Astronomy & Celestial Mechanics
the sky, computed
Concept

B-modes — where it appears

The curl-like, handed part of a polarisation pattern on the sky, with polarisation at forty-five degrees to the direction its strength changes. Density fluctuations make none at first order, so primordial B-modes would mark gravitational waves from inflation.

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

6 potentials against the tilt and the tensor bound. Predictions in the plane of spectral index and tensor-to-scalar ratio, each drawn as a short track from 50 e-folds to 60, the range usually allowed for the pivot scale to have left before the end of inflation. The vertical band is the measured index, 0.9649 ± 0.0042 with its two-sigma extent, and the shaded region above 0.036 is excluded at 95 per cent by the B-mode polarisation limit — drawn as two independent limits, which the published constraint is not quite: the real likelihood is a correlated contour, and it is somewhat tighter than this box in the corner where the tilt is high. λφ⁴: nₛ 0.9412, r 0.3137 at 50 e-folds; 0.9508, 0.2623 at 60 — outside; m²φ²: nₛ 0.9604, r 0.1584 at 50 e-folds; 0.9669, 0.1322 at 60 — outside; linear φ: nₛ 0.9701, r 0.0796 at 50 e-folds; 0.9751, 0.0664 at 60 — outside; φ^⅔: nₛ 0.9734, r 0.0532 at 50 e-folds; 0.9778, 0.0443 at 60 — outside; natural, f = 7: nₛ 0.9569, r 0.0906 at 50 e-folds; 0.9628, 0.0670 at 60 — outside; Starobinsky: nₛ 0.9616, r 0.0042 at 50 e-folds; 0.9678, 0.0030 at 60 — inside. The simplest potential of all, a mass term, is excluded over its whole range of e-folds, and not by the tilt, which it matches — by the tensors.

A ratio that is an energy and a distance

The tensor-to-scalar ratio is the one inflationary observable that measures the height of the potential rather than its shape, and the quantity it fixes is an energy — a ratio of 0.01 means inflation happened at 10¹⁶ GeV. It fixes a second thing as well, how far the field travelled, and near the present bound that distance is several Planck masses, which is where the theory stops being able to vouch for itself.

cosmology · Inflation Polarised dust, synchrotron and the signal between them. The amplitude of B-mode polarisation at angular multipole 80, in microkelvin of CMB temperature on a logarithmic scale, against frequency from 20 to 450 GHz, for a patch of sky as clean as the cleanest large field observed. Dust is a modified blackbody with emissivity index 1.53 at 19.6 K, normalised to 4.6 µK² at 353 GHz; synchrotron falls as frequency to the power −3.1 in antenna temperature, normalised to an illustrative 1 µK² at 23 GHz. The horizontal lines are a primordial signal with tensor-to-scalar ratio 0.01, about 0.048 µK, and the lensing B-modes, about 0.071 µK. The foregrounds together are faintest at 81 GHz, at 0.038 µK, 0.8 times the signal. At 150 GHz the dust alone is 0.105 µK, the amplitude a tensor ratio of 0.046 would produce; at 353 GHz it is 2.23 µK, 47 times the signal. No frequency has the signal above the foreground.

A foreground drawn by the field it traces

The grains that polarise starlight along the Galaxy's magnetic field glow, at millimetre wavelengths, with light polarised across it — and that glow is brighter than the primordial signal cosmologists are looking for at every frequency above eighty gigahertz and in every patch of sky. Its pattern on the sky is set by how loosely the interstellar filaments follow the field, and removing it rests on a bet that the clouds along each line of sight share one temperature.

galaxies · Dust polarisation A family that runs the full height of the plane. The spectral tilt and the tensor-to-scalar ratio (logarithmic) predicted by inflationary potentials, against the measured tilt (0.9649 ± 0.0042, shaded, two standard deviations) and the upper bound on the ratio (0.036, solid line). The two curves are the T-model α-attractor, V ∝ tanh²(φ/√6α), for α from ten thousandths to a thousand, at 50 and 60 e-folds before the end of inflation: at large α the model is a quadratic potential and sits above the bound; as α falls the ratio drops without limit while the tilt settles at 1 − 2/N. The dots on each curve are α = 1, close to Starobinsky's model, at a ratio of 0.0046 and 0.0032. The short segments are power-law potentials, all excluded or nearly so. The dashed line at 0.001 is a target of the next generation of polarisation experiments: a null result there would exclude α = 1 and leave every smaller α standing.

A null that removes a model and not its family

The plateau potentials that survive every measurement of inflation predict a tensor-to-scalar ratio a few thousandths high, and the next polarisation experiments are designed to reach it. A null result there would exclude Starobinsky's model. It would not exclude the family it belongs to: the α-attractors stretch one shape by one parameter, their tilt stays where the measurement put it, and their ratio slides down as α does, without a floor.

cosmology · Inflation

Named alongside it

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

Tensor to scalar ratioE-foldsLyth boundPrimordial gravitational wavesReheatingScalar spectral indexSlow-rollDust polarisationE-modesEnergy scale of inflationForeground removalGrain alignment

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