The term cosmography has two distinct meanings: traditionally it has been the protoscience of mapping the general features of the cosmos, heaven and Earth; more recently, it has been used to describe the ongoing effort to determine the large-scale features of the observable universe.
The 14th-century work 'Aja'ib al-makhluqat wa-ghara'ib al-mawjudat by Persian physician Zakariya al-Qazwini is considered to be an early work of cosmography. Traditional Hindu, Buddhist and Jain cosmography schematize a universe centered on Mount Meru surrounded by rivers, continents and seas. These cosmographies posit a universe being repeatedly created and destroyed over time cycles of immense lengths.
In 1551, Martín Cortés de Albacar, from Zaragoza, Spain, published Breve compendio de la esfera y del arte de navegar . Translated into English and reprinted several times, the work was of great influence in Britain for many years. He proposed spherical charts and mentioned magnetic deviation and the existence of magnetic poles.
Peter Heylin's 1652 book Cosmographie (enlarged from his Microcosmos of 1621) was one of the earliest attempts to describe the entire world in English, and being the first known description of Australia and among the first of California. The book has 4 sections, examining the geography, politics, and cultures of Europe, Asia, Africa, and America, with an addendum on Terra Incognita , including Australia, and extending to Utopia, Fairyland, and the "Land of Chivalrie".
In 1659, Thomas Porter published a smaller, but extensive Compendious Description of the Whole World, which also included a chronology of world events from Creation forward. These were all part of a major trend in the European Renaissance to explore (and perhaps comprehend) the known world.
In astrophysics, the term "cosmography" is beginning to be used to describe attempts to determine the large-scale matter distribution and kinematics of the observable universe, dependent on the Friedmann–Lemaître–Robertson–Walker metric but independent of the temporal dependence of the scale factor on the matter/energy composition of the Universe.  
In recent decades, an acceleration in the expansion of the Universe has been observed. Several dynamic mechanisms have been proposed to explain this otherwise mysterious phenomenon. These include modified gravity and dark energy.  Many observations focus on the high-redshift region. For example, the supernova in a joint light-curve analysis (JLA) compilation can span the redshift region up to 1.3; the cosmic microwave background (CMB) even can retrospect to the very early universe at z ~ 1100. To legitimate the expansion at high redshift, they introduced an improved redshift parametrization y = z/(1 + z)  cosmography in the y-based expansion is mathematically safe and useful, because of 0 < y < 1, even for the high redshift. Later, some other methods of redshift were also proposed 
The word was also commonly used by Buckminster Fuller in his lectures.
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood.
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or blueshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum.
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.
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe, and should, therefore, produce no observable irregularities in the large-scale structuring over the course of evolution of the matter field that was initially laid down by the Big Bang.
The 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, because the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. 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. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.
In particle physics, the hypothetical dilaton particle is a particle of a scalar field that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears as a radion in Kaluza–Klein theory's compactifications of extra dimensions. In Brans–Dicke theory of gravity, Newton's constant is not presumed to be constant but instead 1/G is replaced by a scalar field and the associated particle is the dilaton.
In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity. The theory was first proposed by Élie Cartan in 1922. Einstein–Cartan theory is the simplest Poincaré gauge theory.
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand, one would like to account for a universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties ; on the other hand, there is the deep question on the origin of the second law of thermodynamics.
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. This expansion involves neither space nor objects in space "moving" in a traditional sense, but rather it is the metric that changes in scale. As the spatial part of the universe's spacetime metric increases in scale, objects become more distant from one another at ever-increasing speeds. To any observer in the universe, it appears that all of space is expanding, and that all but the nearest galaxies recede at speeds that are proportional to their distance from the observer. While objects within space cannot travel faster than light, this limitation does not apply to the effects of changes in the metric itself. Objects that recede beyond the cosmic event horizon will eventually become unobservable, as no new light from them will be capable of overcoming the universe's expansion, limiting the size of our observable universe.
Gravitational-wave astronomy is an emerging branch of observational astronomy which aims to use gravitational waves to collect observational data about objects such as neutron stars and black holes, events such as supernovae, and processes including those of the early universe shortly after the Big Bang.
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 physical cosmology, fractal cosmology is a set of minority cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is a fractal across a wide range of scales. More generally, it relates to the usage or appearance of fractals in the study of the universe and matter. A central issue in this field is the fractal dimension of the universe or of matter distribution within it, when measured at very large or very small scales.
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, 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.
In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the indefinite orthogonal group SO(4,1), that of de Sitter space. In the standard theory of general relativity, de Sitter space is a highly symmetrical special vacuum solution, which requires a cosmological constant or the stress–energy of a constant scalar field to sustain.
In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way that supernovae provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler" for length scale in cosmology. The length of this standard ruler is given by the maximum distance the acoustic waves could travel in the primordial plasma before the plasma cooled to the point where it became neutral atoms, which stopped the expansion of the plasma density waves, "freezing" them into place. The length of this standard ruler can be measured by looking at the large scale structure of matter using astronomical surveys. BAO measurements help cosmologists understand more about the nature of dark energy by constraining cosmological parameters.
Extended theories of gravity are alternative theories of gravity developed from the exact starting points investigated first by Albert Einstein and Hilbert. These are theories describing gravity, which are metric theory, "a linear connection" or related affine theories, or metric-affine gravitation theory. Rather than trying to discover correct calculations for the matter side of the Einstein field equations; which include inflation, dark energy, dark matter, large-scale structure, and possibly quantum gravity; it is proposed, instead, to change the gravitational side of the equation.
Mustapha Ishak-Boushaki is a theoretical physicist, cosmologist and professor at the University of Texas at Dallas. He is known for his contributions to the studies of cosmic acceleration and dark energy, gravitational lensing, and testing alternatives to general relativity; as well as his authorship of Testing General Relativity in Cosmology, a review article published in Living Reviews in Relativity. He was elected in 2021 as Fellow of American Association for the Advancement of Science (AAAS) with the quote: "For distinguished contributions to the field of theoretical cosmology, particularly for testing modifications to general relativity at cosmological scales, and for sustained excellence in teaching and mentoring of students."