Cosmological models
Model of the Universe based on general relativity
With the assumption of the cosmological principle that the Universe is homogeneous and isotropic everywhere, a specific solution of the field equations that describes the Universe is the metric tensor called the Friedmann–Lemaître–Robertson–Walker metric,
The solutions for R(t) depend on k and Λ, but some qualitative features of such solutions are general. First and most importantly, the length scale R of the Universe can remain constant only if the Universe is perfectly isotropic with positive curvature (k=1) and has one precise value of density everywhere, as first noted by Albert Einstein. However, this equilibrium is unstable: because the Universe is known to be inhomogeneous on smaller scales, R must change over time. When R changes, all the spatial distances in the Universe change in tandem; there is an overall expansion or contraction of space itself. This accounts for the observation that galaxies appear to be flying apart; the space between them is stretching. The stretching of space also accounts for the apparent paradox that two galaxies can be 40 billion light-years apart, although they started from the same point 13.8 billion years ago and never moved faster than the speed of light.
Second, all solutions suggest that there was a gravitational singularity in the past, when R went to zero and matter and energy were infinitely dense. It may seem that this conclusion is uncertain because it is based on the questionable assumptions of perfect homogeneity and isotropy (the cosmological principle) and that only the gravitational interaction is significant. However, the Penrose–Hawking singularity theorems show that a singularity should exist for very general conditions. Hence, according to Einstein's field equations, R grew rapidly from an unimaginably hot, dense state that existed immediately following this singularity (when R had a small, finite value); this is the essence of the Big Bang model of the Universe. Understanding the singularity of the Big Bang likely requires a quantum theory of gravity, which has not yet been formulated.
Third, the curvature index k determines the sign of the mean spatial curvature of spacetime averaged over sufficiently large length scales (greater than about a billion light-years). If k=1, the curvature is positive and the Universe has a finite volume. A Universe with positive curvature is often visualized as a three-dimensional sphere embedded in a four-dimensional space. Conversely, if k is zero or negative, the Universe has an infinite volume. It may seem counter-intuitive that an infinite and yet infinitely dense Universe could be created in a single instant at the Big Bang when R=0, but exactly that is predicted mathematically when k does not equal 1. By analogy, an infinite plane has zero curvature but infinite area, whereas an infinite cylinder is finite in one direction and a torus is finite in both. A toroidal Universe could behave like a normal Universe with periodic boundary conditions.
The ultimate fate of the Universe is still unknown, because it depends critically on the curvature index k and the cosmological constant Λ. If the Universe were sufficiently dense, k would equal +1, meaning that its average curvature throughout is positive and the Universe will eventually recollapse in a Big Crunch, possibly starting a new Universe in a Big Bounce. Conversely, if the Universe were insufficiently dense, k would equal 0 or −1 and the Universe would expand forever, cooling off and eventually reaching the Big Freeze and the heat death of the Universe. Modern data suggests that the rate of expansion of the Universe is not decreasing, as originally expected, but increasing; if this continues indefinitely, the Universe may eventually reach a Big Rip. Observationally, the Universe appears to be flat (k = 0), with an overall density that is very close to the critical value between recollapse and eternal expansion.
Multiverse hypothesis
Some speculative theories have proposed that our Universe is but one of a set of disconnected universes, collectively denoted as the multiverse, challenging or enhancing more limited definitions of the Universe. Scientific multiverse models are distinct from concepts such as alternate planes of consciousness and simulated reality.Max Tegmark developed a four-part classification scheme for the different types of multiverses that scientists have suggested in response to various Physics problems. An example of such multiverses is the one resulting from the chaotic inflation model of the early universe. Another is the multiverse resulting from the many-worlds interpretation of quantum mechanics. In this interpretation, parallel worlds are generated in a manner similar to quantum superposition and decoherence, with all states of the wave functions being realized in separate worlds. Effectively, in the many-worlds interpretation the multiverse evolves as a universal wavefunction. If the Big Bang that created our multiverse created an ensemble of multiverses, the wave function of the ensemble would be entangled in this sense.
The least controversial category of multiverse in Tegmark's scheme is Level I. The multiverses of this level are composed by distant spacetime events "in our own universe". If space is infinite, or sufficiently large and uniform, identical instances of the history of Earth's entire Hubble volume occur every so often, simply by chance. Tegmark calculated that our nearest so-called doppelgänger, is 1010115 meters away from us (a double exponential function larger than a googolplex). In principle, it would be impossible to scientifically verify the existence of an identical Hubble volume. However, this existence does follow as a fairly straightforward consequence from otherwise unrelated scientific observations and theories.
It is possible to conceive of disconnected spacetimes, each existing but unable to interact with one another. An easily visualized metaphor of this concept is a group of separate soap bubbles, in which observers living on one soap bubble cannot interact with those on other soap bubbles, even in principle. According to one common terminology, each "soap bubble" of spacetime is denoted as a universe, whereas our particular spacetime is denoted as the Universe, just as we call our moon the Moon. The entire collection of these separate spacetimes is denoted as the multiverse. With this terminology, different Universes are not causally connected to each other. In principle, the other unconnected Universes may have different dimensionalities and topologies of spacetime, different forms of matter and energy, and different physical laws and physical constants, although such possibilities are purely speculative. Others consider each of several bubbles created as part of chaotic inflation to be separate Universes, though in this model these universes all share a causal origin.
Historical conceptions
Historically, there have been many ideas of the cosmos (cosmologies) and its origin (cosmogonies). Theories of an impersonal Universe governed by physical laws were first proposed by the Greeks and Indians. Ancient Chinese philosophy encompassed the notion of the Universe including both all of space and all of time. Over the centuries, improvements in astronomical observations and theories of motion and gravitation led to ever more accurate descriptions of the Universe. The modern era of cosmology began with Albert Einstein's 1915 general theory of relativity, which made it possible to quantitatively predict the origin, evolution, and conclusion of the Universe as a whole. Most modern, accepted theories of cosmology are based on general relativity and, more specifically, the predicted Big Bang.Mythologies
Main articles: Creation myth, Cosmogony, and Religious cosmologyMany cultures have stories describing the origin of the world and universe. Cultures generally regard these stories as having some truth. There are however many differing beliefs in how these stories apply amongst those believing in a supernatural origin, ranging from a god directly creating the Universe as it is now to a god just setting the "wheels in motion" (for example via mechanisms such as the big bang and evolution).
Ethnologists and anthropologists who study myths have developed various classification schemes for the various themes that appear in creation stories. For example, in one type of story, the world is born from a world egg; such stories include the Finnish epic poem Kalevala, the Chinese story of Pangu or the Indian Brahmanda Purana. In related stories, the Universe is created by a single entity emanating or producing something by him- or herself, as in the Tibetan Buddhism concept of Adi-Buddha, the ancient Greek story of Gaia (Mother Earth), the Aztec goddess Coatlicue myth, the ancient Egyptian god Atum story, and the Judeo-Christian Genesis creation narrative in which the Abrahamic God created the Universe. In another type of story, the Universe is created from the union of male and female deities, as in the Maori story of Rangi and Papa. In other stories, the Universe is created by crafting it from pre-existing materials, such as the corpse of a dead god — as from Tiamat in the Babylonian epic Enuma Elish or from the giant Ymir in Norse mythology – or from chaotic materials, as in Izanagi and Izanami in Japanese mythology. In other stories, the Universe emanates from fundamental principles, such as Brahman and Prakrti, the creation myth of the Serers, or the yin and yang of the Tao.
Philosophical models
The pre-Socratic Greek philosophers and Indian philosophers developed some of the earliest philosophical concepts of the Universe. The earliest Greek philosophers noted that appearances can be deceiving, and sought to understand the underlying reality behind the appearances. In particular, they noted the ability of matter to change forms (e.g., ice to water to steam) and several philosophers proposed that all the physical materials in the world are different forms of a single primordial material, or arche. The first to do so was Thales, who proposed this material to be water. Thales' student, Anaximander, proposed that everything came from the limitless apeiron. Anaximenes proposed the primordial material to be air on account of its perceived attractive and repulsive qualities that cause the arche to condense or dissociate into different forms. Anaxagoras proposed the principle of Nous (Mind), while Heraclitus proposed fire (and spoke of logos). Empedocles proposed the elements to be earth, water, air and fire. His four-element model became very popular. Like Pythagoras, Plato believed that all things were composed of number, with Empedocles' elements taking the form of the Platonic solids. Democritus, and later philosophers—most notably Leucippus—proposed that the Universe is composed of indivisible atoms moving through a void (vacuum), although Aristotle did not believe that to be feasible because air, like water, offers resistance to motion. Air will immediately rush in to fill a void, and moreover, without resistance, it would do so indefinitely fast.Although Heraclitus argued for eternal change, his contemporary Parmenides made the radical suggestion that all change is an illusion, that the true underlying reality is eternally unchanging and of a single nature. Parmenides denoted this reality as τὸ ἐν (The One). Parmenides' idea seemed implausible to many Greeks, but his student Zeno of Elea challenged them with several famous paradoxes. Aristotle responded to these paradoxes by developing the notion of a potential countable infinity, as well as the infinitely divisible continuum. Unlike the eternal and unchanging cycles of time, he believed that the world is bounded by the celestial spheres and that cumulative stellar magnitude is only finitely multiplicative.
The Indian philosopher Kanada, founder of the Vaisheshika school, developed a notion of atomism and proposed that light and heat were varieties of the same substance. In the 5th century AD, the Buddhist atomist philosopher Dignāga proposed atoms to be point-sized, durationless, and made of energy. They denied the existence of substantial matter and proposed that movement consisted of momentary flashes of a stream of energy.
The notion of temporal finitism was inspired by the doctrine of creation shared by the three Abrahamic religions: Judaism, Christianity and Islam. The Christian philosopher, John Philoponus, presented the philosophical arguments against the ancient Greek notion of an infinite past and future. Philoponus' arguments against an infinite past were used by the early Muslim philosopher, Al-Kindi (Alkindus); the Jewish philosopher, Saadia Gaon (Saadia ben Joseph); and the Muslim theologian, Al-Ghazali (Algazel).
Astronomical concepts
Astronomical models of the Universe were proposed soon after astronomy began with the Babylonian astronomers, who viewed the Universe as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of Anaximander and Hecataeus of Miletus.Later Greek philosophers, observing the motions of the heavenly bodies, were concerned with developing models of the Universe-based more profoundly on empirical evidence. The first coherent model was proposed by Eudoxus of Cnidos. According to Aristotle's physical interpretation of the model, celestial spheres eternally rotate with uniform motion around a stationary Earth. Normal matter is entirely contained within the terrestrial sphere.
De Mundo (composed before 250 BC or between 350 and 200 BC), stated, "Five elements, situated in spheres in five regions, the less being in each case surrounded by the greater—namely, earth surrounded by water, water by air, air by fire, and fire by ether—make up the whole Universe".
This model was also refined by Callippus and after concentric spheres were abandoned, it was brought into nearly perfect agreement with astronomical observations by Ptolemy. The success of such a model is largely due to the mathematical fact that any function (such as the position of a planet) can be decomposed into a set of circular functions (the Fourier modes). Other Greek scientists, such as the Pythagorean philosopher Philolaus, postulated (according to Stobaeus account) that at the center of the Universe was a "central fire" around which the Earth, Sun, Moon and Planets revolved in uniform circular motion.
The Greek astronomer Aristarchus of Samos was the first known individual to propose a heliocentric model of the Universe. Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner describes Aristarchus's heliocentric model. Archimedes wrote:
You, King Gelon, are aware the Universe is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the Universe is many times greater than the Universe just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface
Aristarchus thus believed the stars to be very far away, and saw this as the reason why stellar parallax had not been observed, that is, the stars had not been observed to move relative each other as the Earth moved around the Sun. The stars are in fact much farther away than the distance that was generally assumed in ancient times, which is why stellar parallax is only detectable with precision instruments. The geocentric model, consistent with planetary parallax, was assumed to be an explanation for the unobservability of the parallel phenomenon, stellar parallax. The rejection of the heliocentric view was apparently quite strong, as the following passage from Plutarch suggests (On the Apparent Face in the Orb of the Moon):
Cleanthes a contemporary of Aristarchus and head of the Stoics thought it was the duty of the Greeks to indict Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the Universe [i.e. the Earth], ... supposing the heaven to remain at rest and the Earth to revolve in an oblique circle, while it rotates, at the same time, about its own axis
The only other astronomer from antiquity known by name who supported Aristarchus's heliocentric model was Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus. According to Plutarch, Seleucus was the first to prove the heliocentric system through reasoning, but it is not known what arguments he used. Seleucus' arguments for a heliocentric cosmology were probably related to the phenomenon of tides. According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun. Alternatively, he may have proved heliocentricity by determining the constants of a geometric model for it, and by developing methods to compute planetary positions using this model, like what Nicolaus Copernicus later did in the 16th century. During the Middle Ages, heliocentric models were also proposed by the Indian astronomer Aryabhata, and by the Persian astronomers Albumasar and Al-Sijzi.
The Aristotelian model was accepted in the Western world for roughly two millennia, until Copernicus revived Aristarchus's perspective that the astronomical data could be explained more plausibly if the Earth rotated on its axis and if the Sun were placed at the center of the Universe.
In the center rests the Sun. For who would place this lamp of a very beautiful temple in another or better place than this wherefrom it can illuminate everything at the same time?
— Nicolaus Copernicus, in Chapter 10, Book 1 of De Revolutionibus Orbium Coelestrum (1543)
As noted by Copernicus himself, the notion that the Earth rotates is very old, dating at least to Philolaus (c. 450 BC), Heraclides Ponticus (c. 350 BC) and Ecphantus the Pythagorean. Roughly a century before Copernicus, the Christian scholar Nicholas of Cusa also proposed that the Earth rotates on its axis in his book, On Learned Ignorance. Al-Sijzi also proposed that the Earth rotates on its axis. Empirical evidence for the Earth's rotation on its axis, using the phenomenon of comets, was given by Tusi (1201–1274) and Ali Qushji (1403–1474).
This cosmology was accepted by Isaac Newton, Christiaan Huygens and later scientists. Edmund Halley (1720) and Jean-Philippe de Chéseaux (1744) noted independently that the assumption of an infinite space filled uniformly with stars would lead to the prediction that the nighttime sky would be as bright as the Sun itself; this became known as Olbers' paradox in the 19th century. Newton believed that an infinite space uniformly filled with matter would cause infinite forces and instabilities causing the matter to be crushed inwards under its own gravity. This instability was clarified in 1902 by the Jeans instability criterion. One solution to these paradoxes is the Charlier Universe, in which the matter is arranged hierarchically (systems of orbiting bodies that are themselves orbiting in a larger system, ad infinitum) in a fractal way such that the Universe has a negligibly small overall density; such a cosmological model had also been proposed earlier in 1761 by Johann Heinrich Lambert. A significant astronomical advance of the 18th century was the realization by Thomas Wright, Immanuel Kant and others of nebulae.
In 1919, when Hooker Telescope was completed, the prevailing view still was that the Universe consisted entirely of the Milky Way Galaxy. Using the Hooker Telescope, Edwin Hubble identified Cepheid variables in several spiral nebulae and in 1922–1923 proved conclusively that Andromeda Nebula and Triangulum among others, were entire galaxies outside our own, thus proving that Universe consists of multitude of galaxies.
The modern era of physical cosmology began in 1917, when Albert Einstein first applied his general theory of relativity to model the structure and dynamics of the Universe.
