather than about an appearance. It is false below about a hundred megaparsecs, where the galaxy distribution is a web of filaments and voids, and it is verified above it by counting.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The same recession law from two different galaxies. Twenty galaxies at fixed comoving positions after the whole picture has been multiplied by 1.34, with each galaxy's displacement drawn from where it was to where it is. Every arrow's tail sits at the old separation and its tip at the new one, so the arrow is exactly 0.34 times its tail's distance from the highlighted galaxy — proportional to separation for one reason and no other: a uniform scaling moves everything in proportion to its distance from whatever point the scaling is measured about. The right-hand panel measures from a different galaxy and gets the identical law with the identical constant. That is the content of a linear velocity–distance relation. It is the signature of an expansion with no centre, and the observation that every galaxy recedes is therefore not evidence that this one is the centre — it is evidence that none of them is.

The shift that is not a Doppler shift

Every galaxy beyond the Local Group has its lines shifted to the red, by an amount proportional to its distance. Read as a velocity that looks like a confession that everything is fleeing from here; read as a change of scale it says the opposite, because a uniform expansion produces exactly the same law measured from any galaxy in it.

cosmology · Expansion A slice 1,000 megaparsecs across. 872 galaxies in a wedge 1000 comoving megaparsecs deep, generated as a Thomas process — Poisson centres at 0.00012 per square megaparsec, 13 galaxies each on average, scattered about their centre with a Gaussian of 22 Mpc. That is not a simulation of how structure formed and does not pretend to be; it is the simplest clustered process whose correlation function is known exactly, which is what lets the next figure check a measurement against something rather than against itself. What it does reproduce is the impression: at this scale the distribution is obviously not uniform, there are groups and there are gaps, and the eye finds patterns in it readily — including several that are not there, because the eye finds patterns in a Poisson field too. The question the next two figures ask is the only one that settles it: at what separation does the clustering stop, and is there a scale above which a box of this universe looks like any other box?

Homogeneous above a hundred megaparsecs

Every cosmological calculation in this field assumes the universe is the same everywhere. Looked at on any scale a person can picture, it plainly is not — it is stars in galaxies in groups in clusters in filaments around voids. The assumption is not a claim about appearance; it is a claim about a statistic, and the statistic has a scale attached.

cosmology · Large-scale structure The dipole a 370 km/s motion has to put into counts of distant sources. The amplitude of the dipole in the number of sources per unit solid angle expected from the Sun's motion at 369.82 km/s relative to the microwave background, β = 1.234e-3, split into its two parts: aberration, 2β, which crowds sources towards the direction of motion, and the Doppler boost, x(1 + α)β, which brightens sources there and lifts fainter ones above the flux limit. For radio sources, with counts steepening as S^(−1) and spectra falling as ν^(−0.75), the expected dipole is 0.0046; for mid-infrared quasars, with counts steepening as S^(−1.7) and spectra falling as ν^(−1.26), the expected dipole is 0.0072, and the measured one is 0.0155 — 2.16 times larger, which would need a speed of 797 km/s. A dipole of a few parts in a thousand needs a catalogue of more than a million sources to see at all. The disagreement is not with the direction, which lies close to the microwave background's, but with the size, and it is not yet explained: either the samples carry a systematic nobody has found, or the matter and the radiation do not share one rest frame on these scales — in which case the assumption that the universe looks the same from everywhere is wrong in a way it has never been caught being wrong before.

The Sun's speed counted in quasars comes out twice too large

The microwave background is warmer in one direction by a part in a thousand, and that dipole is read as the Sun's motion through it at 370 kilometres per second. The same motion must crowd the counts of distant galaxies and quasars towards the same direction by an amount that can be calculated exactly. When a million quasars were counted, the direction agreed and the size came out more than twice too large — as though the Sun were moving at 800 kilometres per second relative to the matter.

cosmology · Expansion

Named alongside it

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

Peculiar velocityAberrationCMB dipoleComoving coordinatesCorrelation functionCosmic webCosmological redshiftCounts in spheresDoppler boostingExpansion of spaceGalaxy biasHomogeneity scale

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