Comoving and proper distancesIn standard cosmology, comoving distance and proper distance (or physical distance) are two closely related distance measures used by cosmologists to define distances between objects. Comoving distance factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space (though this may change due to other, local factors, such as the motion of a galaxy within a cluster).
Mathematics of general relativityWhen studying and formulating Albert Einstein's theory of general relativity, various mathematical structures and techniques are utilized. The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics of general relativity. Note: General relativity articles using tensors will use the abstract index notation. The principle of general covariance was one of the central principles in the development of general relativity.
Wilkinson Microwave Anisotropy ProbeThe Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic microwave background (CMB) – the radiant heat remaining from the Big Bang. Headed by Professor Charles L. Bennett of Johns Hopkins University, the mission was developed in a joint partnership between the NASA Goddard Space Flight Center and Princeton University.
Dark energyIn physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the universe does not expand at a constant rate; rather, the universe's expansion is accelerating. Understanding the universe's evolution requires knowledge of its starting conditions and composition. Before these observations, scientists thought that all forms of matter and energy in the universe would only cause the expansion to slow down over time.
Observable universeThe observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from New Horizons.
Cosmological horizonA cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Cosmological horizons set the size and scale of the observable universe. This article explains a number of these horizons. Particle horizon The particle horizon (also called the cosmological horizon, the comoving horizon, or the cosmic light horizon) is the maximum distance from which light from particles could have traveled to the observer in the age of the universe.
Static universeIn cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have so-called spatial curvature; that is to say that it is 'flat' or Euclidean. A static infinite universe was first proposed by English astronomer Thomas Digges (1546–1595).
Particle horizonThe particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from particles could have traveled to the observer in the age of the universe. Much like the concept of a terrestrial horizon, it represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present epoch defines the size of the observable universe.
Recessional velocityRecessional velocity is the rate at which an extragalactic astronomical object recedes (becomes more distant) from an observer as a result of the expansion of the universe. It can be measured by observing the wavelength shifts of spectral lines emitted by the object, known as the object's cosmological redshift. Hubble's law is the relationship between a galaxy's distance and its recessional velocity, which is approximately linear for galaxies at distances of up to a few hundred megaparsecs.
Standard rulerA standard ruler is an astronomical object for which the actual physical size is known. By measuring its angular size in the sky, one can use simple trigonometry to determine its distance from Earth. In simple terms, this is because objects of a fixed size appear smaller the further away they are. Measuring distances is of great importance in cosmology, as the relationship between the distance and redshift of an object can be used to measure the expansion rate and geometry of the Universe.
Hubble's lawHubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum. Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model.
Jeans instabilityIn stellar physics, the Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation, named after James Jeans. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter. For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to where is the enclosed mass, is the pressure, is the density of the gas (at radius ), is the gravitational constant, and is the radius.
Gravitational collapseGravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formation in the universe. Over time an initial, relatively smooth distribution of matter will collapse to form pockets of higher density, typically creating a hierarchy of condensed structures such as clusters of galaxies, stellar groups, stars and planets.
InflatonThe inflaton field is a hypothetical scalar field which is conjectured to have driven cosmic inflation in the very early universe. The field, originally postulated by Alan Guth, provides a mechanism by which a period of rapid expansion from 10−35 to 10−34 seconds after the initial expansion can be generated, forming a universe consistent with observed spatial isotropy and homogeneity.
Scale factor (cosmology)The relative expansion of the universe is parametrized by a dimensionless scale factor . Also known as the cosmic scale factor or sometimes the Robertson Walker scale factor, this is a key parameter of the Friedmann equations. In the early stages of the Big Bang, most of the energy was in the form of radiation, and that radiation was the dominant influence on the expansion of the universe. Later, with cooling from the expansion the roles of matter and radiation changed and the universe entered a matter-dominated era.
Shape of the universeThe shape of the universe, in physical cosmology, is the local and global geometry of the universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as a continuous object. The spatial curvature is described by general relativity, which describes how spacetime is curved due to the effect of gravity.
Big CrunchThe Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potentially followed by a reformation of the universe starting with another Big Bang. The vast majority of evidence indicates that this hypothesis is not correct. Instead, astronomical observations show that the expansion of the universe is accelerating rather than being slowed by gravity, suggesting that the universe is far more likely to end in heat death.
Age of the universeIn physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe: a measurement based on direct observations of an early state of the universe, which indicate an age of 13.787 billion years as interpreted with the Lambda-CDM concordance model as of 2021; and a measurement based on the observations of the local, modern universe, which suggest a younger age.
Inflationary epochNOTOC In physical cosmology, the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion. This rapid expansion increased the linear dimensions of the early universe by a factor of at least 1026 (and possibly a much larger factor), and so increased its volume by a factor of at least 1078. Expansion by a factor of 1026 is equivalent to expanding an object 1 nanometer (10−9 m, about half the width of a molecule of DNA) in length to one approximately 10.
Accelerating expansion of the universeObservations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered during 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration.
