Glossary

The distance at which one astronomical unit subtends one arcsecond, so a star with a parallax of $p$ arcseconds lies $1/p$ parsecs away. It is the working unit of distance in astronomy; the nearest star, Proxima Centauri, is 1.30 pc away.

$1\text{pc}=3.086\times 10^{16}\text{m}\approx 3.26$ light-years $\approx 206265$ AU

In the folio: Measuring the cosmosSee also Parallax, Kiloparsec, megaparsec, gigaparsec, Light-year

$10^3$, $10^6$ and $10^9$ parsecs. Rough landmarks: the Milky Way's disc is about 30 kpc across, the Andromeda galaxy is 0.78 Mpc away, galaxy clusters span a few Mpc, the sound horizon is 147 Mpc, and the observable universe has a comoving radius of about 14.3 Gpc.

$1\text{Mpc}=3.086\times 10^{22}\text{m}$

In the folio: Measuring the cosmosSee also Parsec, Sound horizon, Observable universe

The distance light travels in a Julian year. Common in popular writing, rarely used in research, where the parsec is preferred.

$1\text{ly}=9.461\times 10^{15}\text{m}=0.3066\text{pc}$

See also Parsec

The mean Earth–Sun distance, fixed by definition since 2012. It is the baseline of the parallax that defines the parsec.

$1\text{au}=1.495978707\times 10^{11}\text{m}$ exactly

See also Parsec, Parallax

One sixtieth of an arcminute, $1/3600$ of a degree. Milliarcseconds (mas) and microarcseconds (μas) measure the parallaxes Gaia records and the black-hole images the Event Horizon Telescope resolves: the ring around M87* is 42 μas across, the apparent size of an orange on the Moon.

$1^{\prime \prime }=4.848\mu \text{rad}$

See also Parallax, Black-hole shadow

Thousands, millions and billions of years. The folio's timelines read naturally in these: the CMB was released at 380 kyr, the first stars formed at roughly 100–200 Myr, and the universe is 13.8 Gyr old.

$1\text{yr}=3.156\times 10^7\text{s}$ (Julian year); $1\text{Gyr}=10^9\text{yr}$

In the folio: Cosmic historySee also Cosmic time, Age of the universe

The mass of the Sun, the unit for stars, black holes and galaxies. The symbol ☉ always means "of the Sun": $L_{\odot }$, $R_{\odot }$, $M_{\odot }$. A galaxy like the Milky Way holds about $10^{12}{M}_{\odot }$ including its dark halo; a supermassive black hole, $10^6$–$10^{10}{M}_{\odot }$.

$M_{\odot }=1.989\times 10^{30}\text{kg}$

In the folio: Stars forge the elementsSee also Solar luminosity, Solar radius

The Sun's total radiated power, used as the unit on the luminosity axis of the Hertzsprung–Russell diagram. Stars span roughly $10^{-4}$ to $10^6{L}_{\odot }$.

$L_{\odot }=3.828\times 10^{26}\text{W}$ (IAU nominal value)

In the folio: Stars forge the elementsSee also Hertzsprung–Russell diagram, Mass–luminosity relation

The Sun's radius, the natural unit for stellar sizes. A white dwarf is about $0.01R_{\odot }$, Earth-sized; a red supergiant can exceed $1000R_{\odot }$.

$R_{\odot }=6.957\times 10^8\text{m}$

See also White dwarf, Supergiant

The unit of the Hubble constant: recession speed gained per unit distance. It is an inverse time in disguise, and $H_0=67.4$ in these units is $2.18\times 10^{-18}{\text{s}}^{-1}$, whose inverse, the Hubble time, is 14.5 Gyr.

$1{\text{km s}}^{-1}{\text{Mpc}}^{-1}=3.241\times 10^{-20}{\text{s}}^{-1}$

In the folio: What the Universe is made ofSee also Hubble constant, Hubble time and Hubble distance

The Hubble constant divided by 100 km s⁻¹ Mpc⁻¹, so $h\approx 0.674$. Quantities whose value depends on $H_0$ are often quoted with explicit powers of $h$ (such as ${\Omega }_b{h}^2$ or $8h^{-1}\text{Mpc}$), which keeps them independent of the still-disputed value.

$H_0=100h{\text{km s}}^{-1}{\text{Mpc}}^{-1}$

See also Hubble constant, Hubble tension

A subscript 0 means "today": $H_0$, $T_0$, $q_0$, ${\rho }_{\text{crit},0}$. The scale factor is normalised so that $a_0=1$.

See also Scale factor, Hubble constant

Cosmologists date events by redshift rather than by time, because redshift is what is observed and needs no model, while converting it to an age requires one. In Planck ΛCDM: $z\approx 1090$ is 380 kyr, $z=14.44$ is about 280 Myr, $z=6$ about 0.9 Gyr, $z=2$ about 3.3 Gyr, $z=1$ about 5.9 Gyr, and $z=0.3$ about 10.3 Gyr after the Big Bang.

In the folio: Cosmic historySee also Cosmological redshift, Lookback time

The early universe is labelled by the thermal energy $k_{B}T$ of its particles: the electroweak crossover at 160 GeV, the QCD crossover at 155 MeV, neutrino decoupling at 1 MeV. In the radiation era a useful rule of thumb links this to time.

$1\text{eV}/k_B=11605\text{K}$; $t\sim 1\text{s}\times {\left(1\text{MeV}/k_{B}T\right)}^2$

In the folio: Cosmic historySee also Radiation era, Electroweak crossover, QCD crossover

A relative precision of $10^{-6}$. COBE's FIRAS showed the CMB spectrum to be a blackbody to about 50 ppm, the most perfect thermal spectrum measured in nature.

In the folio: The cosmic microwave backgroundSee also FIRAS, Blackbody spectrum

The hot, dense early state from which the expanding universe evolved, not an explosion into pre-existing space. Extrapolating the expansion back gives a formal $t=0$ where classical general relativity stops being trustworthy; the observational evidence (the CMB, light-element abundances, the expansion itself) concerns the hot phase after it.

In the folio: Cosmic historySee also Planck era, Cosmic time, Cosmic microwave background

The proper time measured by an observer at rest with respect to the expansion (a comoving observer). Every "years after the Big Bang" in the folio is cosmic time.

See also Comoving coordinates, Age of the universe

The cosmic time elapsed since the Big Bang in the best-fitting model, $13.80\pm 0.02$ Gyr from Planck ΛCDM. It is model-dependent: it comes from integrating the expansion history, not from a direct clock, although the oldest stars (about 13 Gyr) provide an independent lower bound.

$t_0={\int }_0^{\infty }\frac{dz}{(1+z)H(z)}$

In the folio: What the Universe is made ofSee also Expansion history, Lookback time

How long ago light now arriving set out. Light from $z=1$ left about 7.9 Gyr ago, more than half the age of the universe.

See also Redshift as a clock, Age of the universe

Times earlier than about one Planck time, when quantum effects of gravity cannot be neglected and no tested theory applies. The Planck scale has nothing to do with the Planck satellite.

$t_P=\sqrt{\hslash G/c^5}\approx 5.4\times 10^{-44}\text{s}$, $E_P=\sqrt{\hslash c^5/G}\approx 1.22\times 10^{19}\text{GeV}$

In the folio: Cosmic historySee also Inflation, Planck (satellite)

A proposed brief epoch of accelerating, nearly exponential expansion, by a factor of at least $e^{60}$, at roughly $10^{-36}$–$10^{-32}$ s, usually modelled with a scalar field (the inflaton). It explains why the universe is so flat and why regions that were never in causal contact share one temperature (the horizon problem), and it stretches quantum fluctuations into the seeds of all structure. Its predictions of a slightly tilted spectrum ($n_s<1$) and primordial gravitational waves (tensor ratio $r$) make it testable; the second has not been seen.

In the folio: Cosmic historySee also Reheating, Scalar spectral index, Tensor-to-scalar ratio, Primordial fluctuations

The end of inflation, when the inflaton's energy decays into the hot plasma of ordinary particles that the standard Big Bang story starts from.

See also Inflation

At about 160 GeV, roughly $10^{-11}$ s, the Higgs field settles into its non-zero value and the W and Z bosons gain mass. Lattice calculations show that in the Standard Model this is a smooth crossover rather than a sharp phase transition, so it should leave no bubbles or gravitational-wave background.

In the folio: Cosmic historySee also Energy as temperature, QCD crossover

At about 155 MeV, some 10–20 μs after the Big Bang, the quark–gluon plasma cools enough for quarks and gluons to bind into protons, neutrons and other hadrons ("quarks bind into hadrons" in the folio). Like the electroweak transition, it is a crossover, not a sharp transition.

In the folio: Cosmic historySee also Electroweak crossover, Baryons

Whatever process left the universe with slightly more matter than antimatter, about one extra baryon per $1.6\times 10^9$ photons. It requires baryon-number violation, C and CP violation and a departure from equilibrium (Sakharov's conditions); the Standard Model's CP violation is far too small, so the explanation is open.

In the folio: Open problemsSee also Baryon-to-photon ratio

At about 1 MeV, roughly 1 s, weak interactions become slower than the expansion and neutrinos stop exchanging energy with the plasma. They have streamed freely ever since, forming the cosmic neutrino background.

In the folio: Cosmic historySee also Cosmic neutrino background, Electron–positron annihilation

Just after neutrino decoupling, electron–positron pairs annihilate and heat the photons but not the already-decoupled neutrinos. This is why the neutrino background is colder than the CMB.

$T_{\nu }/T_{\gamma }=(4/11{)}^{1/3}$, giving $T_{\nu }\approx 1.95\text{K}$ today

See also Neutrino decoupling, Cosmic neutrino background

The formation of the light nuclei, mostly in the first 3–20 minutes: deuterium, helium-3, helium-4 and a trace of lithium-7. Heavier nuclei barely form, because no stable nucleus has mass 5 or 8. The outcome depends almost only on the baryon-to-photon ratio, and agrees with the value the CMB reads 380,000 years later, one of cosmology's strongest consistency checks.

In the folio: The cosmic microwave backgroundSee also Primordial helium fraction, Deuterium abundance, Lithium problem, Baryon-to-photon ratio

The fraction of baryonic mass in helium-4 when nucleosynthesis ends, about 0.245. It is set mainly by how many neutrons survived until nuclei could form, which makes it a sensitive probe of the expansion rate at about 1 MeV.

In the folio: The cosmic microwave backgroundSee also Big Bang nucleosynthesis

The number ratio of deuterium to hydrogen, about $2.5\times 10^{-5}$. Deuterium is easily destroyed and not produced by stars, so its primordial value is a direct "baryometer" of the baryon density, measured in distant gas clouds seen against quasars.

In the folio: The cosmic microwave backgroundSee also Big Bang nucleosynthesis, Baryon-to-photon ratio

Old halo stars contain about three times less lithium-7 than nucleosynthesis predicts for the CMB's baryon density. It is the one persistent mismatch in the light elements, and may reflect lithium destruction inside the stars rather than new physics.

In the folio: The cosmic microwave backgroundSee also Big Bang nucleosynthesis

The first roughly 50,000 years, when the energy density was dominated by photons and neutrinos and the scale factor grew as $a\propto t^{1/2}$. It was followed by the matter era, $a\propto t^{2/3}$, and since $z\approx 0.3$ by the dark-energy era.

See also Matter–radiation equality, Dark-energy domination, Equation of state

The moment the matter density overtook the radiation density, at $z\approx 3400$, about 51 kyr. Before it, radiation pressure kept dark-matter clumps from growing much; after it, structure growth begins in earnest.

${\rho }_m={\rho }_r$ at $1+z_{\text{eq}}={\Omega }_m/{\Omega }_r$

In the folio: Cosmic historySee also Radiation era, Expansion history

The capture of electrons by nuclei to form neutral atoms, around $z\approx 1100$ at about 3000 K. That is far below the 13.6 eV binding energy of hydrogen (157,000 K) because photons outnumber baryons by more than a billion, so even the rare photons in the Wien tail keep re-ionising atoms until the plasma is quite cool. The name is a misnomer: nuclei and electrons had never been combined before.

In the folio: Cosmic historySee also Photon decoupling, Baryon-to-photon ratio

With few free electrons left after recombination, photons stop scattering and travel freely: the "CMB released" mark at about 380 kyr, $z\approx 1090$. The shell of space from which they last scattered, now about 14 Gpc away, is the last-scattering surface, the farthest light can be seen.

In the folio: Cosmic historySee also Recombination, Cosmic microwave background

The hundred million years or more between photon decoupling and the first stars, when the universe held neutral gas and fading CMB light but no luminous sources.

See also First stars, Reionisation

The first generation of stars, formed at roughly 100–200 Myr from hydrogen and helium alone. Without heavier elements to cool the gas, they are expected to have been massive and short-lived. None has been observed directly yet.

In the folio: Cosmic historySee also Stellar populations, Dark ages, Reionisation

The re-ionisation of intergalactic hydrogen by ultraviolet light from the first stars and galaxies, complete by $z\approx 6$, about 1 Gyr. Evidence comes from absorption troughs in distant quasar spectra and from the fraction of CMB photons scattered by the freed electrons.

In the folio: Cosmic historySee also Optical depth to reionisation, First stars

The peak of cosmic star formation and black-hole growth, around $z\approx 2$, about 3 Gyr after the Big Bang. Galaxies then formed stars roughly ten times faster than today.

In the folio: Cosmic historySee also Redshift as a clock

Since about $z\approx 0.3$, roughly 10 Gyr after the Big Bang, the dark-energy density has exceeded that of matter. The expansion began to accelerate earlier, at $z\approx 0.6$, because acceleration needs only ${\rho }_{\Lambda }>{\rho }_m/2$.

In the folio: Cosmic historySee also Dark energy, Deceleration parameter

The assumption that on large enough scales, above a few hundred megaparsecs, the universe is homogeneous and isotropic. It reduces general relativity to a single function of time, the scale factor.

See also FLRW metric

The Friedmann–Lemaître–Robertson–Walker spacetime, the most general homogeneous, isotropic metric. All of the expansion is carried by $a(t)$ and the curvature constant $k$.

$d{s}^2=-c^{2}d{t}^2+a^2(t)\left[\frac{d{r}^2}{1-k{r}^2}+r^{2}d{\Omega }^2\right]$

See also Scale factor, Curvature, Friedmann equations

The relative size of the universe: the distance between any two comoving galaxies is proportional to $a(t)$. It is normalised to $a_0=1$ today and related directly to redshift.

$a=1/(1+z)$

In the folio: Expansion: the Friedmann equationsSee also Cosmological redshift, Comoving coordinates

Coordinates that expand with the universe, so galaxies at rest relative to the expansion keep fixed coordinates. Comoving distances are physical distances scaled to today, which is why the sound horizon is quoted as 147 Mpc even though it was 1100 times smaller when it formed.

See also Comoving distance, Scale factor, Peculiar velocity

The fractional expansion rate at any epoch. It falls with time in a decelerating universe and tends to a constant if dark energy is a cosmological constant.

$H=\dot{a}/a$

In the folio: Expansion: the Friedmann equationsSee also Hubble constant, Expansion history

The present expansion rate, $H(z=0)$. Planck's CMB data within ΛCDM give $67.4\pm 0.5$ km s⁻¹ Mpc⁻¹; local distance-ladder measurements give larger values, up to about 73. It is a constant in space, not in time.

In the folio: What the Universe is made ofSee also Hubble tension, Kilometres per second per megaparsec, Dimensionless Hubble constant

For nearby galaxies, recession speed is proportional to distance. It holds only for $z\ll 1$; beyond that, distances must be computed from the full expansion history. Lemaître derived it in 1927 and Hubble established it observationally in 1929.

$v\approx H_{0}d$

In the folio: Measuring the cosmosSee also Hubble flow, Comoving distance

The motion of galaxies due to the expansion alone. Galaxies far enough away that their own motions are small next to it, beyond roughly 100 Mpc, are said to be "in the Hubble flow".

See also Peculiar velocity, Hubble–Lemaître law

A galaxy's motion relative to the Hubble flow, typically a few hundred km s⁻¹, caused by the pull of nearby structure. It is why nearby galaxies make poor tracers of $H_0$.

See also Hubble flow, CMB dipole

Natural scales built from $H_0$: the age a universe expanding at constant rate would have, and the distance at which the Hubble–Lemaître law reaches the speed of light.

$1/H_0\approx 14.5\text{Gyr}$, $c/H_0\approx 4.45\text{Gpc}$

See also Hubble constant

Einstein's equations for an FLRW universe. The first ties the expansion rate to the total density, curvature and cosmological constant; the second gives the acceleration. Pressure appears in the second with the same sign as density, so ordinary pressure decelerates the expansion; only a component with $p<-\rho c^2/3$ can accelerate it.

$H^2=\frac{8\pi G}{3}\rho -\frac{k{c}^2}{a^2}+\frac{\Lambda c^2}{3}$

$\frac{\ddot{a}}{a}=-\frac{4\pi G}{3}\left(\rho +\frac{3p}{c^2}\right)+\frac{\Lambda c^2}{3}$

In the folio: Expansion: the Friedmann equationsSee also Critical density, Equation of state, Cosmological constant

The total density for which space is exactly flat. Today it corresponds to about five hydrogen atoms per cubic metre. The folio's density plot is drawn in units of today's value, $\rho /{\rho }_{\text{crit},0}$.

${\rho }_{\text{crit}}=\frac{3H^2}{8\pi G}\approx 8.5\times 10^{-27}{\text{kg m}}^{-3}$ today

In the folio: Expansion: the Friedmann equationsSee also Density parameter, Curvature

A component's density as a fraction of the critical density. Subscripts name the component: ${\Omega }_r$ radiation, ${\Omega }_m$ all matter, ${\Omega }_b$ baryons, ${\Omega }_c$ cold dark matter, ${\Omega }_{\Lambda }$ dark energy, ${\Omega }_k$ the curvature term. Without a further label they mean today's values: ${\Omega }_{\Lambda }\approx 0.685$, ${\Omega }_m\approx 0.315$ (${\Omega }_c\approx 0.265$, ${\Omega }_b\approx 0.049$), ${\Omega }_r\approx 9\times 10^{-5}$.

${\Omega }_i={\rho }_i/{\rho }_{\text{crit}}$, ${\Omega }_r+{\Omega }_m+{\Omega }_{\Lambda }+{\Omega }_k=1$

In the folio: What the Universe is made ofSee also Critical density, Cosmic energy budget

Whether space is closed ($k=+1$, like a sphere), flat ($k=0$) or open ($k=-1$). Its contribution to the expansion is written as a density parameter. The position of the first acoustic peak shows $|{\Omega }_k|<0.002$: space is flat to within the precision of the measurements.

${\Omega }_k=-k{c}^2/(a_0{H}_0{)}^2$

In the folio: What the Universe is made ofSee also Acoustic peaks, FLRW metric

The ratio of a component's pressure to its energy density. It fixes how the density dilutes as space expands, which is why the folio's lines for radiation, matter and dark energy have different slopes.

$w=p/\rho c^2$, $\rho \propto a^{-3(1+w)}$: radiation $w=\frac{1}{3}$, $\rho \propto a^{-4}$; matter $w=0$, $\rho \propto a^{-3}$; $\Lambda$: $w=-1$, constant

In the folio: Expansion: the Friedmann equationsSee also Friedmann equations, Evolving dark energy

The expansion rate as a function of redshift, the last line of the folio's Friedmann box. Each term dilutes at its own rate, so radiation, matter and dark energy dominate in turn.

$\frac{H^2(z)}{H_0^2}={\Omega }_r(1+z{)}^4+{\Omega }_m(1+z{)}^3+{\Omega }_k(1+z{)}^2+{\Omega }_{\Lambda }$

In the folio: Expansion: the Friedmann equationsSee also Density parameter, Matter–radiation equality

A dimensionless measure of how the expansion rate changes. The name dates from when the expansion was assumed to be slowing; today's value is negative, meaning acceleration.

$q=-\ddot{a}a/{\dot{a}}^2$, $q_0\approx {\Omega }_m/2-{\Omega }_{\Lambda }\approx -0.53$

In the folio: Expansion: the Friedmann equationsSee also Dark-energy domination

A constant term in Einstein's equations, equivalent to a vacuum energy with $w=-1$ that does not dilute as space expands. It is the "Λ" of ΛCDM and the simplest explanation of the acceleration. Its measured value is about $10^{120}$ times smaller than naive quantum-field estimates of vacuum energy, the cosmological-constant problem.

$\Lambda =3{\Omega }_{\Lambda }{H}_0^2/c^2\approx 1.1\times 10^{-52}{\text{m}}^{-2}$; energy density $\approx 5\times 10^{-10}{\text{J m}}^{-3}$

In the folio: Expansion: the Friedmann equationsSee also Dark energy, ΛCDM, Evolving dark energy

The stretching of light's wavelength by the expansion during its journey: wavelengths grow in proportion to the scale factor. It is not a Doppler shift, though it reduces to one for nearby objects. Time is stretched by the same factor, so distant supernovae fade $1+z$ times more slowly.

$1+z={\lambda }_{\text{obs}}/{\lambda }_{\text{emit}}=1/a(t_{\text{emit}})$

In the folio: Measuring the cosmosSee also Scale factor, Redshift as a clock

The distance to an object today, along the line of sight, with the expansion taken out. It is the integral of light's progress through the expansion history, and the basic distance from which the observable ones follow.

$d_C={\int }_0^z\frac{cd{z}^{\prime }}{H(z^{\prime })}$

In the folio: Measuring the cosmosSee also Luminosity distance, Angular-diameter distance

The distance that makes the inverse-square law work, defined by flux $F=L/4\pi d_L^2$. In an expanding universe it exceeds the comoving distance, because each photon arrives redshifted and the photons arrive more slowly. Standard candles measure it.

$d_L=(1+z)d_C$ (flat space)

In the folio: Measuring the cosmosSee also Standard candle, Comoving distance

The distance that makes size equal angle times distance. Standard rulers measure it. It reaches a maximum near $z\approx 1.6$ and then falls, so very distant galaxies look larger on the sky than intermediate ones of the same size.

$d_A=d_C/(1+z)$ (flat space); in general $d_L=(1+z{)}^2{d}_A$

In the folio: Measuring the cosmosSee also Standard ruler, Comoving distance

The region from which light has had time to reach us, now about 14.3 Gpc (46 billion light-years) in comoving radius. It is much larger than 13.8 billion light-years because the space light crossed has expanded since. Its edge is the particle horizon.

See also Comoving distance, Photon decoupling

The chain of methods that reaches cosmological distances: geometric parallaxes calibrate Cepheids and the tip of the red giant branch, which calibrate Type Ia supernovae in nearby galaxies, which then reach the Hubble flow. An error in any rung propagates up the ladder.

In the folio: Measuring the cosmosSee also Parallax, Cepheid variable, Tip of the red giant branch, Type Ia supernova

The apparent shift of a nearby star against distant ones as Earth orbits the Sun. It is pure geometry and needs no physics of the star. Gaia's microarcsecond astrometry carries it to several kiloparsecs.

$d[\text{pc}]=1/p[\text{arcsec}]$

In the folio: Measuring the cosmosSee also Parsec, Gaia

An object of known luminosity, whose observed flux then gives its luminosity distance. Cepheids and the tip of the red giant branch are standard candles.

In the folio: Measuring the cosmosSee also Luminosity distance, Standardisable candle, Standard siren

An object whose luminosity varies but can be inferred from something else observed. Type Ia supernovae are the example: brighter explosions fade more slowly (the Phillips relation), so correcting for light-curve width makes them consistent to about 5–7% in distance.

In the folio: Measuring the cosmosSee also Type Ia supernova, Standard candle

An object or pattern of known physical size, whose angular size gives its angular-diameter distance. The baryon acoustic scale is the cosmological standard ruler.

In the folio: Measuring the cosmosSee also Baryon acoustic oscillations, Sound horizon, Angular-diameter distance

A gravitational-wave source whose signal gives its luminosity distance directly, without a ladder. GW170817 gave $H_0\approx 70$ km s⁻¹ Mpc⁻¹, with errors still too large to settle the Hubble tension.

See also GW170817, Luminosity distance

A pulsating supergiant whose period of brightness variation, days to weeks, is tightly related to its luminosity (the Leavitt law, 1912). Hubble used Cepheids to show in 1925 that other galaxies exist; SH0ES uses them to calibrate supernovae.

In the folio: Measuring the cosmosSee also Standard candle, SH0ES, Cosmic distance ladder

The sharp upper limit to the brightness of old, low-mass red giants, set by helium igniting in their cores at a nearly fixed core mass. It makes a standard candle found in any old stellar population, used by CCHP as an alternative to Cepheids.

In the folio: Measuring the cosmosSee also Red giant, CCHP, Cosmic distance ladder

The thermonuclear explosion of a carbon–oxygen white dwarf that has grown to near the Chandrasekhar mass. At peak it shines with a few billion solar luminosities, enough to be seen across billions of light-years. Supernovae of this type revealed the accelerating expansion in 1998. "SNe" is the plural.

In the folio: Measuring the cosmosSee also Standardisable candle, White dwarf, Chandrasekhar limit, Iron-peak elements

Sound waves in the plasma before recombination, driven by the competition between gravity and photon pressure. When the plasma became neutral the waves froze, leaving a slight excess of galaxy pairs separated by the sound horizon, about 147 Mpc. Galaxy surveys such as DESI measure this scale across cosmic time as a standard ruler.

In the folio: Measuring the cosmosSee also Sound horizon, Standard ruler, DESI, Acoustic peaks

The comoving distance a sound wave could travel in the photon–baryon plasma before baryons were released from the photons at $z\approx 1060$ (the drag epoch). It is computed from known physics plus the densities of baryons, dark matter and radiation, which is how CMB and BAO data pin down $H_0$ without a distance ladder.

$r_d={\int }_{z_d}^{\infty }\frac{c_{s}dz}{H(z)}\approx 147\text{Mpc}$, sound speed $c_s\lesssim c/\sqrt{3}$

In the folio: Measuring the cosmosSee also Baryon acoustic oscillations, Hubble tension

The mapping of the three-dimensional positions of millions of galaxies by measuring their redshifts. It is how baryon acoustic oscillations and the growth of structure are measured.

See also DESI, Baryon acoustic oscillations

The thermal radiation released at photon decoupling, 380,000 years after the Big Bang, and stretched about 1100-fold by the expansion since, from a 3000 K glow into microwaves. Discovered in 1965 by Penzias and Wilson. There are about 411 CMB photons in every cubic centimetre of space.

$T_0=2.7255\text{K}$

In the folio: The cosmic microwave backgroundSee also Photon decoupling, Blackbody spectrum, Anisotropy

The Planck spectrum of radiation in thermal equilibrium, fixed entirely by temperature. Expansion preserves its form, lowering only the temperature. Plotted per unit frequency, as in the folio, the CMB peaks at 160 GHz; plotted per unit wavelength it peaks at 1.06 mm, which is not the same point, a classic source of confusion.

$B_{\nu }(T)=\frac{2h{\nu }^3}{c^2}\frac{1}{e^{h\nu /k_{B}T}-1}$

In the folio: The cosmic microwave backgroundSee also Specific intensity, FIRAS

Power per unit area, per unit frequency, per unit solid angle, in W m⁻² Hz⁻¹ sr⁻¹. It is the quantity on the vertical axis of the folio's CMB spectrum; for thermal radiation it equals the Planck function.

In the folio: The cosmic microwave backgroundSee also Blackbody spectrum

The Far-Infrared Absolute Spectrophotometer on COBE, which compared the sky with an on-board blackbody and found the CMB spectrum to be thermal to about 50 ppm. John Mather shared the 2006 Nobel Prize for it.

In the folio: The cosmic microwave backgroundSee also COBE, Blackbody spectrum

The tiny variations in CMB temperature across the sky, about one part in $10^5$ after the dipole is removed. They map density fluctuations at last scattering, the seeds of all later structure, and were first detected by COBE in 1992.

In the folio: The cosmic microwave backgroundSee also CMB dipole, Angular power spectrum, Primordial fluctuations

A 3.4 mK difference between one side of the sky and the other, caused by the Solar System's motion of about 370 km s⁻¹ relative to the CMB rest frame. It is removed before the primordial anisotropies are studied.

In the folio: The cosmic microwave backgroundSee also Anisotropy, Peculiar velocity

The strength of CMB fluctuations as a function of angular scale, from expanding the sky map in spherical harmonics. Multipole $\ell$ corresponds to angular scale $\theta \approx 180^{\circ }/\ell$, and plots usually show ${\mathcal{D}}_{\ell }=\ell (\ell +1)C_{\ell }/2\pi$.

See also Multipole, Acoustic peaks

The spherical-harmonic index labelling angular scale on the sky: small $\ell$ is large angles, $\ell \approx 220$ is about one degree, and Planck measured out to $\ell \approx 2500$, a few arcminutes.

In the folio: The cosmic microwave backgroundSee also Angular power spectrum

Peaks in the angular power spectrum from sound waves caught at maximum compression or rarefaction at last scattering. The first, at $\ell \approx 220$, has the angular size expected of the sound horizon in flat space, which shows $|{\Omega }_k|<0.002$. The relative heights of the peaks measure the baryon density, and the third peak requires dark matter, ${\Omega }_c\approx 5.4{\Omega }_b$.

In the folio: The cosmic microwave backgroundSee also Baryon acoustic oscillations, Curvature, Cold dark matter

The CMB's fluctuations are partly linearly polarised, at about a tenth of the amplitude of the temperature fluctuations, a few microkelvin, because Thomson scattering of light with a quadrupole anisotropy leaves a net polarisation. The pattern splits into E-modes and B-modes.

In the folio: The cosmic microwave backgroundSee also E-modes and B-modes

The two geometric patterns of CMB polarisation, by analogy with electric and magnetic fields: E-modes have no curl, B-modes no divergence. Density fluctuations produce only E-modes, which are measured. Primordial gravitational waves from inflation would add B-modes; these have not been found, though B-modes produced by gravitational lensing of E-modes have.

In the folio: The cosmic microwave backgroundSee also Tensor-to-scalar ratio, Inflation, Gravitational lensing

The power in primordial gravitational waves relative to density fluctuations. Its value would fix the energy scale of inflation. Current CMB polarisation data, chiefly from BICEP/Keck, give $r<0.036$.

$V^{1/4}\approx 1.0\times 10^{16}\text{GeV}(r/0.01{)}^{1/4}$

In the folio: The cosmic microwave backgroundSee also E-modes and B-modes, Inflation, BICEP/Keck

How the amplitude of primordial density fluctuations depends on scale. $n_s=1$ would be exactly scale-invariant (the Harrison–Zel'dovich spectrum); Planck measures $0.965\pm 0.004$, slightly more power on large scales, as simple inflation models predict.

$P(k)\propto k^{n_s-1}$ (dimensionless power), amplitude $A_s\approx 2.1\times 10^{-9}$

In the folio: What the Universe is made ofSee also Primordial fluctuations, Inflation

The initial density ripples, about one part in $10^5$, from which galaxies and clusters grew. Observations show them to be nearly Gaussian, nearly scale-invariant ("seed fluctuations" in the folio) and adiabatic, with all components perturbed together.

In the folio: What the Universe is made ofSee also Scalar spectral index, Inflation, Cosmic web

The number of baryons per CMB photon, about $6.1\times 10^{-10}$. Unchanged since the matter–antimatter asymmetry was set, it is the single parameter that fixes Big Bang nucleosynthesis. Cosmologists more often quote the equivalent ${\Omega }_b{h}^2\approx 0.0224$.

$\eta =n_b/n_{\gamma }\approx 274\times 10^{-10}{\Omega }_b{h}^2$

In the folio: What the Universe is made ofSee also Big Bang nucleosynthesis, Baryogenesis, Baryons

The fraction of CMB photons scattered by free electrons after reionisation, about 0.054. It is one of the six ΛCDM parameters, measured from large-angle polarisation.

See also Reionisation, ΛCDM

The standard model of cosmology: a flat FLRW universe containing a cosmological constant (Λ), cold dark matter (CDM), baryons, photons and neutrinos, with nearly scale-invariant adiabatic initial fluctuations. It fits the CMB, BAO, supernovae, light elements and large-scale structure with six parameters: ${\Omega }_b{h}^2$, ${\Omega }_c{h}^2$, the angular size of the sound horizon ${\theta }_{\ast }$, the optical depth $\tau$, and the fluctuation amplitude $A_s$ and tilt $n_s$.

In the folio: What the Universe is made ofSee also Cosmological constant, Cold dark matter, Planck 2018 parameters

The final cosmological results of the Planck satellite, still the reference parameter set and the source of most numbers in the folio's budget: age $13.80\pm 0.02$ Gyr, $H_0=67.4\pm 0.5$, ${\Omega }_{\Lambda }=0.685$, ${\Omega }_m=0.315$, $n_s=0.965$.

In the folio: What the Universe is made ofSee also Planck (satellite), ΛCDM

Today's energy density by component: dark energy 68.5%, dark matter 26.5%, baryons 4.9%, neutrinos at most about 0.5%, CMB photons about 0.005%. The fractions change with time, since each component dilutes at its own rate.

In the folio: What the Universe is made ofSee also Density parameter, Dark energy, Cold dark matter, Baryons

In cosmology, all ordinary matter: protons and neutrons and, by convention, electrons too, although electrons are leptons. They are about 4.9% of the budget. Only about a tenth of them are in stars; most are diffuse, hot gas around and between galaxies, much of it hard to detect.

In the folio: What the Universe is made ofSee also Baryon-to-photon ratio, Intergalactic medium, Metals

The thin gas between galaxies, with the circumgalactic medium around them. It holds most of the universe's baryons, much of it at $10^5$–$10^7$ K (the warm–hot intergalactic medium), where it is difficult to see in emission or absorption.

In the folio: What the Universe is made ofSee also Baryons, Reionisation

In astronomy, every element heavier than helium. A star's metallicity, the fraction of such elements, records how much earlier generations of stars had enriched its gas; the Sun's is about 1.4% by mass.

See also Stellar populations, Stellar nucleosynthesis

Matter that gravitates but neither emits nor absorbs light, inferred independently from galaxy rotation curves, cluster dynamics, gravitational lensing, the CMB acoustic peaks and the growth of structure. It is about 85% of all matter. Its nature is unknown.

In the folio: Dark matter and the cosmic webSee also Cold dark matter, Rotation curve, Bullet Cluster, WIMP, Axion

Dark matter whose particles moved slowly when structure began to form. "Cold" refers to velocity, not temperature: slow particles let small clumps form first and merge into larger ones. Its density is ${\Omega }_c\approx 0.265$, about 5.4 times that of baryons.

In the folio: Dark matter and the cosmic webSee also Dark matter, Structure formation, ΛCDM

Whatever causes the expansion to accelerate, about 68.5% of today's energy density. A cosmological constant is the simplest possibility; a slowly evolving field (quintessence) is the main alternative, and recent DESI results hint at evolution.

In the folio: What the Universe is made ofSee also Cosmological constant, Evolving dark energy, Dark-energy domination

The relic neutrinos from neutrino decoupling, about 336 per cubic centimetre across all flavours, at 1.95 K. Their contribution to the energy budget depends on the sum of neutrino masses: at least about 0.1% given the minimum masses from oscillations, at most about 0.5% on cosmological bounds. Their effect on early expansion is quoted as $N_{\text{eff}}\approx 3.04$ effective species.

In the folio: What the Universe is made ofSee also Neutrino decoupling, Electron–positron annihilation

A galaxy's orbital speed plotted against distance from its centre. If the visible mass were all there is, speeds beyond the stars would fall as $r^{-1/2}$; observed curves stay flat far beyond the starlight, showing enclosed mass growing with radius. Vera Rubin and Kent Ford made the decisive measurements around 1970.

$v^2=GM(<r)/r$

In the folio: Dark matter and the cosmic webSee also Dark-matter halo, Dark matter

The roughly spherical cloud of dark matter in which each galaxy sits, extending several times beyond its visible edge. The Milky Way's halo has about $10^{12}{M}_{\odot }$, more than ten times the mass of its stars and gas.

In the folio: Dark matter and the cosmic webSee also Rotation curve, Cosmic web

The bending of light by mass, which maps mass whether or not it shines. Strong lensing produces arcs, multiple images and Einstein rings; weak lensing is a statistical distortion of background galaxy shapes by about 1%, measured over millions of galaxies.

deflection $\alpha =4GM/c^{2}b$ for impact parameter $b$

In the folio: Dark matter and the cosmic webSee also Weak lensing, Bullet Cluster

Small, coherent distortions of the shapes of distant galaxies by intervening matter. Surveys such as KiDS, DES and HSC use it to measure how clumpy matter is today, and have tended to find slightly less clustering than the CMB predicts.

In the folio: Cracks in the standard model?See also S₈ tension, Gravitational lensing

A pair of galaxy clusters that passed through each other. Their hot gas, most of the ordinary matter, was slowed and left in the middle, while the lensing mass passed through with the galaxies. The separation shows that most of the mass is collisionless and not ordinary matter, a hard case for modified gravity without dark matter.

In the folio: Dark matter and the cosmic webSee also Dark matter, Gravitational lensing, Galaxy cluster

The largest gravitationally bound structures: hundreds to thousands of galaxies and $10^{14}$–$10^{15}{M}_{\odot }$, mostly dark matter. Most of their ordinary matter is gas at $10^7$–$10^8$ K that glows in X-rays.

See also Coma cluster, Bullet Cluster, Cosmic web

A rich, nearby galaxy cluster about 100 Mpc away. In 1933 Fritz Zwicky found its galaxies moving far too fast to be held by their visible mass, the first evidence for what became dark matter.

In the folio: MilestonesSee also Galaxy cluster, Dark matter

The large-scale pattern of matter: dense nodes where clusters sit, joined by filaments and sheets, around voids tens of megaparsecs across. It grew by gravity from the primordial fluctuations.

In the folio: Dark matter and the cosmic webSee also Structure formation, Primordial fluctuations, Voids

Vast underdense regions of the cosmic web, typically 10–50 Mpc across, containing few galaxies.

In the folio: Dark matter and the cosmic webSee also Cosmic web

The gravitational growth of small primordial overdensities into halos, galaxies and clusters. With cold dark matter it is hierarchical, or bottom-up: small halos collapse first and merge into larger ones.

In the folio: Dark matter and the cosmic webSee also Cold dark matter, Cosmic web, S₈ tension

A weakly interacting massive particle, of roughly GeV to TeV mass. A particle of weak-scale interactions, thermally produced in the early universe, would naturally leave about the observed dark-matter density. Direct-detection experiments have now excluded much of the simplest parameter space.

In the folio: Dark matter and the cosmic webSee also Direct detection, Dark matter

A very light hypothetical particle introduced to explain why the strong interaction conserves CP (the strong-CP problem), and a natural dark-matter candidate at micro- to milli-electronvolt masses. Haloscopes search for it converting into microwave photons in strong magnetic fields.

In the folio: Dark matter and the cosmic webSee also Dark matter

Black holes that might have formed from the collapse of rare, large density fluctuations in the first second, rather than from stars. They remain a dark-matter candidate only in narrow mass ranges, the rest being excluded by lensing, CMB and gravitational-wave limits.

In the folio: Dark matter and the cosmic webSee also Dark matter, Black hole

The search for dark-matter particles scattering off nuclei in deep underground detectors, such as liquid-xenon experiments like LZ. No confirmed signal yet; the most sensitive detectors are approaching the irreducible background from solar and atmospheric neutrinos, the "neutrino fog".

In the folio: Dark matter and the cosmic webSee also WIMP

A mild disagreement, about two to three standard deviations in some analyses, between the clumpiness of matter measured by weak lensing today and that predicted from the CMB in ΛCDM. It is quoted with $S_8={\sigma }_8\sqrt{{\Omega }_m/0.3}$, where ${\sigma }_8\approx 0.81$ is the root-mean-square matter fluctuation in spheres of $8h^{-1}$ Mpc. Some recent surveys find it smaller.

In the folio: Cracks in the standard model?See also Weak lensing, Structure formation, Hubble tension

Stellar luminosity plotted against surface temperature. By a convention from spectral classification, temperature increases to the left. Most stars lie on the main sequence; giants and supergiants lie above it, white dwarfs below.

In the folio: Stars forge the elementsSee also Main sequence, Effective temperature, Spectral type

The temperature of a blackbody that would emit the star's flux per unit area. It sets the star's colour, from about 3000 K (red) to over 30,000 K (blue-white); the Sun's is 5772 K.

$L=4\pi R^2\sigma T_{\text{eff}}^4$

In the folio: Stars forge the elementsSee also Hertzsprung–Russell diagram, Spectral type

The classification of stars by their spectral lines, which in effect orders them by temperature: O hottest, M coolest, each subdivided 0–9. A luminosity class follows: V for main sequence, III for giants, I for supergiants. The Sun is G2V.

See also Effective temperature, Hertzsprung–Russell diagram

The band on the HR diagram of stars fusing hydrogen into helium in their cores, where a star spends about 90% of its life. Its position on the band is set almost entirely by its mass.

In the folio: Stars forge the elementsSee also Mass–luminosity relation, Main-sequence lifetime

On the main sequence, luminosity rises steeply with mass. The exponent varies from about 2.3 for low-mass stars to about 1 for the most massive; 3.5 is the classic average for stars like the Sun.

$L\propto M^{3.5}$

In the folio: Stars forge the elementsSee also Main-sequence lifetime

Fuel grows with mass but luminosity grows much faster, so massive stars burn out first: a $10M_{\odot }$ star lasts about 30 Myr, the Sun about 10 Gyr, and the smallest red dwarfs trillions of years.

$t_{\text{MS}}\approx 10\text{Gyr}(M/M_{\odot }{)}^{-2.5}$

In the folio: Stars forge the elementsSee also Mass–luminosity relation, Red dwarf

A small, cool main-sequence star of about 0.08–0.6 $M_{\odot }$ (spectral type M). The commonest stars, about three-quarters of the total. Their lifetimes far exceed the present age of the universe, so none has yet died.

In the folio: Stars forge the elementsSee also Main-sequence lifetime

A star that has exhausted the hydrogen in its core and swollen to tens or hundreds of solar radii while hydrogen burns in a shell. The Sun will become one in about 5 Gyr. The brightest red giants mark the tip of the red giant branch.

In the folio: Stars forge the elementsSee also Tip of the red giant branch, Asymptotic giant branch

An evolved massive star, with luminosity up to about $10^6{L}_{\odot }$ and, for red supergiants, radii above $1000R_{\odot }$. Betelgeuse is an example. Supergiants end as core-collapse supernovae.

In the folio: Stars forge the elementsSee also Core-collapse supernova

The fusion sequence that powers the Sun, converting four protons into helium-4. About 2% of the energy leaves as neutrinos. Stars above about 1.3 $M_{\odot }$ instead rely mainly on the CNO cycle, in which carbon, nitrogen and oxygen catalyse the same net reaction. Hans Bethe worked out both in 1939.

$4p\to {}^4\text{He}+2e^{+}+2{\nu }_e+26.7\text{MeV}$

In the folio: Stars forge the elementsSee also Stellar nucleosynthesis

The building of elements heavier than helium inside stars and their explosions. The 1957 review by Burbidge, Burbidge, Fowler and Hoyle ("B²FH") set out the processes. The folio's table lists the main sources: low-mass stars for carbon, nitrogen and s-process elements; massive stars and their supernovae for oxygen to calcium; white-dwarf supernovae for iron-peak elements; neutron-star mergers for r-process elements.

In the folio: Stars forge the elementsSee also s-process, r-process, Alpha elements, Iron-peak elements

Slow neutron capture: nuclei absorb neutrons slowly enough that unstable isotopes beta-decay before the next capture, climbing the valley of stability. It runs in asymptotic-giant-branch stars and makes about half of the elements heavier than iron, including barium and lead.

In the folio: Stars forge the elementsSee also Asymptotic giant branch, r-process

Rapid neutron capture: in extremely neutron-rich explosive environments nuclei absorb neutrons faster than they can decay, then decay back to stability, making the heaviest elements, including europium, platinum, gold and uranium. Neutron-star mergers were confirmed as a site by the kilonova of GW170817.

In the folio: Stars forge the elementsSee also Kilonova, Neutron star, s-process

The last fusion stage of low- and intermediate-mass stars, with helium and hydrogen burning in alternating shells around a carbon–oxygen core. These stars shed their envelopes, returning carbon, nitrogen and s-process elements to space, and leave a white dwarf inside a planetary nebula ("dying low-mass stars" in the folio).

In the folio: Stars forge the elementsSee also s-process, White dwarf, Red giant

The death of a star above about 8 $M_{\odot }$: its iron core, which can no longer release energy by fusion, collapses to a neutron star or black hole, and the rebound and neutrino heating blow off the envelope. Nearly all of the $\sim 10^{46}$ J released leaves as neutrinos, as observed from SN 1987A. These supernovae supply most oxygen, magnesium, silicon and calcium.

In the folio: Stars forge the elementsSee also Alpha elements, Neutron star, Type Ia supernova

Elements built up by adding helium nuclei: oxygen, neon, magnesium, silicon, sulphur, calcium. They come mostly from massive stars and core-collapse supernovae, so their abundance relative to iron dates a star's gas.

In the folio: Stars forge the elementsSee also Core-collapse supernova, Iron-peak elements

Chromium to nickel, around the maximum of nuclear binding energy per nucleon. Type Ia supernovae make much of them, about 0.6 $M_{\odot }$ of nickel-56 per explosion, which decays through cobalt-56 to iron-56 and powers the supernova's light.

In the folio: Stars forge the elementsSee also Type Ia supernova, Alpha elements

Generations of stars classified by metal content: Population I, metal-rich and young, like the Sun; Population II, metal-poor and old, in the halo and globular clusters; Population III, the hypothetical metal-free first stars.

See also First stars, Metals

A stellar remnant held up against gravity by quantum degeneracy pressure (white dwarfs, neutron stars) or not held up at all (black holes).

In the folio: Compact objects and gravitational wavesSee also Degeneracy pressure, White dwarf, Neutron star, Black hole

Pressure from the Pauli exclusion principle: fermions packed densely must occupy high-momentum states. It persists at zero temperature, which is why a white dwarf or neutron star needs no fuel to support itself.

In the folio: Compact objects and gravitational wavesSee also White dwarf, Neutron star, Chandrasekhar limit

The remnant core of a low- or intermediate-mass star, supported by electron degeneracy. Typically $0.6M_{\odot }$ in a body the size of Earth, with density near $10^9$ kg m⁻³; it slowly cools over billions of years.

In the folio: Compact objects and gravitational wavesSee also Chandrasekhar limit, Type Ia supernova, Degeneracy pressure

The maximum mass of a white dwarf, about 1.4 $M_{\odot }$, above which electron degeneracy pressure, its electrons now relativistic, cannot resist gravity.

In the folio: Compact objects and gravitational wavesSee also White dwarf, Type Ia supernova

The collapsed core of a massive star, supported by neutron degeneracy and nuclear forces: about 1.2–2.1 $M_{\odot }$ in a sphere about 12 km in radius, at the density of an atomic nucleus. The maximum mass, near 2.2–2.3 $M_{\odot }$ and set by the poorly known nuclear equation of state, is called the TOV limit.

nuclear saturation density $\approx 2.7\times 10^{17}{\text{kg m}}^{-3}$

In the folio: Compact objects and gravitational wavesSee also Pulsar, Kilonova, Degeneracy pressure

A rotating, magnetised neutron star whose radio beams sweep past Earth, giving pulses with clock-like regularity. Discovered by Jocelyn Bell Burnell in 1967. Millisecond pulsars, spun up by companions, rival atomic clocks.

In the folio: MilestonesSee also Neutron star, Pulsar timing array

A gravitational-wave detector the size of the Galaxy: decades of precise timing of dozens of millisecond pulsars, searching for correlated arrival-time shifts caused by passing waves with periods of years. In 2023 several arrays reported evidence for a nanohertz background, most likely from pairs of supermassive black holes.

In the folio: Compact objects and gravitational wavesSee also Pulsar, Gravitational waves

A region of spacetime from which nothing, not even light, escapes, bounded by the event horizon. Stellar-mass black holes form from massive stars; supermassive ones of $10^6$–$10^{10}{M}_{\odot }$ sit at the centres of galaxies.

Schwarzschild radius $r_s=2GM/c^2\approx 2.95\text{km}(M/M_{\odot })$

In the folio: Compact objects and gravitational wavesSee also Black-hole shadow, Gravitational waves, Primordial black holes

The dark central region seen against glowing gas around a black hole, bounded by the orbit of light. For a non-spinning hole it appears about 5.2 Schwarzschild radii across. The Event Horizon Telescope imaged it for M87*, a $6.5\times 10^9{M}_{\odot }$ black hole, in 2019, and for Sgr A* in 2022.

shadow diameter $=2\sqrt{27}GM/c^2\approx 5.2r_s$

In the folio: Compact objects and gravitational wavesSee also M87* and Sgr A*, Event Horizon Telescope

The two black holes imaged so far. M87* is at the centre of the giant elliptical galaxy M87, 16.8 Mpc away. Sagittarius A* is at the centre of the Milky Way, $4\times 10^6{M}_{\odot }$ and 8.2 kpc away. The asterisk is part of the name.

In the folio: Compact objects and gravitational wavesSee also Black-hole shadow

Ripples in spacetime geometry that travel at the speed of light, radiated by accelerating masses with a changing quadrupole moment. Ground-based detectors hear compact binaries at tens to thousands of hertz; pulsar timing arrays listen at nanohertz.

In the folio: Compact objects and gravitational wavesSee also Strain, Inspiral, merger and ringdown, LIGO–Virgo–KAGRA

The fractional change in length a passing wave produces. Detected signals have $h\sim 10^{-21}$, which over LIGO's 4 km arms is a change of a few $10^{-18}$ m, hundreds of times smaller than a proton.

$h\sim \Delta L/L$

In the folio: Compact objects and gravitational wavesSee also Gravitational waves

The three stages of a compact-binary signal. In the inspiral the orbit shrinks as waves carry energy away, so frequency and amplitude rise (a "chirp") at a rate set by the chirp mass. Merger is the plunge and coalescence. In the ringdown the remnant black hole settles, oscillating at frequencies fixed by its mass and spin.

In the folio: Compact objects and gravitational wavesSee also Gravitational waves, GW150914

The first gravitational waves detected, on 14 September 2015: two black holes of 36 and 29 $M_{\odot }$ merged 410 Mpc away, radiating about $3M_{\odot }{c}^2$, some $5\times 10^{47}$ J, in a fraction of a second. Event names give the date as GW + YYMMDD.

In the folio: Compact objects and gravitational wavesSee also Inspiral, merger and ringdown, LIGO–Virgo–KAGRA

The merger of two neutron stars on 17 August 2017, 40 Mpc away. A short gamma-ray burst arrived 1.7 s later, showing that gravitational waves travel at the speed of light to within about one part in $10^{15}$. A kilonova followed. It was the first standard-siren measurement of $H_0$.

In the folio: Compact objects and gravitational wavesSee also Kilonova, Gamma-ray burst, Standard siren, r-process

The optical and infrared glow, lasting days, from radioactive decay of freshly made r-process nuclei thrown out in a neutron-star merger, about a thousand times brighter than a classical nova.

In the folio: Compact objects and gravitational wavesSee also GW170817, r-process

A brief flash of gamma rays from a relativistic jet. Short bursts, under about two seconds, come from compact-object mergers; long ones from the collapse of rapidly rotating massive stars.

In the folio: Compact objects and gravitational wavesSee also GW170817

The network of ground-based laser-interferometer detectors: the two LIGO observatories in the US (4 km arms), Virgo in Italy (3 km) and KAGRA in Japan (underground and cryogenic). Several detectors locate a source on the sky and separate signals from local noise.

In the folio: Compact objects and gravitational wavesSee also Gravitational waves, GWTC-4.0

Version 4.0 of the LVK Gravitational-Wave Transient Catalog (2025), which extends the list of detected compact-binary mergers through the first part of the fourth observing run, to 218 candidates.

In the folio: Compact objects and gravitational wavesSee also LIGO–Virgo–KAGRA

The disagreement between the Hubble constant inferred from the early universe and that measured locally: $67.4\pm 0.5$ from Planck CMB with ΛCDM against $73.0\pm 1.0$ km s⁻¹ Mpc⁻¹ from SH0ES's Cepheid-calibrated supernovae, about five standard deviations apart. CCHP's JWST red-giant distances give $70.4\pm 1.9$, between the two. It is either a sign of physics missing from ΛCDM, such as extra energy before recombination, or an unrecognised systematic error.

In the folio: Cracks in the standard model?See also Hubble constant, SH0ES, CCHP, Sound horizon

"Supernovae, H₀, for the Equation of State", the team led by Adam Riess that calibrates Type Ia supernovae with Cepheids, using Hubble and JWST, and finds $H_0\approx 73$. It reports that JWST confirms its Cepheid distances.

In the folio: Cracks in the standard model?See also Hubble tension, Cepheid variable

The Carnegie–Chicago Hubble Program, led by Wendy Freedman, which calibrates supernovae with the tip of the red giant branch and other old-star methods measured with JWST, and finds $H_0\approx 70$.

In the folio: Cracks in the standard model?See also Hubble tension, Tip of the red giant branch

The possibility that dark energy changes with time, usually tested with $w(a)=w_0+w_a(1-a)$, where Λ is $w_0=-1$, $w_a=0$. DESI's 2025 baryon-acoustic-oscillation results, combined with the CMB and supernovae, prefer evolution over a constant Λ at 2.8 to 4.2 standard deviations, depending on which supernova sample is used.

In the folio: Cracks in the standard model?See also Dark energy, DESI, Equation of state

JWST finds more bright galaxies above $z\approx 10$ than many models predicted. The record is MoM-z14 at $z=14.44$, about 280 Myr after the Big Bang. The tension is with models of how efficiently early galaxies formed stars, not necessarily with ΛCDM itself.

In the folio: Cracks in the standard model?See also JWST, Redshift as a clock

NASA's Cosmic Background Explorer (1989–1993). FIRAS established the CMB blackbody spectrum, and its DMR instrument detected the first anisotropies in 1992, earning Mather and Smoot the 2006 Nobel Prize.

In the folio: MilestonesSee also FIRAS, Anisotropy

The European Space Agency's CMB mission (2009–2013), which mapped the temperature and polarisation of the whole sky to arcminute resolution. Its 2018 results remain the reference ΛCDM parameters. Named after Max Planck, it is unrelated to the Planck era.

In the folio: What the Universe is made ofSee also Planck 2018 parameters, Planck era

A series of CMB polarisation telescopes at the South Pole searching for primordial B-modes. Their 2021 analysis, with Planck data, gives the bound $r<0.036$.

See also Tensor-to-scalar ratio, E-modes and B-modes

The European Space Agency's astrometry mission (2013–2025), which measured positions, parallaxes and motions of nearly two billion stars and anchors the bottom rung of the distance ladder.

In the folio: Measuring the cosmosSee also Parallax, Cosmic distance ladder

The 2.4 m NASA/ESA optical and ultraviolet space telescope launched in 1990. It measured the Cepheids behind the SH0ES distance ladder.

See also SH0ES, JWST

The James Webb Space Telescope, a 6.5 m infrared observatory launched in December 2021, whose first deep fields were released in July 2022. Its infrared reach shows galaxies at $z>10$, and its sharpness separates individual stars for the distance ladder.

In the folio: Cracks in the standard model?See also Early galaxies, Hubble tension

The Dark Energy Spectroscopic Instrument, with 5000 robotically positioned fibres on the 4 m Mayall telescope in Arizona, measuring redshifts of tens of millions of galaxies and quasars to map baryon acoustic oscillations across the last 11 billion years.

In the folio: Cracks in the standard model?See also Baryon acoustic oscillations, Evolving dark energy

A worldwide array of radio dishes combined by very-long-baseline interferometry into an Earth-sized telescope observing at 1.3 mm (230 GHz), reaching about 20 μas resolution, enough to resolve the shadows of M87* and Sgr A*.

In the folio: Compact objects and gravitational wavesSee also Black-hole shadow, Arcsecond