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Cosmic microwave background anisotropies are direction-dependent perturbations of the relic radiation temperature and polarization.

The large-scale structure of the universe is the cosmic distribution of matter on scales where galaxies and halos form a web of clusters, filaments, sheets, and voids.

Field theory in cosmology applies classical and quantum fields to the homogeneous universe and its perturbations.

This is the first-order sector of cosmological perturbation theory.

Linear cosmological perturbation theory expands the metric and matter fields to first order about a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric.

For an adiabatically expanding homogeneous universe, the entropy density satisfiesso the entropy $s{a}^3$ in a comoving volume is constant.

The baryon-to-photon ratio is the number density of baryons divided by the number density of photons. In the present universe it is of order $10^{-9}$.

Big Bang nucleosynthesis formed the light nuclei during the first minutes of cosmic expansion after weak freeze-out and the deuterium bottleneck.

The deceleration parameter is $q=-a\ddot{a}/{\dot{a}}^2$; negative values describe accelerated expansion.

In a curvature-dominated open FLRW regime, the scale factor is approximately linear in cosmic time and $tH$ approaches one.

The age is the proper cosmic time elapsed from the scale-factor singularity $a=0$ to the present epoch.

The age of the universe is the cosmological quantity; an FLRW model computes it by integrating proper cosmic time from its initial scale-factor singularity.

Energy conservation in FLRW gives $\dot{\rho }=-3H(\rho +P)$ when $\rho$ and $P$ are energy density and pressure.

The FLRW metric is the homogeneous and isotropic spacetime metric with scale factor $a(t)$ and constant spatial curvature $k$.

Luminosity distance is defined by $F=L/(4\pi d_L^2)$ and includes geometric dilution, photon redshift, and arrival-rate dilation.

A fluid with $w<-1$ grows in density during expansion and can produce a finite-time Big Rip singularity.

For pressureless subhorizon matter perturbations, a Fourier mode in conformal time obeyswhere $\mathcal{H}=a^{\prime }/a$.

These equations describe the small-amplitude phase of structure formation; nonlinear growth requires a more general treatment.

Cosmic inflation is an early period of accelerated expansion, often modeled by a scalar field whose potential energy dominates its kinetic energy.

A Big Crunch is a future finite-time singularity in which a recollapsing universe reaches vanishing scale factor.

Cosmological radiation has equation of state $P_r={\rho }_r/3$ and density scaling ${\rho }_r\propto a^{-4}$.