Cosmology

A particle count taken from a dwarf galaxy

Nearly every neutron that survives the first three minutes ends inside a helium nucleus, so the primordial helium abundance is not chemistry — it is the reading of a race between the weak interaction and the expansion. The expansion rate carries the square root of the number of relativistic species, which is why an emission line in a metal-poor galaxy counts neutrinos.

Assumes Nucleosynthesis, Expansion and Microwave background.

19 min read 8 figures Light is the only messenger Measuring the unreachable

The first rung of this anchor ran the whole network against its single adjustable number and let four abundances land where they fell. Deuterium did the work there: its curve is the steep one, so inverting it at the measured abundance pins the baryon density, and the pinning agrees with a sky map made four hundred thousand years later. Helium was in that picture as the flattest of the four lines, and a flat line is not a baryometer.

It is something else. The helium mass fraction barely responds to the baryon density because it is barely a nuclear result at all — it is a count of neutrons taken at one moment, and the moment is set by a race that has no baryons in it. The losing side of that race is the weak interaction; the winning side is the expansion; and the expansion rate depends on how many kinds of relativistic particle were present, whether or not any of them ever interacted with anything the calculation knows about.

The helium abundance as a count of neutrino species. The primordial helium mass fraction against the number of light neutrino species, integrated at a deuterium-bottleneck temperature of 0.0855 MeV and a neutron lifetime of 877.75 s. The curve rises at 0.01348 in Y_p per species near the standard model, and it is not quite a line: freeze-out temperature goes as the sixth root of g_*, so a species added at N_eff = 4.5 buys 25 per cent less helium than one added at 2 — a slope ratio of 0.749 against the 0.769 that scaling requires. The reading below is therefore taken off the drawn curve rather than off a slope. The horizontal band is the measurement — ⁴He (Aver 2015), Y_p = 0.2449 ± 0.004, taken from recombination lines in metal-poor dwarf galaxies and extrapolated to zero metallicity. Where the band crosses the line is the answer: N_eff = 2.84, with the ends of the observed interval giving 2.56 to 3.13. The standard model has three, and 3.046 rather than 3 because the neutrinos are not quite decoupled when the electron–positron pairs annihilate and take a sliver of the heat. The strength of this is not its precision, which is a third of a species and worse than the microwave background's; it is that the two constraints come from utterly different epochs, and that this one is a laboratory result about particle content obtained from an emission line in a galaxy. — Fig. 1 The primordial helium mass fraction against the number of light neutrino species, integrated at a bottleneck temperature of 0.0855 MeV and a neutron lifetime of 877.75 s. The horizontal band is the measurement, Y_p = 0.2449 ± 0.0040 from recombination lines in metal-poor dwarf galaxies extrapolated to zero metallicity; the vertical band is what it implies, N_eff = 2.84 ± 0.29, read off the curve by bisection rather than by dividing a slope. The standard model’s 3.046 sits inside it. The precision is a third of a species and is worse than either the microwave background or the LEP measurement of the Z width manages — and the interest is not the precision.

That figure is the argument, and everything below is an account of why the curve in it is where it is, followed by an account of the two things it rests on that are not measurements of the sky at all.

Helium is twice a neutron fraction

The statement that does the work is almost embarrassingly simple. Once deuterium survives, the chain that follows is fast and it is one-way: deuterium to tritium and helium-3, and those to ⁴He, which has the largest binding energy per nucleon of anything reachable before the mass-5 and mass-8 gaps stop the chain. Nothing sends a neutron back out. So essentially every neutron present when the chain fires ends up inside a helium nucleus, paired with a proton, and

Y_p = 2\,X_n, \qquad X_n = \frac{n}{n+p}

where $Y_p$ is helium’s share of the mass and $X_n$ is the neutron fraction at that instant. The factor of two is the two nucleons a neutron drags in with it. Predicting the primordial helium abundance is therefore not a problem in nuclear chemistry; it is a problem of knowing the neutron fraction at one moment, and the entire reaction network enters only through when that moment is.

$The neutron fraction left behind, for 3.046 neutrino species. The neutron-to-proton ratio through the first three minutes, integrated from thermal equilibrium at 3 MeV down to the deuterium bottleneck at 0.0855 MeV, for 1 values of the number of light neutrino species. Temperature falls to the right, so the picture reads left to right as time. The dashed line is the equilibrium ratio e^(−Δm/T), which every track follows while the weak interactions are fast enough to enforce it and none follows afterwards: the rates fall as T⁵ and the expansion rate only as T², so the race is lost once and never regained. The dot on each track is where the total conversion rate drops below the expansion rate — 0.639 MeV for N_eff = 3.046. After that the only thing still changing the ratio is free neutron decay, which is the slow downward drift over the rest of the picture and which is why the answer depends on how long the bottleneck lasts. The species count enters in exactly one place: the energy density carries g_* = 2 + (7/8)(4 + 2N_eff) while the pairs are still there, the expansion rate carries its square root, and a faster clock loses the race sooner and at a higher temperature. Every neutron surviving to the right-hand edge ends inside a ⁴He nucleus, so the helium mass fraction is twice the neutron fraction there — 0.2477 respectively. Nothing in this figure is a fitting function: the conversion rate is the standard massless-electron approximation normalised on the measured free-neutron lifetime, 877.75 s, and the ratio is stepped through it.$

Fig. 2 The neutron-to-proton ratio integrated from thermal equilibrium at 3 MeV down to the bottleneck, for the standard three neutrino species. Temperature falls to the right, so the picture reads left to right as time. The dashed line is the equilibrium ratio e^(−Δm/T): while the weak interactions are fast enough to enforce it, the ratio follows it down. The dot marks where the total conversion rate drops below the expansion rate, at 0.639 MeV, after which the ratio has been left behind and only free neutron decay still changes it — the slow downward drift across the rest of the picture. Twice the value at the right-hand edge is 0.2477.

The equilibrium ratio is the Boltzmann factor for a mass difference of 1.29333 MeV, which is where the whole asymmetry comes from: neutrons are heavier than protons, so at any temperature there are fewer of them, and the shortfall deepens as the temperature falls. At 10 MeV the difference is negligible and the ratio is close to one. By 1 MeV it is roughly a third.

The race the ratio loses

What stops the ratio following its equilibrium curve to zero is an ordinary competition of rates, and it is one-sided in the strongest possible way.

The interactions that convert a neutron into a proton — capture of a positron, capture of an electron neutrino, and free decay — all have cross sections that go as the square of the Fermi constant, and their thermally averaged rate goes as $T^5$ . The expansion rate in a radiation-dominated universe goes as $T^2$ . Five against two means that once the rate falls behind it can never catch up: the race is lost exactly once, and the losing is what the word freeze-out names.

The rate written into the figure above is the standard approximation with the electron mass neglected,

\lambda(n\!\to\!p) \;=\; \frac{255}{\tau_n}\,\frac{12 + 6x + x^2}{x^5}, \qquad x = \frac{\Delta m}{T}

and the thing worth noticing about it is its normalisation. It carries no coupling constant. It carries $\tau_n$ , the free-neutron lifetime, because the same matrix element that governs the decay governs every one of the conversions, and the decay is the one channel a laboratory can measure directly. The reverse rate is fixed by detailed balance at $e^{-x}$ times the forward one. So the figure’s conversion rates come from a bottle of ultracold neutrons in Los Alamos, and nothing about them is fitted to the sky. That is a point worth holding on to, because a laboratory disagreement about that number turns up again below.

The fifth power is worth a sentence of its own, since it is doing more work than the ratio of rates suggests. Four of those powers are phase space — the available energy for the outgoing particles scales as the temperature, and a weak process integrates over three momenta and a delta function — and the fifth is the density of the incoming neutrinos and positrons that the neutron has to meet. At 1 MeV the conversion rate is about three times the expansion rate and the ratio is still tracking equilibrium closely; at 0.5 MeV it is half, and the tracking has stopped. The whole of the transition occupies less than a factor of three in temperature, which is why a picture of it looks like a curve leaving a line rather than a curve slowly diverging from one. It is also why treating freeze-out as an instant, and the ratio as one sixth thereafter, gets the answer to a few per cent — an approximation this collection’s rung on the expansion itself would not tolerate but which is honest here, and which the integration above is drawn precisely to avoid needing.

Where the species get in

Now the part that makes an abundance into a particle count. The expansion rate during the radiation era depends on the energy density and on nothing else:

H = 1.66\,\sqrt{g_*}\;\frac{T^2}{m_{\rm Pl}}, \qquad g_* = 2 + \tfrac{7}{8}\left(4 + 2N_{\rm eff}\right)

The two is the photon’s polarisations; the four is the electron and positron with their spins; the $2N_{\rm eff}$ is the neutrinos and antineutrinos; the seven-eighths is the difference between Fermi and Bose statistics at the same temperature. Every relativistic species in the universe at that epoch is in $g_*$ , and $g_*$ enters $H$ under a square root.

A species that has never been detected still contributes, provided only that it was relativistic and in thermal contact early enough. It does not have to interact with anything now. It does not have to interact with baryons at all. It merely has to have been there, carrying energy density, making the clock run faster.

$The neutron fraction left behind, for 2, 3.046, 5 neutrino species. The neutron-to-proton ratio through the first three minutes, integrated from thermal equilibrium at 3 MeV down to the deuterium bottleneck at 0.0855 MeV, for 3 values of the number of light neutrino species. Temperature falls to the right, so the picture reads left to right as time. The dashed line is the equilibrium ratio e^(−Δm/T), which every track follows while the weak interactions are fast enough to enforce it and none follows afterwards: the rates fall as T⁵ and the expansion rate only as T², so the race is lost once and never regained. The dot on each track is where the total conversion rate drops below the expansion rate — 0.615 MeV for N_eff = 2, 0.639 MeV for N_eff = 3.046, 0.674 MeV for N_eff = 5. After that the only thing still changing the ratio is free neutron decay, which is the slow downward drift over the rest of the picture and which is why the answer depends on how long the bottleneck lasts. The species count enters in exactly one place: the energy density carries g_* = 2 + (7/8)(4 + 2N_eff) while the pairs are still there, the expansion rate carries its square root, and a faster clock loses the race sooner and at a higher temperature. Every neutron surviving to the right-hand edge ends inside a ⁴He nucleus, so the helium mass fraction is twice the neutron fraction there — 0.2324, 0.2477, 0.2708 respectively. Nothing in this figure is a fitting function: the conversion rate is the standard massless-electron approximation normalised on the measured free-neutron lifetime, 877.75 s, and the ratio is stepped through it.$

Fig. 3 The same integration at two, three and five neutrino species. The ordering is the argument: a larger g_* means a faster expansion, which means the T⁵ conversion rate falls behind sooner — at 0.615, 0.639 and 0.674 MeV respectively — and a ratio abandoned at a higher temperature is a larger ratio, because the equilibrium curve it was following had not yet fallen as far. More species, earlier freeze-out, more neutrons, more helium: 0.2324, 0.2477 and 0.2708. The three tracks are indistinguishable above 1 MeV, where equilibrium still holds and the expansion rate cannot be read off the ratio at all.

The chain has four links and each one is a sign rather than a coefficient: more species, faster clock, earlier loss, more helium. A hidden particle species does not leave a fingerprint anywhere in that argument. It leaves a number, and the number is about half a per cent of the helium mass fraction per species — small, but not small compared with what a good spectrum of an H II region can do.

What has actually been looked for with this lever is worth naming, because the abstraction hides how specific the searches are. A fourth, sterile neutrino that mixed enough to be brought into equilibrium before freeze-out would add exactly one to $N_{\rm eff}$ and raise the predicted helium by 0.013 — sitting right at the edge of what the measurement excludes. A relativistic particle decoupling earlier than the neutrinos contributes less than one, because the entropy released by every annihilation between its decoupling and freeze-out dilutes it; the same arithmetic that makes the neutrinos colder than the photons after the pairs go makes an earlier species colder still. And a scalar field carrying energy density contributes a fraction of a species with no particle interpretation at all. The measurement does not distinguish between these. It measures energy density in relativistic form at one second, and reports it in units of a neutrino.

There is one refinement in the constant. The standard model has three neutrino families, and $N_{\rm eff}$ is 3.046 rather than 3 because the neutrinos have not quite finished decoupling when the electron–positron pairs annihilate, so they catch a sliver of the heat released and end up marginally hotter than a clean decoupling would leave them. The excess is a calculational detail with no free parameter in it, and it is the size of the effect being hunted, which is a good way to appreciate how demanding the measurement is.

The curve bends, and the bend is a prediction

Freeze-out happens where a $T^5$ rate crosses a $\sqrt{g_*}\,T^2$ one, so the freeze-out temperature scales as $g_*^{1/6}$ — a sixth root, which is about as weak a dependence as a physical quantity can have and still be a dependence. The consequence is that each additional species buys less helium than the one before it.

The agreement between the drawn curve’s shape and $g_*^{1/6}$ is worth more than it looks. The integration knows nothing about that scaling — it steps a differential equation through a rate and an expansion law — and the scaling is an asymptotic argument about where two power laws cross. Two independent routes to the same shape is the ordinary way this collection checks that a picture is of the thing it claims, and here the routes agree to about five per cent — the residue being the neutron decay between freeze-out and firing, which the asymptotic argument leaves out and the integration does not.

Why this is not the deuterium measurement

The first rung’s inference and this one both come out of one reaction network, and they are nonetheless separate measurements of separate things. The clearest way to see it is to look at what each abundance does across the interval the baryon density is actually known to.

Four abundances, one free parameter. The abundances big-bang nucleosynthesis predicts, against the one number it is free to choose: η₁₀, the ratio of baryons to photons in units of 10⁻¹⁰. Four curves spanning nine decades, from a helium mass fraction of about a quarter down to a lithium abundance of one atom in ten billion, and they are not four independent predictions — they all come out of the same reaction network run at the same density. The horizontal bands are what is measured in the sky, each at its published one sigma. The measurement that matters is deuterium, because its curve is the steep one: inverting the drawn curve at D/H = 2.527e-5 gives η₁₀ = 6.11, and the ends of the observed interval give 6.06 to 6.15. The vertical band is what the microwave background gives, 6.13 ± 0.04, from the height of the second acoustic peak relative to the first. Those two agree to 0.4 per cent, and they have nothing whatever in common: one is a nuclear-reaction network run in the first three minutes and read off a quasar absorption line, the other is a fluid oscillation at four hundred thousand years read off a sky map. Lithium is the exception and it is not a small one — the network predicts 4.70e-10 at the microwave background's density and the halo stars show 1.60e-10, a factor of 2.9 too much, which is unresolved. — Fig. 5 The four abundances again, restricted to a window in the baryon-to-photon ratio about a quarter as wide as the first rung’s. Deuterium falls by a factor of 1.5 across it — its curve is visibly steep, which is what makes it a baryometer. Helium is a horizontal line by comparison: its predicted mass fraction moves by 0.0024 across the whole window, which is less than the measurement’s own error bar and less than a fifth of a neutrino species. Lithium’s discrepancy is unchanged, because a factor of three does not care about a twelve per cent shift in η.

That flatness is the point. Helium’s insensitivity to the baryon density is what disqualifies it as a baryometer and what qualifies it as a species counter, because it means the answer read off the helium curve is not contaminated by whatever uncertainty the baryon density still carries. The two readings share a network and share almost no information, which is the property that makes the concordance in the first rung a test rather than a consistency check. The baryon budget can move by ten per cent without moving this essay’s answer by a tenth of a species.

The same independence runs the other way against the microwave background. The acoustic peaks constrain $N_{\rm eff}$ too, and rather better — the extra radiation shifts the epoch of matter–radiation equality and changes the damping tail — but they do so at four hundred thousand years, through the propagation of sound in a photon–baryon fluid whose photon number comes from the best blackbody ever measured. The helium reading is taken at one second. Two constraints on one quantity, five orders of magnitude apart in time, is the shape of evidence this subject rarely gets.

The one number the integration cannot supply

Every figure above carries a temperature that has not been justified: 0.0855 MeV, the point at which the network fires. It deserves the scepticism, because it is the weakest thing in the calculation.

Deuterium is bound by only 2.2246 MeV, and it sits in a bath containing about a billion photons for every baryon, so the tail of the photon distribution keeps photodissociating it long after the mean photon energy has fallen below the binding energy. The bottleneck breaks when the deuterium abundance becomes large enough for the burning reactions to outrun the destruction, and that is a threshold on a smoothly rising quantity, not an event. Different reasonable criteria put it anywhere between about 0.06 and 0.10 MeV. This matters because the interval between freeze-out and the firing is spent decaying: every extra second is neutrons lost.

$What the bottleneck temperature decides, and what it does not. The same integration read twice, against the one number in it that is a threshold rather than a measurement: the temperature at which deuterium survives in enough quantity for the network to fire. On the left, the predicted helium mass fraction, which moves from 0.2003 to 0.2661 as that temperature is taken from 0.06 to 0.105 MeV — 28 per cent, because every second before the network fires is a second in which neutrons are decaying and the answer is twice the neutron fraction. On the right, the sensitivity of that same prediction to one extra neutrino species, which moves only from 0.01221 to 0.01297: 6.1 per cent across the identical range. The reason is that the derivative is a difference between two runs that share the delay, so the delay largely cancels out of it while it does not cancel out of either run. The ratio of the two swings is 4.6. This is what makes the previous figure's reading survive its own weakest input: the absolute abundance would be a poor prediction if the bottleneck were the only thing known about it, and the species count is not, because the species count is read off the slope. The marked temperature is 0.0855 MeV, at which this integration gives Y_p = 0.2477 against the 0.247 a full reaction network gives, and a sensitivity of 0.01255 against the 0.0128 the published codes give.$

Fig. 6 The same integration read twice against that temperature. On the left, the predicted helium mass fraction, which moves from 0.2003 to 0.2661 — 28 per cent — as the bottleneck is taken from 0.06 to 0.105 MeV, because the delay before firing is time in which neutrons decay. On the right, the sensitivity of that same prediction to one extra species, which moves from 0.01221 to 0.01297: 6.1 per cent across the identical range, a ratio of 4.6. The marked value is 0.0855 MeV, at which the integration gives Y_p = 0.2477 against the 0.247 a full reaction network gives.

The two panels are the same numbers arranged twice, and the difference between them is the whole reason the reading survives. The absolute abundance is at the mercy of the bottleneck; the derivative is not, because it is a difference between two runs that share the delay, so most of the delay cancels out of it. A quantity that is badly determined and a quantity derived from it that is well determined is not a paradox — it is the ordinary behaviour of a difference, and it is why the species count is read off the slope of the curve rather than off its height.

Narrowing to the range a modern network actually spans does not change the conclusion, only the numbers.

$What the bottleneck temperature decides, and what it does not. The same integration read twice, against the one number in it that is a threshold rather than a measurement: the temperature at which deuterium survives in enough quantity for the network to fire. On the left, the predicted helium mass fraction, which moves from 0.2328 to 0.2578 as that temperature is taken from 0.075 to 0.095 MeV — 10 per cent, because every second before the network fires is a second in which neutrons are decaying and the answer is twice the neutron fraction. On the right, the sensitivity of that same prediction to one extra neutrino species, which moves only from 0.01238 to 0.01276: 3.1 per cent across the identical range. The reason is that the derivative is a difference between two runs that share the delay, so the delay largely cancels out of it while it does not cancel out of either run. The ratio of the two swings is 3.3. This is what makes the previous figure's reading survive its own weakest input: the absolute abundance would be a poor prediction if the bottleneck were the only thing known about it, and the species count is not, because the species count is read off the slope. The marked temperature is 0.0855 MeV, at which this integration gives Y_p = 0.2477 against the 0.247 a full reaction network gives, and a sensitivity of 0.01255 against the 0.0128 the published codes give.$

Fig. 7 The same pair over the interval the published codes disagree within. The abundance still swings 10 per cent, which on its own would be four times the measurement’s error bar and would sink the whole exercise. The sensitivity swings 3.1 per cent, which is a twentieth of a species and is invisible next to the measurement. This is what it means for a result to be robust against its own weakest input: not that the input is unimportant, but that the quantity being read is not the quantity the input controls.

A laboratory disagreement with a cosmological consequence

The conversion rate is normalised on the neutron lifetime, and the neutron lifetime is measured two ways that do not agree. A bottle experiment stores ultracold neutrons and counts the survivors: 877.75 ± 0.28 s. A beam experiment passes a cold neutron beam through a trap and counts the protons produced: 888.0 ± 2.0 s. The difference is about ten seconds and something over four standard deviations, and it has stood for two decades while both techniques have improved.

That is a modest number and an instructive one. The cosmological inference is not ruined by the laboratory disagreement, but it is displaced by an amount comparable to the effects it is being used to look for, so a paper quoting $N_{\rm eff}$ from helium has to say which lifetime it used. The parallel elsewhere in this collection is exact in structure if not in scale: the same expansion constant measured twice, five sigma apart, where two methods each internally consistent disagree and the disagreement is itself the result. Here the disagreeing measurements are both terrestrial and the consequence is astronomical, which is the less usual direction.

What is actually measured

The band in the first figure is not helium. It is a ratio of emission-line strengths, and the distance from one to the other is worth stating, because this collection’s standing obligation is to say what an instrument recorded.

An extragalactic H II region — an ionised cloud around young stars in a small, gas-rich, chemically unevolved galaxy — emits recombination lines of hydrogen and of helium. The ratio of a helium line to a hydrogen line gives the ratio of the two ion abundances, once the emissivities are known, and the emissivities depend on the electron temperature and density, which have to be got from other line ratios in the same spectrum. Then the neutral helium that the ionising spectrum failed to reach has to be added back, and the helium locked in doubly ionised form subtracted, and the underlying stellar absorption at the same wavelengths corrected for, and the whole thing done for several dozen galaxies.

None of those objects is primordial. Every one has made some helium in stars, so the measured abundance is extrapolated to zero metallicity along the correlation between helium and oxygen, and the intercept is the number quoted. The quoted uncertainty of 0.0040 is dominated not by photon statistics but by that modelling chain — by collisional excitation of the helium lines, by the temperature adopted, and by the choice of which galaxies are clean enough to include. Different groups working from overlapping data have published intercepts from 0.2419 to 0.2551, and the spread between them exceeds any one of their error bars.

It is worth setting the result beside the one laboratory measurement of the same quantity. The width of the Z boson at LEP depends on how many neutrino species it can decay into invisibly, and that experiment gives 2.9840 ± 0.0082 — three species, to a third of a per cent, from a collider. The two numbers are not measuring quite the same thing: LEP counts neutrinos light enough and coupled strongly enough to be produced in a Z decay, and helium counts everything relativistic and thermalised at one second, coupled or not. A discrepancy between them would therefore have been a discovery rather than an error, which is the reason for measuring a known quantity badly by a second method. The error bar that comes from counting is not what limits either of them.

So the honest summary of this rung is that the physics is clean and the measurement is not. The reading is limited by an atomic-physics-and-extrapolation problem in a handful of nearby dwarf galaxies, and any improvement in it will come from spectroscopy rather than from the early universe.

The generalisation

The structure worth extracting is that a quantity can be a good probe of something it barely depends on, provided the dependence it does have is on nothing else.

Helium’s response to the number of relativistic species is weak — half a per cent per species, through a square root and a sixth root. What makes it usable is that almost nothing else moves it: not the baryon density, which is what deuterium is for; not the details of the nuclear network, which only set when the counting stops; not the abundance of anything heavier. The signal is small and it is nearly alone, and being nearly alone is worth more than being large.

The same shape appears wherever this collection finds a measurement of something invisible. The solar neutrino flux is a thermometer good to a tenth of a per cent because the boron-8 rate depends on the central temperature to the twenty-fifth power and on very little else. Nothing in the sky is weighed in kilograms because every astronomical mass is a product $GM$ , and the poorly known factor is the terrestrial one — the mirror image of this essay, where the poorly known factor is again terrestrial and again a laboratory constant.

The corollary is the warning. A quantity that responds weakly to the thing being measured responds weakly to its systematics too, which is why the helium result is quoted at a third of a species while the microwave background reaches 0.17 — and why the two are worth having together rather than in place of one another.

Where the ladder goes next

Two thirds of the neutrons that existed at freeze-out survive to be counted, and the missing third decayed. The next rung takes the same integration and asks what the surviving deuterium is: not the trace that seeds the chain, but the small residue that fails to burn, whose abundance is the steep function the first rung inverted. That residue is set by a competition between burning and expansion in exactly the same style as this one, and it is what makes deuterium a baryometer rather than a species counter.

Further rungs on this anchor: the lithium problem’s proposed resolutions, and why stellar depletion is the least unattractive of them; helium-3, and why an abundance that is both produced and destroyed in stars cannot be extrapolated backwards at all; inhomogeneous nucleosynthesis, pursued seriously in the 1980s to make the baryon density equal the matter density, and the reason it does not work; and the constraint this same figure places on a light sterile neutrino, which is the particle-physics reading of the same band.

What links here

The 8 of 9 essays linking to this one that name the most of the same objects.

The residue that failed to burn cosmology
A factor of three, and the flatness that prices every cure cosmology
An abundance with no direction to correct in cosmology
The universe that was lumpy at one second cosmology
The epoch nobody saw moves the tilt cosmology
A mass measured by what it stopped from forming cosmology
Nine dates for every surface in the solar system orbits
The metals a galaxy keeps measure what it threw away galaxies

The objects this essay names

Each one links to every other essay that touches it.

Baryon-to-photon ratio Big bang nucleosynthesisDetailed balanceDeuterium bottleneckEffective number of neutrino speciesFreeze outNeutron lifetimeNeutron proton ratio Primordial heliumRelativistic degrees of freedomThermal equilibriumWeak interaction

Helium is twice a neutron fraction #

The race the ratio loses #

Where the species get in #

The curve bends, and the bend is a prediction #

Why this is not the deuterium measurement #

The one number the integration cannot supply #

A laboratory disagreement with a cosmological consequence #

What is actually measured #

The generalisation #

Where the ladder goes next #

Where this goes next