Astronomy & Celestial Mechanics
the sky, computed
Concept

Matter power spectrum — where it appears

The variance of density fluctuations in the universe as a function of spatial scale. Weak lensing, galaxy clustering and cluster counts all measure parts of it, and on small scales it depends on how galaxies push their gas around.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

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 matter power spectrum with galaxies' feedback taken out. The ratio of the matter power spectrum with baryonic feedback to the spectrum without it, against wavenumber in h per megaparsec on a logarithmic scale, for three strengths of feedback that span the range the large hydrodynamic simulations disagree over. Gas blown out of haloes by supernovae and active nuclei removes mass from scales below a few megaparsecs, so the ratio falls below one from about 0.5 h per megaparsec and is deepest near 4 h per megaparsec, at 9, 17 and 26 per cent; at still smaller scales gas that has cooled into galaxy centres adds mass back. The marks show the wavenumber that dominates a lensing measurement at multipoles 100, 1000, 5000, taken where the lensing kernel for sources at redshift 1 peaks: 0.09, 0.87, 4.35 h per megaparsec. The shape is a parametric stand-in placed where simulations put the effect, not a simulation.

A measurement of dark matter that needs a model of galaxies

Weak lensing weighs all the matter, dark and ordinary, by how it bends light. But the ordinary matter does not sit where gravity alone would put it — galaxies' supernovae and black holes blow a large part of it out of their haloes — and the scales where that happens are the scales that carry most of a lensing survey's statistical power. Ignored, it reads as a less clumpy universe, in the direction of the disagreement lensing has with the microwave background.

galaxies · Weak lensing One likelihood, read with three priors. A Gaussian likelihood in the effective neutrino mass sum, peaking at −0.08 eV with a width of 0.05 eV — of the shape that combinations of microwave-background and baryon-acoustic data have been reported to give. Read with no prior it says the data prefer a negative sum. Read with the physical prior, sum ≥ 0 (shaded right of zero), its 95 per cent upper limit is 0.059 eV, at the normal-ordering floor. Read with the oscillation prior, sum ≥ 0.059 eV, its limit is 0.102 eV — but only 0.3 per cent of the likelihood lies above the floor at all, which is the more informative number: the data and the oscillation experiments disagree at about 2.8 standard deviations.

A bound below the floor is not a mass

Oscillation experiments prove that neutrinos weigh at least 0.059 eV between them. Cosmology's latest upper bound on their total is 0.064 eV, and a bound computed differently would sit below the floor. The usual reading is that cosmology has nearly weighed the neutrino. The better one is that the fit's likelihood peaks at a negative mass: the data see more clustering than any real neutrino allows, and the bound is a symptom of that tension rather than a measurement of anything.

cosmology · Density parameters

Named alongside it

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

Density parameterFree-streamingNeutrino massAGN feedbackBaryon acoustic oscillationsBaryonic feedbackCosmic shearDegeneracyEffective number of speciesMass hierarchyMatter radiation equalityNeutrino oscillation

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