Astronomy & Celestial Mechanics
the sky, computed
Concept

Linear theory — where it appears

The description of cosmic structure while density differences are still small, so each wavelength grows independently. It predicts the growth of fluctuations and the peculiar velocities they induce, and fails once regions collapse into groups and clusters.

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

How deep a hole the Hubble tension needs, and how deep holes are. The typical departure of the matter density from the mean, averaged over a sphere — one standard deviation, σ, from the linear power spectrum with σ₈ = 0.81 — against the sphere's radius, both on logarithmic axes. It falls from 0.55 at 20 Mpc to 0.022 at 300 Mpc. A local expansion rate 8.3 per cent above the global one, the size of the Hubble tension, needs the sphere the supernovae sample to be underdense by 0.47 (dashed), with a growth rate of 0.53. Across the radii the supernovae span (shaded, 100–600 Mpc) that is 4 to 67 standard deviations.

A hole too deep for the sky to have made

If the Milky Way sat inside a vast underdense region, everything around it would be expanding faster than the universe as a whole, and the locally measured Hubble constant would come out high — which is what Cepheids and supernovae find. The idea needs no new physics. It needs a void about half empty across the six hundred megaparsecs the supernovae sample, and the same cosmology that predicts the microwave background prices such a void at dozens of standard deviations.

cosmology · Hubble constant The flow round the Local Group, shell by shell. Radial velocity against distance from the Local Group's centre today, for spherical shells of matter in a standard expanding background with the cosmological constant, round a group whose mass inside the zero-velocity surface is 1×10¹² M☉, 2×10¹² M☉, 4×10¹² M☉. Inside the zero-velocity radius — 0.79 Mpc, 1.00 Mpc, 1.26 Mpc — the shells are falling in; outside it they recede, slowly at first and then at the Hubble rate (dashed, 67.7 km/s per Mpc). At 1.5 Mpc the three groups give 75, 57, 30 km/s against 102 for an undisturbed flow; by 5 Mpc the curves differ by 10 km/s and have nearly rejoined the line. The group's pull is written into the first two or three megaparsecs of the flow, and only there.

A flow too quiet for the lumps it runs between

The galaxies within ten megaparsecs of the Milky Way recede almost exactly as the Hubble law says, scattering about it by a few tens of kilometres a second. The matter they move through is lumpy at the factor-of-several level, and elsewhere galaxies move relative to their neighbours at three hundred. The quiet is a measurement, it limits what the group's own pull can be read from, and it says something about the place rather than about the law.

cosmology · Hubble constant

Named alongside it

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

Hubble constantPeculiar velocityBulk flowCepheid variableCosmic varianceCosmic voidCosmological constantGrowth rateHubble diagramHubble tensionLocal groupPower spectrum

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