The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular diameter distance. [1] The equation is as follows: , where is the redshift, is the luminosity distance and the angular-diameter distance.
When Ivor Etherington introduced this equation in 1933, he mentioned that this equation was proposed by Tolman as a way to test a cosmological model. Ellis proposed a proof of this equation in the context of Riemannian geometry. [2] [1] [3] A quote from Ellis: "The core of the reciprocity theorem is the fact that many geometric properties are invariant when the roles of the source and observer in astronomical observations are transposed". This statement is fundamental in the derivation of the reciprocity theorem.
The Etherington's distance-duality equation has been validated from astronomical observations based on the X-ray surface brightness and the Sunyaev–Zel'dovich effect of galaxy clusters. [4] [5] The reciprocity theorem is considered to be true when photon number is conserved, gravity is described by a metric theory with photons traveling on unique null geodesics. [6] Any violation of the distance duality would be attributed to exotic physics provided that astrophysical effects altering the cosmic distance measurements are well below the statistical errors. For instance, an incorrect modelling of the three-dimensional gas density profile in galaxy clusters may introduce systematic uncertainties in the determination of the cluster angular diameter distance from X-ray and/or SZ observations, thus altering the outcome of the distance-duality test. [7] Similarly, unaccounted extinction from a diffuse dust component in the inter-galactic medium can affect the determination of luminosity distances and cause a violation of the distance-duality relation. [8]
In physical cosmology, the Copernican principle states that humans, on the Earth or in the Solar System, are not privileged observers of the universe, that observations from the Earth are representative of observations from the average position in the universe. Named for Copernican heliocentrism, it is a working assumption that arises from a modified cosmological extension of Copernicus' argument of a moving Earth.
In cosmology, the cosmological constant, alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. He later removed it. Much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy.
Observations 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. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are further away appear dimmer, we can use the observed brightness of these supernovae to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the further an object is from us, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerated rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.
Hubble'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.
The Sunyaev–Zeldovich effect is the spectral distortion of the cosmic microwave background (CMB) through inverse Compton scattering by high-energy electrons in galaxy clusters, in which the low-energy CMB photons receive an average energy boost during collision with the high-energy cluster electrons. Observed distortions of the cosmic microwave background spectrum are used to detect the disturbance of density in the universe. Using the Sunyaev–Zeldovich effect, dense clusters of galaxies have been observed.
The ΛCDM or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda associated with dark energy; second, the postulated cold dark matter ; and third, ordinary matter. It is frequently referred to as the standard modelof Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:
The Arcminute Microkelvin Imager (AMI) consists of a pair of interferometric radio telescopes - the Small and Large Arrays - located at the Mullard Radio Astronomy Observatory near Cambridge. AMI was designed, built and is operated by the Cavendish Astrophysics Group. AMI was designed, primarily, for the study of galaxy clusters by observing secondary anisotropies in the cosmic microwave background (CMB) arising from the Sunyaev–Zel'dovich (SZ) effect. Both arrays are used to observe radiation with frequencies between 12 and 18 GHz, and have very similar system designs. The telescopes are used to observe both previously known galaxy clusters, in an attempt to determine, for example, their masses and temperatures, and to carry out surveys, in order to locate previously undiscovered clusters.
The Very Small Array (VSA) was a 14-element interferometric radio telescope operating between 26 and 36 GHz that is used to study the cosmic microwave background radiation. It was a collaboration between the University of Cambridge, University of Manchester and the Instituto de Astrofisica de Canarias (Tenerife), and was located at the Observatorio del Teide on Tenerife. The array was built at the Mullard Radio Astronomy Observatory by the Cavendish Astrophysics Group and Jodrell Bank Observatory, and was funded by PPARC. The design was strongly based on the Cosmic Anisotropy Telescope.
The South Pole Telescope (SPT) is a 10-metre (390 in) diameter telescope located at the Amundsen–Scott South Pole Station, Antarctica. The telescope is designed for observations in the microwave, millimeter-wave, and submillimeter-wave regions of the electromagnetic spectrum, with the particular design goal of measuring the faint, diffuse emission from the cosmic microwave background (CMB). The first major survey with the SPT—designed to find distant, massive, clusters of galaxies through their interaction with the CMB, with the goal of constraining the dark energy equation of state—was completed in October 2011. In early 2012, a new camera (SPTpol) was installed on the SPT with even greater sensitivity and the capability to measure the polarization of incoming light. This camera operated from 2012–2016 and was used to make unprecedentedly deep high-resolution maps of hundreds of square degrees of the Southern sky. In 2017, the third-generation camera SPT-3G was installed on the telescope, providing nearly an order-of-magnitude increase in mapping speed over SPTpol.
The Atacama Cosmology Telescope (ACT) was a cosmological millimeter-wave telescope located on Cerro Toco in the Atacama Desert in the north of Chile. ACT made high-sensitivity, arcminute resolution, microwave-wavelength surveys of the sky in order to study the cosmic microwave background radiation (CMB), the relic radiation left by the Big Bang process. Located 40 km from San Pedro de Atacama, at an altitude of 5,190 metres (17,030 ft), it was one of the highest ground-based telescopes in the world.
In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the Big Bang model. It uses general relativity to compute the gravitational forces causing small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. It only applies to situations in which the universe is predominantly homogeneous, such as during cosmic inflation and large parts of the Big Bang. The universe is believed to still be homogeneous enough that the theory is a good approximation on the largest scales, but on smaller scales more involved techniques, such as N-body simulations, must be used.
In astronomy, the intracluster medium (ICM) is the superheated plasma that permeates a galaxy cluster. The gas consists mainly of ionized hydrogen and helium and accounts for most of the baryonic material in galaxy clusters. The ICM is heated to temperatures on the order of 10 to 100 megakelvins, emitting strong X-ray radiation.
An inhomogeneous cosmology is a physical cosmological theory which, unlike the currently widely accepted cosmological concordance model, assumes that inhomogeneities in the distribution of matter across the universe affect local gravitational forces enough to skew our view of the Universe. When the universe began, matter was distributed homogeneously, but over billions of years, galaxies, clusters of galaxies, and superclusters have coalesced, and must, according to Einstein's theory of general relativity, warp the space-time around them. While the concordance model acknowledges this fact, it assumes that such inhomogeneities are not sufficient to affect large-scale averages of gravity in our observations. When two separate studies claimed in 1998-1999 that high redshift supernovae were further away than our calculations showed they should be, it was suggested that the expansion of the universe is accelerating, and dark energy, a repulsive energy inherent in space, was proposed to explain the acceleration. Dark energy has since become widely accepted, but it remains unexplained. Accordingly, some scientists continue to work on models that might not require dark energy. Inhomogeneous cosmology falls into this class.
In modern cosmological theory, diffusion damping, also called photon diffusion damping, is a physical process which reduced density inequalities (anisotropies) in the early universe, making the universe itself and the cosmic microwave background radiation (CMB) more uniform. Around 300,000 years after the Big Bang, during the epoch of recombination, diffusing photons travelled from hot regions of space to cold ones, equalising the temperatures of these regions. This effect is responsible, along with baryon acoustic oscillations, the Doppler effect, and the effects of gravity on electromagnetic radiation, for the eventual formation of galaxies and galaxy clusters, these being the dominant large scale structures which are observed in the universe. It is a damping by diffusion, not of diffusion.
In 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. Measurements of the cosmic microwave background (CMB) suggest the universe began in a hot Big Bang, from which general relativity explains its evolution and the subsequent large-scale motion. Without introducing a new form of energy, there was no way to explain how scientists could measure an accelerating universe. Since the 1990s, dark energy has been the most accepted premise to account for the accelerated expansion. As of 2021, there are active areas of cosmology research to understand the fundamental nature of dark energy. Assuming that the lambda-CDM model of cosmology is correct, as of 2013, the best current measurements indicate that dark energy contributes 68% of the total energy in the present-day observable universe. The mass–energy of dark matter and ordinary (baryonic) matter contributes 26% and 5%, respectively, and other components such as neutrinos and photons contribute a very small amount. Dark energy's density is very low: 6×10−10 J/m3 (~7×10−30 g/cm3), much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.
The Yuan-Tseh Lee Array for Microwave Background Anisotropy, also known as the Array for Microwave Background Anisotropy (AMiBA), is a radio telescope designed to observe the cosmic microwave background and the Sunyaev-Zel'dovich effect in clusters of galaxies.
In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy density and theoretical large value of zero-point energy suggested by quantum field theory.
Abell 665 is a galaxy cluster in the Abell catalogue in the constellation Ursa Major. It is also known as the only cluster in his 1989 catalog to receive Abell's highest richness class of 5. This means that it contains at least 300 galaxies in the magnitude range of m3 to m3+2, where m3 is the magnitude of the third-brightest member of the cluster. The clusters in all other richness classes contain less than 300 such galaxies. Abell 665's combination of high brightness and large distance, made it an excellent candidate along with 37 other clusters to help determine the Hubble constant using the Sunyaev–Zel'dovich effect in 2006.
An embedded lens is a gravitational lens that consists of a concentration of mass enclosed by a relative void in the surrounding distribution of matter: both the mass and the presence of a void surrounding it will affect the path of light passing through the vicinity. This is in contrast to the simpler, more familiar gravitational lens effect, in which there is no surrounding void. While any shape and arrangement of increased and decreased mass densities will cause gravitational lensing, an ideal embedded lens would be spherical and have an internal mass density matching that of the surrounding region of space. The gravitational influence of an embedded lens differs from that of a simple gravitational lens: light rays will be bent by different angles and embedded lenses of a cosmologically significant scale would affect the spatial evolution (expansion) of the universe.
In cosmology, the missing baryon problem is an observed discrepancy between the amount of baryonic matter detected from shortly after the Big Bang and from more recent epochs. Observations of the cosmic microwave background and Big Bang nucleosynthesis studies have set constraints on the abundance of baryons in the early universe, finding that baryonic matter accounts for approximately 4.8% of the energy contents of the Universe. At the same time, a census of baryons in the recent observable universe has found that observed baryonic matter accounts for less than half of that amount. This discrepancy is commonly known as the missing baryon problem. The missing baryon problem is different from the dark matter problem, which is non-baryonic in nature.
