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A grand unified theory embeds the strong and electroweak gauge groups in a larger group, for example $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_Y\subset SU(5)$. quarks and leptons can belong to common representations, while heavy extra gauge or scalar bosons connect them. The resulting interactions can violate baryon number, unlike ordinary perturbative Standard Model reactions. Running gauge couplings and proton-decay searches test such ideas; unification is a theoretical possibility, not an established observation.^[ref]

baryogenesis must explain why a nearly matter-antimatter-symmetric early state evolves into a surviving baryon asymmetry. In the usual local CPT-invariant framework, the Sakharov conditions require baryon-number violation, C and CP violation, and departure from thermal equilibrium. baryon conservation would forbid creating a net excess; exact conjugation symmetries would pair baryon-producing processes with equal antibaryon production; equilibrium with no imposed asymmetry would erase a source term through detailed balance.

For heavy particles $X$ and $\bar{X}$, let decay channels carry different baryon numbers. CP-violating interference can make their branching fractions differ, even though CPT symmetry requires equal total widths. Defining the mean baryon number produced per decay as $ϵ$, an out-of-equilibrium abundance can generate $n_B/s$ of order $ϵ$ times its initial number per entropy, reduced by inefficient production and washout. A rough condition is that decays become effective after inverse production has ceased, with the relevant reaction rate compared with the Hubble parameter. Complex couplings alone do not guarantee a nonzero rate asymmetry: a relative absorptive phase is also needed.

Survival matters as much as production. Electroweak sphalerons violate $B+L$ while conserving baryon-minus-lepton number $B-L$, so a minimal GUT-generated asymmetry with $B-L=0$ can be washed out if sphalerons and the other relevant reactions equilibrate. Generating nonzero $B-L$, as in suitable heavy-Majorana-neutrino leptogenesis, can avoid this problem. A viable GUT baryogenesis model must generate an asymmetry and demonstrate that subsequent reactions do not erase it. The Sakharov conditions are necessary ingredients under these assumptions, not a numerical prediction of the observed abundance.

The cosmic microwave background is relic thermal radiation from the hot early universe. Its temperature anisotropy is expanded in spherical harmonics, with angular power spectrum $C_{\ell }^{TT}$. Thomson scattering of a local radiation quadrupole generates linear polarization around last scattering and again during reionization. Polarization maps are decomposed into E-mode polarization and B-mode polarization, giving spectra such as $EE$, $TE$ and $BB$ in addition to temperature information.

Cosmic microwave background acoustic peak positions compare the sound horizon with the angular-diameter distance to last scattering, constraining geometry and expansion history. Relative peak heights constrain baryon loading and matter-radiation equality; the damping tail constrains diffusion and other early-universe physics. The scalar spectral index and primordial scalar amplitude constrain inflationary perturbations. Coherent acoustic structure and temperature-polarization correlations support predominantly adiabatic initial perturbations. Large-angle E-mode polarization measures the reionization optical depth, helping break its degeneracy with the scalar amplitude inferred from small-scale temperature anisotropy.

Under a specified cosmological model, these data constrain ordinary and cold dark matter densities, the Hubble constant, spatial curvature and cosmic age. Complementary distance information helps break the geometrical degeneracy: temperature peaks alone do not uniquely establish a cosmological constant. The Planck 2013 parameter analysis used Planck temperature data and, in important combinations, WMAP low-multipole polarization; it should not be described as a full Planck polarization release.^[ref]

Linear scalar cosmological perturbations generate E-mode polarization but no primordial B-mode polarization in the simplest treatment. tensor cosmological perturbations can generate B-mode polarization, making them a possible probe of inflationary gravitational waves. gravitational lensing converts some E-mode power into B-mode polarization, however, and Galactic dust and synchrotron radiation also contribute polarized foregrounds. Multifrequency observations, foreground modelling, beam calibration and control of temperature-to-polarization leakage are therefore necessary. Polarization does not by itself establish a primordial tensor signal. temperature and polarization jointly test the expansion history and primordial perturbations, while complementary data and foreground control determine how uniquely parameters can be inferred.

Cosmological variables and conventions. The scale factor $R(t)$ describes the relative separation of comoving observers; dots denote derivatives with respect to cosmic time $t$. The Hubble parameter is $H(t)=\dot{R}/R$, usually time dependent; “Hubble constant” conventionally means its present value. Here $\rho$ is mass-equivalent density, so $ϵ=\rho c^2$ is energy density, while $P$ is isotropic pressure. $G$ is the gravitational constant and $c$ the speed of light. The constant $K$ specifies cosmological spatial curvature: with $R$ a length, $K=k{c}^2$ and $k=+1,0,-1$ describe closed, flat and open spatial geometries. Alternative normalizations of $R$ move a constant factor into $K$. In the printed equations $\Lambda$ has units ${\mathrm{s}}^{-2}$: it is $c^2$ times a cosmological constant defined in inverse square metres. This time-unit convention for the cosmological constant prevents a missing factor of $c^2$.

Continuity and the first law. Differentiating the first Friedmann equation with constant $K$ and $\Lambda$, and then eliminating $\ddot{R}/R$ with the second, givesThus, on an expanding or contracting branch,The relation extends continuously to a regular turning point. For a physical volume $V(t)=V_{\ast }{R}^3(t)$ bounded by fixed comoving coordinates, $\dot{V}=3HV$. Multiplication by $c^{2}V$ givesThis adiabatic work in a comoving volume is the first law of thermodynamics for adiabatic evolution with fixed entropy and no additional chemical work. It expresses local energy conservation, including pressure work. It does not assert that $U$ is constant: radiation loses internal energy as it does work; negative pressure makes $U$ grow during expansion. A generic expanding spacetime has no global time-translation symmetry from which a conserved total energy follows.

Constant scalar-field energy density. Setting $\dot{\rho }=0$ in the continuity equation, with $H\ne 0$, givesFor a homogeneous canonical scalar field, in units $c=1$, $ϵ={\dot{\varphi }}^2/2+V(\varphi )$ and $P={\dot{\varphi }}^2/2-V(\varphi )$. A stationary potential-dominated field has precisely this equation of state. A general evolving scalar field need not have $w=-1$; the constant-density assumption is essential.

Expansion at the stipulated Higgs energy density. With zero explicit $\Lambda$ and zero $K$, constant ${ϵ}_H$ givesThe plus sign selects the expanding branch; there is also a contracting solution. The scalar-field energy is already included in $\rho$, so adding it again as an explicit cosmological constant would double count it. Using $1\mathrm{GeV}=1.602176634\times 10^{-10}\mathrm{J}$ gives ${ϵ}_H=2.4033\times 10^{45}\mathrm{J}{\mathrm{m}}^{-3}$, ${\rho }_H=2.6740\times 10^{28}\mathrm{kg}{\mathrm{m}}^{-3}$ and $H_H\simeq 3.87\times 10^9{\mathrm{s}}^{-1}$. ThereforeThis vacuum-dominated doubling time describes accelerated expansion in de Sitter spacetime, with $\ddot{R}/R=H_H^2>0$. The stipulated energy density exceeds the critical density in energy units used in Question 2 by $3\times 10^{54}$, so it cannot persist as the dominant component of the present universe. The calculation exhibits the cosmological constant problem: the absolute gravitational vacuum energy must be enormously smaller than such a particle-physics scale today. It does not establish that the Standard Model Higgs field actually remains constant or supplies a viable inflationary epoch.

The acoustic ruler and accelerated expansion. Before baryon drag becomes ineffective, pressure in the photon-baryon fluid drives acoustic waves around initial linear cosmological density perturbations. Their comoving sound horizon at the baryon drag epoch isAfter decoupling, this preferred separation survives in galaxy clustering as baryon acoustic oscillations: a peak in the two-point correlation function and oscillations in the matter power spectrum. Its value is calibrated by early-universe physics, commonly constrained by the cosmic microwave background. The SDSS luminous-red-galaxy measurement established a peak near $100h^{-1}\mathrm{Mpc}$; its use as a distance indicator depends on the ruler calibration rather than the length of an individual galaxy.^[ref]

For a ruler perpendicular to the line of sight and one parallel to it,where $D_M=(1+z)D_A$ is the transverse comoving distance and $D_A$ the angular diameter distance. These measure $D_M/r_d$ and $H{r}_d$, respectively. Comparing multiple redshifts tests the distance–redshift relation and expansion history. In particular,so sufficiently precise measurements of the shape of $H(z)$ can test $q<0$. In general relativity, accelerated expansion requires a sufficiently negative total $\rho +3P/c^2$; a positive cosmological constant supplies it.

A single acoustic angular scale does not independently determine acceleration, cosmological spatial curvature, the absolute sound horizon and the dark-energy equation of state. One combines redshift coverage with early-universe calibration and independent matter-density or distance information, comparing accelerating and nonaccelerating models. The galaxy selection function and redshift completeness must be modeled with random catalogues, survey covariance estimated with mock catalogues, and redshift-space distortions, galaxy bias and nonlinear broadening controlled. These tests distinguish a cosmological feature from a survey artifact. The evidence is the measured expansion history within an explicit cosmological framework, rather than the existence of an acoustic peak alone.

A galaxy cluster deflects light from background galaxies according to its projected gravitational field. In a thin gravitational lens approximation,The distances are angular-diameter distances; only mass in the appropriate foreground/background geometry lenses the chosen source this way. Near critical curves, strong gravitational lensing produces highly magnified arcs and multiple images of the same source. Farther out, weak gravitational lensing produces small coherent shear distortions, inferred statistically because individual galaxies have unknown intrinsic ellipticities. The measured reduced shear is $g=\gamma /(1-\kappa )$. Transparent lensing obeys surface-brightness conservation in gravitational lensing at fixed source redshift while changing solid angle and integrated flux.

Strong-lensing image positions and source redshifts constrain the central projected mass; weak shear extends the map to larger radii. Multiple source planes help constrain geometry and degeneracies, but the mass-sheet degeneracy illustrates why image shapes alone do not uniquely fix absolute mass. Point-spread-function anisotropy, selection, shape calibration, cluster-member contamination, source redshift errors and unrelated line-of-sight structure require controls. Lensing does not require hydrostatic equilibrium, making it valuable for disturbed clusters, although interpretation still depends on the gravitational model.

An instructive observation is the merging Bullet Cluster: weak-lensing mass concentrations approximately follow the collisionless galaxies while the dominant visible baryonic plasma, traced by X-rays, is displaced. Clowe and collaborators combined ground-based and Hubble images for lensing reconstruction and compared them with the gas distribution, providing evidence for mass beyond the observed baryons.^[ref]

The Friedmann-Lemaître-Robertson-Walker metric describes homogeneous, isotropic spatial slices. Here $t$ is cosmic time, equal to the proper time of a comoving observer; $R(t)$ is the length-valued scale factor; and $\chi ,\theta ,\varphi$ are dimensionless comoving radial, polar and azimuthal coordinates. The speed of light is $c$, andfor positive, zero and negative cosmological spatial curvature. The convention used makes $d{s}^2$ a squared time interval, with signature $(+---)$; multiplying the metric by $c^2$ gives the more usual squared-length convention. At fixed $t$, radial proper length is $R(t)d\chi$, while a sphere has area $4\pi R^2(t)S^2(\chi )$.

luminosity distance is defined by $F=L/(4\pi d_L^2)$ for bolometric radiative flux $F$ and intrinsic luminosity $L$. Radial null propagation gives $d\chi =\pm cdt/R(t)$. Applying the same path integral to two successive wave crests gives $\Delta t_0/R_0=\Delta t_e/R_e$, hence $1+z=R_0/R_e$. Each photon loses an energy factor $1+z$, and their arrival rate loses another. For transparent propagation and isotropic emission,The two redshift factors have distinct physical origins; geometrical dilution alone is insufficient.

With $H=\dot{R}/R$, differentiating $1+z=R_0/R$ yields $dt/dz=-[(1+z)H(z){]}^{-1}$. Therefore the radial comoving coordinate isThis is independent of any particular matter model; the transverse comoving distance is $R_{0}S(\chi )$, which equals $R_0\chi$ only for flat space.

For pressureless matter, the continuity equation ${\dot{\rho }}_m+3H{\rho }_m=0$ integrates to ${\rho }_m={\rho }_{m0}(R_0/R{)}^3={\rho }_{m0}(1+z{)}^3$. The cosmological constant is kept separately from this matter density. In the flat Friedmann equation, defineThe flat dust-vacuum Hubble parameter is thereforeIn the equation's convention ${\rho }_m$ is mass-equivalent energy density and $\Lambda$ has units ${\mathrm{s}}^{-2}$; the geometrical cosmological constant convention instead writes $c^2{\Lambda }_{\mathrm{geom}}$. The model contains dust and vacuum energy with negligible radiation over the relevant late epochs: “matter-dominated” here does not require matter to exceed vacuum energy today.

The cosmic microwave background supplies a standard ruler through its acoustic scale: the angular positions of the Cosmic microwave background acoustic peaks constrain cosmological spatial curvature, while their relative heights constrain matter and baryon densities. Together with independent distance information, these favour a nearly flat Lambda-CDM model containing substantial cold dark matter and vacuum energy. The cosmic microwave background alone has a geometrical degeneracy between parameters affecting distance to last scattering; its analysis also includes early radiation, which the late-time formula above omits. The nine-year WMAP results were already available as a December 2012 preprint.^[ref]

A standardized Type Ia supernova at appreciable redshift is fainter, hence farther in luminosity distance, than in a matter-only Einstein-de Sitter universe with the same local expansion scale. Fitting the supernova Hubble diagram supports late acceleration; in flat dust plus vacuum, $q_0={\Omega }_{m0}/2-{\Omega }_{\Lambda 0}$ is negative for ${\Omega }_{\Lambda 0}>1/3$. Light-curve and colour corrections, extinction, calibration, selection bias and possible population evolution must be controlled. The supernova evidence and cosmic microwave background constraints are complementary; together they favour this model without proving that every alternative dark-energy model is impossible.^[ref][ref]

For the final comparison, assume $z>0$, a common $H_0$ and $0<{\Omega }_{\Lambda 0}<1$ in model (a). ThenThus $H_c<H_a<H_b$ and the integrands obey $1/H_b<1/H_a<1/H_c$. Because all three models are flat, compare the normalization-independent distance $R_0\chi =c\int d{z}^{\prime }/H(z^{\prime })$, rather than separately normalized coordinates. The luminosity-distance ordering of flat dust-vacuum universes is $d_{L,b}<d_{L,a}<d_{L,c}$, henceModel (b) gives the largest received flux, model (c) the smallest. Equalities replace the strict ordering at the endpoint values of the vacuum fraction; all have the same leading local Hubble law as $z\to 0$.

A galaxy cluster deflects background light through its projected gravitational field. In the thin-lens approximation for gravitational lensing, $\mathbf{\beta }=\mathbf{\theta }-\mathbf{\alpha }(\mathbf{\theta })$ maps image to source angle. Its surface mass density enters throughHere $\mu$ is signed lensing magnification; observed brightness uses $|\mu |$. The $D$'s are angular diameter distances to lens, source and between them; ${\gamma }_s$ denotes lensing shear, not a Lorentz factor. strong gravitational lensing creates arcs and multiple images near critical curves. For an axisymmetric lens, a tangential Einstein ring satisfies mean enclosed convergence one, givingThis is projected enclosed mass, not a general three-dimensional mass profile inferred from a single arc.

weak gravitational lensing uses coherent distortions of many background galaxies. Their intrinsic orientations average approximately to zero, allowing an estimate of reduced shear $g={\gamma }_s/(1-\kappa )$ and a projected mass map. The method traces all gravitating material without assuming hydrostatic equilibrium, which is valuable in merging clusters. Accurate work requires correction of the point spread function, calibrated shape measurement, source redshifts, foreground-member rejection and selection effects. Intrinsic shape noise, unrelated line-of-sight structures and lens-model degeneracies remain. The mass-sheet degeneracy leaves reduced shear unchanged under $\kappa \mapsto \lambda \kappa +(1-\lambda )$ and ${\gamma }_s\mapsto \lambda {\gamma }_s$, so absolute mass normalization needs additional information.

In the Bullet Cluster, weak gravitational lensing places the main projected mass peaks near the collisionless galaxies, displaced from the X-ray-emitting gas that contains most observed baryon mass. Comparing the lensing, optical and X-ray maps supports a dominant weakly collisional dark component under the usual gravity model; lensing alone does not identify its particle species. Cluster lensing measures projected gravitational mass independently of gas temperature or dynamical equilibrium.^[ref]

Write the dimensionless scale factor as $a=R/R_0$ and the density contrast as $\delta =(\rho -\bar{\rho })/\bar{\rho }$. Gravity amplifies overdensities while expansion and pressure oppose growth. In a sub-Hubble Newtonian single-fluid approximation, a comoving Fourier mode obeysFor pressureless matter in an Einstein-de Sitter background, the growing solution is $\delta \propto t^{2/3}\propto a$ and the decaying solution is $t^{-1}$. Jeans support suppresses growth when the pressure term dominates. The equation is not a substitute for relativistic perturbation theory on horizon-sized scales.

cold dark matter clusters without baryonic pressure support. Sub-horizon growth is much weaker during radiation domination, and baryons are initially tied to the photon fluid, producing acoustic oscillations rather than unrestricted collapse. Horizon entry, radiation-matter equality, acoustic evolution and diffusion therefore give a scale-dependent transfer function. The primordial curvature spectrum and the later matter-density spectrum are not the same function: evolution and the gravitational constraints relate them. Late dark-energy domination reduces the growth rate.

When $|\delta |$ approaches unity, linear theory fails. Collapse, virialization, mergers and tidal interactions form a hierarchy of haloes. Gas must cool and lose angular momentum to make dense stellar systems; feedback then changes its supply and distribution. Simulations combine collisionless gravitational dynamics with increasingly complex gas physics rather than extending the linear growing mode indefinitely. Galaxy clustering measures biased tracers of matter; gravitational lensing and CMB constraints provide complementary tests. Approximately adiabatic, nearly scale-invariant initial perturbations explain the coherent acoustic pattern and supply seeds for this later growth.^[ref]

The cosmic microwave background has an almost perfect blackbody spectrum at about $2.725\mathrm{K}$. This is strong evidence for an earlier hot, dense phase in which radiation thermalized, followed by expansion that redshifted the photon spectrum while preserving its Planck form. COBE FIRAS compared the sky with a precision reference blackbody; instrument temperature, gain, foregrounds and calibrator emissivity were crucial controls. Agreement with a blackbody constrains substantial late energy injection or photon-production distortions.^[ref]

After subtracting the dominant dipole associated mainly with observer motion, anisotropies at the level of roughly $10^{-5}$ reveal primordial structure. COBE DMR established large-angular-scale anisotropy; multifrequency measurements and independent maps were needed to distinguish it from Galactic emission and instrumental artifacts.^[ref] Approximate isotropy supports a homogeneous background model under the usual cosmological assumptions, but isotropy at one observing position is not alone a proof of spatial homogeneity everywhere.

The temperature CMB angular power spectrum has multiple acoustic peaks. Their coherent pattern follows oscillations in the pre-recombination photon-baryon fluid. Peak positions compare the sound horizon with angular diameter distance and hence constrain geometry together with expansion parameters. Relative peak heights test baryon inertia, matter–radiation equality and gravitational-potential evolution, motivating both baryonic and nonbaryonic matter. Cosmic microwave background diffusion damping suppresses small-scale power. Cosmic microwave background polarization and temperature–polarization correlations provide further tests of scattering, acoustic phase and reionization; gravitational lensing remaps the observed pattern and probes intervening structure.

By the time of this examination, the Planck 2013 temperature and lensing analysis supported a spatially flat six-parameter model with cold dark matter and a cosmological constant. This is a joint fit within an explicit model, not an inference that each peak uniquely measures one parameter.^[ref] Foreground separation requires frequency coverage, sky masks, beam and noise characterization, and consistency across instruments. The primary microwave background has geometric and other parameter degeneracies, so acoustic-ruler, supernova and structure observations are valuable complements. The spectrum establishes a thermal hot-universe history; anisotropy and polarization constrain its geometry, contents and primordial perturbations. None of these observations by itself demonstrates a unique cosmic inflation mechanism.

A baryon with constituent content four quarks and one antiquark, whose net baryon number is one. Such content admits more flavour representations than three quarks alone. A representation in the tensor product is not evidence by itself of a bound state.

Physical cosmology connects the universe's history to the measurable behaviour of its contents. The Friedmann equations describe cosmic expansion; atomic physics, radiation pressure and gravity determine what that expanding universe looks like. A particularly revealing example is the route from cosmological recombination through the photon-baryon fluid to the Cosmic microwave background acoustic peaks. The universe supplies the initial conditions and the laboratory; the prediction must still pass through a model of the telescope before it can be compared with observations.

The practical reward is that one sky contains several different tests. The Cosmic microwave background power spectrum carries information about the sound horizon, the cosmological baryon density and cosmic geometry. These are related quantities with different observational signatures. Angular sound-horizon degeneracy explains why measuring a characteristic angle alone cannot count the universe's baryons.

A black hole formed in the early universe rather than as the endpoint of a star. It is not subject to the ordinary stellar-remnant baryon budget in the same way as a black hole formed from a baryonic progenitor. Formation scenarios and observational constraints depend strongly on its mass.

Ordinary baryons have three valence quarks, and ordinary mesons have a quark and an antiquark. Additive quantum numbers such as electric charge, baryon number and strangeness are sums of constituent values. This valence description organizes flavor symmetry multiplets while allowing sea constituents and gluons.

The quark model makes a large catalogue manageable: the same few quark flavors generate many different hadrons. It predicts relations between electric charge, strangeness and isospin, rather than assigning these independently to each new particle. It is especially useful for asking which combinations are possible and which additional measurements could distinguish them. A constituent list alone does not determine a mass, a decay rate or whether a proposed combination forms a bound state.

For a three-light-flavor example, take up quarks, down quarks and strange quarks with the following additive quantum numbers. Here $Q$ denotes electric charge in units of the positive elementary charge $e$, $B$ is baryon number, $S$ is strangeness, $I_3$ is the third component of isospin, and $Y=B+S$ is flavor hypercharge. An antiquark reverses all five displayed values. These are flavor coordinates, not spatial coordinates or electroweak hypercharge.

Adding these columns immediately explains familiar hadrons. A proton with valence quarks $uud$ has $Q=2/3+2/3-1/3=1$ and $B=1$; a neutron with $udd$ has $Q=0$ and $B=1$. A positive kaon with $u\bar{s}$ has $Q=2/3+1/3=1$, $B=0$ and $S=+1$. Thus the same constituent rules describe both baryons and mesons.

Two hadrons can have identical additive labels while differing in their internal state. The Lambda baryon and neutral Sigma baryon both have valence content $uds$, yet their total isospin differs. Likewise, the neutral pion flavor direction $(u\bar{u}-d\bar{d})/\sqrt{2}$ and the Eta octet state $(u\bar{u}+d\bar{d}-2s\bar{s})/\sqrt{6}$ both have $Q=Y=0$, but their inner product vanishes. Expanding that inner product gives $(1-1+0)/\sqrt{12}=0$. Constituent counting must therefore be supplemented by quantum superposition and the symmetry of the state.

For hydrogen ionization fraction $X_e$ of order one, the hydrogen-only Saha equation gives $1\sim n_b(2\pi /(m_{e}T){)}^{3/2}{e}^{B/T}$. The baryon-to-photon ratio and photon number density imply $n_b\sim \eta T^3$. Therefore $1\sim \eta (T/m_e{)}^{3/2}{e}^{B/T}$ and the displayed logarithmic balance follows. A small $\eta$ supplies many ionizing photons per baryon, so neutral hydrogen forms at a temperature much smaller than its Hydrogen binding energy. The numerical temperature depends on the ionization-fraction convention and on whether equilibrium remains valid.

Strong and electromagnetic interactions conserve net strangeness; a decay changing it requires the weak interaction. A strange baryon decay into a less-strange baryon and a pion is an example. The weak interaction does not impose a parity selection rule, so a final orbital partial wave cannot by itself determine the parent's parity. Qualitative lifetime classes do not provide an exact lifetime without an amplitude calculation or measurement.

For a stable nonrelativistic thermal relic, compare energy densities rather than number densities. If $m_Y=m_{\mathrm{nr}}/x^3$ and $Y_Y=C{x}^{3/2}{e}^{-x}$, its density relative to baryons is $(C{m}_{\mathrm{nr}}/m_B{Y}_B)x^{-3/2}{e}^{-x}$. Requiring this ratio below an allowed dark-matter-to-baryon ratio $R$ means $x+\frac{3}{2}\log x\ge \log [C{m}_{\mathrm{nr}}/(R{m}_B{Y}_B)]$. With fixed rate parameters this excludes the weakly interacting large-mass branch, while the sufficiently Boltzmann-suppressed smaller-mass branch can satisfy the density bound. Decay or a nonthermal initial abundance requires a different constraint.

A constituent used to specify the net quark flavor content of a hadron. The quark model uses three valence quarks for an ordinary baryon and a quark-antiquark pair for an ordinary meson; this does not exclude additional sea pairs and gluons in the full state.