Concept

Alcock paczynski test — where it appears

A cosmological test that compares an object's size along the line of sight, from a redshift interval, with its size across the sky, from an angle. Only the right distance–redshift relation makes a statistically round structure come out round.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Fingers 3.1 times long, a large scale squashed to 0.92, and a test of gravity. Left: a 360-megaparsec slice of a clustered universe, as the galaxies actually sit. Right: the same galaxies as a redshift survey records them, with the line of sight up the page. Nothing has moved sideways, because an angle is an angle; every displacement is along the line of sight, because that coordinate came from a redshift and a redshift is the expansion plus whatever the galaxy is doing on its own. Two effects, opposite in sign and separated by scale. Inside a cluster the motions are virial and random, 720 kilometres a second of them, which at H₀ = 67.36 is 11 megaparsecs of smearing on an object a few across: the clusters become fingers 3.1 times longer than they are wide, all pointing at the observer, which is the one structure in cosmology that is definitely not real. On the scale of a supercluster the motions are coherent — everything is falling in, so the far side is approaching and the near side receding — and the structure is compressed rather than stretched, to 0.92 of its true extent here, measured on cluster centroids so the fingers have already averaged away. Below: why that compression is worth having. Its amplitude is the rate at which structure is currently growing, and the growth rate is Ωₘ(z) raised to a power that general relativity fixes at about 0.55. A theory of gravity that differs from general relativity on cosmological scales while matching every solar-system test changes that exponent and nothing else, and the two curves drawn — γ = 0.55 and γ = 0.68 — differ by only 4 per cent at redshift a half, against error bars of 12 per cent on the points beside them. The worst systematic in a redshift survey is the measurement — and it is a hard one, because a quarter of a change in the exponent that governs how gravity assembles structure moves the observable by less than the width of the curve it is drawn on. What the picture cannot show is the degeneracy that limits it: what is measured is fσ₈, a product, and separating the growth rate from the amplitude of clustering needs something else entirely.

A map stretched by the thing it measures

A redshift survey plots galaxies at distances derived from their redshifts, and a galaxy's redshift contains its own motion as well as the expansion. So the map is systematically distorted — squashed on large scales, drawn out into radial spikes on small ones — and both distortions are caused by the gravity the survey exists to measure.

cosmology · Large-scale structure

[C II] power is round in the plane of k; CO(4–3) mapped at the wrong distance is elongated 5.1 times along k∥. Contours of the clustering power spectrum in the plane of wavenumber across the sky, k⊥, and along the line of sight, k∥, in h/Mpc, at 10², 10²·⁵, 10³, 10³·⁵ (Mpc/h)³ in arbitrary units, for the target line, [C II] from redshift 6.60 (black), and for the CO(4–3) interloper from redshift 0.84 placed at the target's distance (colour). The target's contours are quarter-circles, because its structure has no preferred direction. The interloper's are ellipses, drawn in towards the k∥ axis and elongated along it by the ratio of the two rescalings, α∥/α⊥ = 5.1: a structure that is round where it really is looks magnified across the sky and flattened along the line of sight where the map puts it. That difference of shape, not of amplitude, is what separates the two in a map where both have been summed.

A line from the wrong redshift lands at the wrong distance

A map of ionised carbon from redshift six is built by assuming every photon at a given frequency came from that line. Carbon monoxide from galaxies at redshift one sends photons to the same frequency, and the map places them five billion light-years too far away. Their structure arrives magnified across the sky and squashed along the line of sight — round where it really is, flattened in the map — and that distortion of shape, which no amount of brightness can hide, is how the impostor is found.

cosmology · Olbers's paradox

Named alongside it

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

Anisotropic clustering Comoving distance Correlation function Fingers of God Growth rate Kaiser effect Line-intensity mapping Linear bias Modified-gravity Multipole expansion Peculiar velocity Power spectrum

All concepts