Astronomy & Celestial Mechanics
the sky, computed
Concept

Modified gravity — where it appears

Any proposal that replaces general relativity rather than adding a new component to it. Such theories can usually be tuned to reproduce any expansion history, so the discriminating test is the growth of structure, which they predict differently.

Named by 6 essays across 2 fields — 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 that is not of positions

One axis of every redshift survey is not a distance but a velocity, and the difference is not noise. Inside a cluster it smears the galaxies into a finger pointing at the observer; on the scale of a supercluster it compresses the structure — and the amount of that compression is a test of gravity.

cosmology · Large-scale structure 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 Four known pieces of hardware, and the anomaly is the sum of them. The reported anomalous acceleration of a deep-space probe, in units of 10⁻¹⁰ metres per second squared, built up from the heat the spacecraft was known to be radiating. The generators put out about two and a half kilowatts of waste heat and sit on booms beside a large dish that reflects a share of it backwards, which is 62 per cent of the total on its own; the instrument compartment radiates through louvres on one face; the radio transmitter beams eight watts at the Earth, which is a torch pointing the wrong way. Sunlight is negligible this far out and is drawn to show that it is. The four sum to 8.65 against a measured 8.74 ± 1.33, and the agreement is the answer. What makes the episode worth keeping is that none of these numbers was discovered later: every one was in the spacecraft's own thermal documentation from before launch, and the model that produced the anomaly was a model of a point mass.

An acceleration that was the spacecraft's own heat

Two probes leaving the solar system were tracked for thirty years and both drifted from their predicted paths by a tenth of a nanometre per second squared. The residual was real, it was constant, and it was the same on both. It was also the waste heat of the reactors that powered them, radiating slightly more one way than the other.

orbits · Non-gravitational forces A void: a deficit of matter, and the outflow it drives. The density contrast of a typical cosmic void against distance from its centre in units of its radius (solid), from the profile fitted to stacked voids in simulations, with a central density 15 per cent of the mean and a compensating overdense ridge just outside the edge. The dashed curve is the excess expansion rate the deficit drives, v/(Hr) = −(f/3)Δ(r), for a growth rate f = 0.75: the centre expands 21 per cent faster than the universe around it, and the outflow speed, which is this rate times the radius, peaks near 0.7 void radii. Beyond the ridge the flow reverses: matter at the ridge is pulled back towards the denser wall. A void is a small open universe expanding inside a flat one, and every galaxy in it is moving outward.

An emptiness that expands faster

A cosmic void is not a hole in the universe but a region with a fifth of the average density, and gravity makes it behave like a small open universe: it expands faster than its surroundings, every galaxy in it streams outward, and in a redshift survey it is stretched along the line of sight — the opposite of what the same gravity does around a cluster. The stretch measures how fast structure grows, and the average void's roundness measures the geometry of the universe.

cosmology · Large-scale structure How much each change moves the growth rate. The percentage difference in fσ₈ from growth in relativity inside a cosmological constant's expansion, against redshift, for three alternatives started from the same early amplitude. Changing the expansion to the evolving fit with DES-SN5YR and keeping relativity moves it by −1.2 per cent at redshift 0.5, and by at most 2.1 per cent anywhere below redshift 2. Keeping the constant's expansion and changing gravity to γ = 0.68 moves it by −8.6 per cent; doing both, −10.3. The shaded band is ±8 per cent, about the error of one of the better redshift-space measurements so far. The difference between a constant and the evolving fit is several times smaller than any single measurement; the difference between two laws of gravity is comparable to one. Growth is a weak test of whether the dark energy is changing and a strong test of whether it is gravity.

The growth that tells a substance from a law

In relativity an expansion history leaves no freedom in how fast structure grows inside it, so every fitted history predicts its own growth. The evolving dark energy the surveys prefer changes that growth by one or two per cent; a change in the law of gravity, with the expansion held fixed, changes it by nine. Growth is a weak test of whether the dark energy is changing and a strong test of whether it is there at all.

cosmology · Dark energy A ratio relativity predicts from one density. The ratio EG — written E with a subscript G in the literature — of the lensing around a set of galaxies to their clustering and infall, against redshift. In relativity it is Ωₘ₀/f(z) and depends on nothing else: with Ωₘ₀ = 0.3153, 0.598 today, 0.455 at z = 0.32 and 0.360 at z = 1, falling because f rises towards one as matter comes to dominate. The dashed curves keep light's bending as in relativity and change how hard matter pulls, by −10% and +10% today, growing with the dark energy's share: a weaker pull slows the infall and raises EG. The point is the first measurement, 0.39 ± 0.06 at z = 0.32 from galaxy–galaxy lensing in the Sloan survey.

A ratio in which the galaxies cancel

Matter falls in one gravitational potential and light is bent by the sum of two, and relativity says the two are equal. A survey that measures both the infall of galaxies and the lensing around them can divide one by the other so that the galaxies' bias and the fluctuations' amplitude both cancel — leaving a ratio that relativity predicts from the matter density alone, and that a gravity which bends light differently from the way it pulls matter cannot fake.

cosmology · Dark energy

Named alongside it

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

Growth rateRedshift-space distortionGalaxy biasGrowth indexPeculiar velocityCorrelation functionDark energyFingers of GodKaiser effectSigma eightStructure growthAlcock paczynski

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