Universe

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Physical cosmology

Key topics

Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe

Early universe

Inflation · Nucleosynthesis GWB · Neutrino Background Cosmic microwave background Expanding universe Redshift · Hubble's law Metric expansion of space Friedmann equations FLRW metric Structure formation Shape of the universe Structure formation Galaxy formation Large-scale structure Components Lambda-CDM model Dark energy · Dark matter History Timeline of cosmology... Cosmology experiments Observational cosmology 2dF · SDSS CoBE · BOOMERanG · WMAP Scientists Einstein · Hawking . Friedman · Lemaître · Hubble · Penzias · Wilson · Gamow · Dicke · Zel'dovich · Mather · Smoot · others

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The Universe is everything that exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and physical constants that govern them. In a well-defined, mathematical sense, the universe can even be said to contain that which does not exist; according to the path-integral formulation of quantum mechanics, even unrealized possibilities contribute to the probability amplitudes of events in the universe.^[1] The universe is sometimes denoted as the cosmos or Nature, as in "cosmology" or "natural philosophy".

Scientific experiments have yielded several general facts about the observable universe. The age of the universe is estimated to be 13.7±0.2 billion years ^[2]. The universe is very large, possibly infinite, being at least 93 billion light years across, and consisting mainly of matter, rather than antimatter. Only 4% of the matter and energy in the universe is luminous, that is, directly observable from its emitted electromagnetic radiation ("light" in its most general sense); the remainder consists of dark energy (73%) and dark matter (23%), both of which are mysterious. The luminous matter within the universe is sparse and consists principally of galaxies, which are distributed uniformly when averaged over length-scales longer than 300 million light years; on smaller length scales, galaxies tend to clump into clusters, superclusters and even larger structures. The light arriving from distant galaxies is detectably redshifted, with the redshift increasing with the galaxy's distance from Earth. The universe is bathed in a microwave radiation that is highly isotropic (uniform across different directions), and corresponds to a blackbody spectrum of roughly 2.7 Kelvin. The relative percentages of the lighter chemical elements — especially hydrogen, deuterium and helium — is apparently the same throughout the universe. The universe is believed to be expanding, in the sense that space itself is enlarging with time; even objects initially at rest to one another will appear to fly apart as new space is created between them. The universe has at least three spatial dimensions and one temporal (time) dimension, although extremely small additional dimensions cannot be ruled out experimentally; spacetime appears to be smoothly and simply connected, with very small curvature, so that Euclidean geometry is accurate on the average throughout the universe. The universe appears to be governed by the same physical laws and constants throughout its extent and history.

Throughout their recorded history, humans have proposed several cosmologies and cosmogonies to account for their observations of the universe. The earliest quantitative models were developed by the ancient Greeks, who proposed that the universe possessed infinite space and had existed eternally, but contained a single set of concentric spheres of finite size (corresponding to the fixed stars, the Sun and various planets) rotating about a spherical but unmoving Earth. Over the centuries, more careful astronomical observations and improved theories of gravity led to the present theory of the Big Bang and, more specifically, the Lambda-CDM model, which accounts for the available data. According to such theories, everything in the universe — all forms of matter and energy, and even spacetime itself — came into being at a single event, a gravitational singularity; as space expanded with time, the matter and energy cooled sufficiently to allow the stable condensation of elementary particles into the primordial nuclei and atoms. Once atoms formed, matter became mostly transparent to electromagnetic radiation; the ambient microwave radiation observed today is the residual radiation that decoupled from the matter.

According to the prevailing scientific models, the Universe is governed by the Standard Model of physics (which governs various forms of matter and fields), as well as special and general relativity (which govern spacetime and its interaction with matter and fields). On cosmological length scales, the dominant interaction in the universe is gravitation. Hence, the theory of general relativity (the most accurate description of gravity presently available) offers the best predictions for the overall development of the universe, including its origin, expansion (which mainly accounts for the observed redshift), large-scale structure and ultimate fate. However, components of the Standard Model — particularly those relating to nucleosynthesis, atomic spectra, and CP violation — are needed to account for other experimental observations, such as the distribution of chemical elements and microwave radiation throughout the universe, as well as the matter-antimatter asymmetry.

According to some speculations, this universe may be one of many disconnected universes, which are collectively denoted as the multiverse. In one theory, there is an infinite variety of universes, each with different values of the physical constants. In another theory, new universes are spawned with every quantum measurement. However, these speculations cannot be tested experimentally since, by definition, other universes cannot interact with our own.

[edit] Etymology, synonyms and definitions

See also: Cosmos and Nature

The word "universe" is derived from Old French univers, from Latin universum, which combines uni- (the combining form of unus, or "one") with versus (perfect passive participle of vertere, or "turn"). The word, therefore, can mean "[everything] rolled into one" or "revolving as one" or "orbiting as one". This may derive from the early Greek model of the universe, in which all matter was contained within rotating, concentric spheres.

Synonyms for the universe include the cosmos, Nature and everything (as in the "theory of everything"). These synonyms were already in use among the ancient Greek philosophers; κοσμος is a Greek word, and Aristotle often refers to the universe as το παν (The All), or απαντα τα οντα (everything that exists). Such synonyms are found in other languages as well, such as the German word Weltall for universe.

[edit] Broadest definition: reality and probability

See also: Introduction to quantum mechanics and Interpretation of quantum mechanics

The broadest definition of the universe is found in De divisione naturae by the medieval philosopher Johannes Scotus Eriugena, who defined it as simply everything: everything that exists and everything that does not exist. Time is not considered in Eriugena's definition; thus, his definition includes everything that exists, has existed and will exist, as well as everything that does not exist, has never existed and will never exist. This all-embracing definition was not adopted by most later philosophers, but it is relevant in quantum physics, particularly the path-integral formulation of Feynman.^[1] According to that formulation, the probability amplitudes for the various outcomes of an experiment given a perfectly defined initial state of the system are determined by summing over all possible paths by which the system could progress from the initial to final state. However, the experiment has only one outcome; only one possible outcome is realized in this universe, via the mysterious process of quantum measurement, also known as the collapse of the wavefunction (but see the many-worlds hypothesis below in the Multiverse section). In this well-defined mathematical sense, even that which does not exist (all possible paths) can influence that which does finally exist (the experimental measurement); prior to measurement, the ultimately non-existent contributes to the universe on an equal footing with the ultimately existent. As a specific example, every electron is intrinsically identical to every other; therefore, probability amplitudes must be computed allowing for the possibility that they exchange positions, something known as exchange symmetry. This conception of the universe embracing both the real and the possible but unreal is loosely related to the Buddhist doctrines of shunyata and interdependent development of reality, and in Gottfried Leibniz's more modern concepts of contingency and the identity of indiscernibles.

[edit] Definition as reality

See also: Reality and Physics

More customarily, the universe is defined as everything that exists, has existed and will exist. According to this definition and our present understanding, the universe consists of three elements: space and time, collectively known as space-time or the vacuum; matter and various forms of energy and momentum occupying space-time; and the physical laws that govern the first two. These elements will be discussed in greater detail below.

This triple division corresponds roughly to the ideas of Aristotle. In his book The Physics (Φυσικης, from which we derive the word "physics"), Aristotle divided ’το παν (everything) into three elements: matter (the stuff of which the universe is made), form (the arrangement of that matter in space) and change (how matter is created, destroyed or altered in its properties, and similarly, how form is altered). Physical laws were conceived as the rules governing the properties of matter, form and their changes. Later philosophers such as Lucretius, Averroes, Avicenna and Baruch Spinoza altered or refined these divisions; for example, Averroes and Spinoza discern natura naturans (the active principles governing the universe) from natura naturata, the passive elements upon which the former act.

[edit] Definition as connected space-time

See also: Bubble universe theory and Chaotic inflation

It is possible to conceive of disconnected space-times, each existing but unable to interact with one another. An easily visualized metaphor 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 space-time is denoted as a universe, whereas our particular space-time is denoted as the Universe, just as we call our moon the Moon. The entire collection of these separate space-times is denoted as the multiverse.^[3] In principle, the other unconnected universes may have different dimensionalities and topologies of space-time, different forms of matter and energy, and different physical laws and physical constants.

[edit] Definition as observable reality

See also: Observable universe and Observational cosmology

According to a still more restrictive definition, the universe is everything within our connected space-time that could ever interact with us and vice versa. According to the theory of general relativity, some regions of space may never interact with ours even in the lifetime of the universe, due to the finite speed of light and the expansion of space. For example, radio messages sent from Earth may never reach some regions of space, even if the universe lives forever; space may expand faster than light can cover it. It is worth emphasizing that those distant regions of space are taken to exist and be part of reality as much as we are; yet we can never interact with them. The spatial region within which we can affect and be affected is denoted as the observable universe. Strictly speaking, the observable universe depends on the observer. By traveling, an observer can come into contact with a greater region of space-time than an observer who remains still, so that the observable universe for the former is larger than for the latter; nevertheless, even the most rapid traveler may not be able to interact with all of space. Typically, the observable universe is taken to mean the universe observable from a stationary observer on Earth.

[edit] Scientific observations

The Hubble Ultra Deep Field image of a small region of the sky, near the constellation Fornax. The light from the smallest, most redshifted galaxies originated roughly 13 billion years ago.

Main articles: Observable universe, Age of the universe, Large-scale structure of the universe, and Abundance of the chemical elements

The universe is very large and possibly infinite in volume. The observable matter is spread over a space at least 93 billion light years across;^[4] for comparison, the diameter of a typical galaxy is only 30,000 light-years, and the typical distance between two neighboring galaxies is only 3 million light-years. For example, our Milky Way galaxy is roughly 100,000 light years in diameter, and our nearest sister galaxy, the Andromeda Galaxy, is located roughly 2.5 million light years away.

The observable matter is spread uniformly (homogeneously) throughout the universe, when averaged over distances longer than 300 million light-years.^[5] However, on smaller length-scales, matter is observed to form "clumps", i.e., to cluster hierarchically; most atoms are condensed into stars, most stars into galaxies, most galaxies into clusters, superclusters and, finally, the largest-scale structures such as the Great Wall of galaxies. The observable matter of the universe is also spread isotropically, meaning that no direction of observation seems different from any other; each region of the sky has roughly the same content.^[6] The universe is also bathed in a highly isotropic microwave radiation that corresponds to a thermal equilibrium blackbody spectrum of roughly 2.725 Kelvin.^[7] The hypothesis, now apparently confirmed, that the large-scale universe is homogeneous and isotropic is known as the cosmological principle.

The present overall density of the universe is very low, roughly 9.9 × 10^-30 grams per cubic centimetre. This mass-energy appears to consist of 73% dark energy, 23% cold dark matter and 4% ordinary matter. Thus the density of atoms is on the order of a single hydrogen atom for every four cubic meters of volume.^[8] The nature of dark energy and dark matter are presently unknown.

The universe is old and evolving. Various data suggest that the universe is at least 10 billion years old; the most precise current estimate is 13.7±0.2 billion years old.^[2] Independent estimates (based on measurements such as radioactive dating) agree, although they are less precise, ranging from 11-20 billions years^[9] to 13–15 billion years.^[10] The universe was not the same at all times; the relative populations of cosmological objects such as quasars and galaxies has changed and space itself appears to be expanding. This expansion accounts for how two galaxies can be 90 billion light years apart, even if they have traveled for only 13.7 billion years at speeds less than the speed of light; the very space between them has expanded. This expansion is consistent with the observation that the light from distant galaxies has been redshifted; the photons emitted have been stretched to longer wavelengths and lower frequency during their journey. The rate of this spatial expansion is accelerating, based on studies of Type Ia supernovae and corroborated by other data.

The relative fractions of different chemical elements — particularly the lightest atoms such as hydrogen, deuterium and helium — seem to be identical throughout the universe and throughout its observable history.^[11] The universe seems to have much more matter than antimatter, an asymmetry possibly related to the observations of CP violation.^[12] The universe appears to have no net electric charge, and therefore gravity appears to be the dominant interaction on cosmological length scales. The universe appears to have no net momentum and angular momentum. The absence of net charge and momentum would follow from accepted physical laws (Gauss's law and the non-divergence of the stress-energy-momentum pseudotensor, respectively), if the universe were finite.

Finally, the universe appears to have a smooth spacetime continuum consisting of three spatial dimensions and one temporal (time) dimension. The spacetime is observed to be very nearly flat (close to zero curvature), meaning that Euclidean geometry is experimentally true with high accuracy.^[13] Spacetime also appears to have a simply connected topology, at least on the length-scale of the observable universe. However, present observations cannot exclude the possibilities that the universe has more dimensions and that its spacetime may have a multiply connected global topology, in analogy with the cylindrical or toroidal topologies of two-dimensional spaces.^[14]

The universe appears to be governed throughout by the same physical laws and physical constants.^[15] According to the prevailing Standard Model of physics, all matter is composed of three generations of leptons and quarks, both of which are fermions. These elementary particles interact via at most three fundamental interactions: the electroweak interaction which includes electromagnetism and the weak nuclear force; the strong nuclear force described by quantum chromodynamics; and gravity, which is best described at present by general relativity. The first two interactions can be described by renormalized quantum field theory, and are mediated by gauge bosons that correspond to a particular type of gauge symmetry. A renormalized quantum field thoery theory of general relativity has not yet been achieved, although various forms of string theory seem promising. The theory of special relativity is believed to hold throughout the universe, provided that the spatial and temporal length scales are sufficiently short; otherwise, the more general theory of general relativity must be applied. There is no explanation for the particular values that physical constants appear to have throughout our universe, such as Planck's constant h or the gravitational constant G. Several conservation laws have been identified, such as the conservation of charge, momentum, angular momentum and energy; in many cases, these conservation laws can be related to symmetries or mathematical identities.

[edit] Historical models

Main article: Timeline of cosmology

Many models of the cosmos (cosmologies) and its origin (cosmogonies) have been proposed, based on the then available data and conceptions of the universe.

[edit] Creation stories

Main articles: Origin belief and Creator deity

Sumerian account of the creatrix goddess Nammu, the precursor of the Assyrian goddess Tiamat; perhaps the earliest surviving creation story.

Many cultures have stories describing the creation of the world, which may be roughly grouped into common types. 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 creation is caused by a single god emanating or producing something by themselves, as in Buddhist concept of Adi-Buddha, the ancient Greek story of Gaia (Mother Earth), the Aztec goddess Coatlicue or the ancient Egyptian god Atum. In another type of story, the world 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 another type of story, the world is created by divine speech, as in the ancient Egyptian story of Ptah or the Biblical account in Genesis. In other stories, the universe is emanates from fundamental principles, such as Brahman and Prakrti, or the yin and yang of the Tao.

Milanese flag (c. 1450) depicting the four classical elements in the outermost ring. Fire and Air are above, holding red and white spheres, respectively; Water and Earth are below, holding blue and green spheres, respectively.

[edit] Philosophical models

Main articles: Pre-Socratic philosophy and Physics (Aristotle)

The first philosophical models of the universe were developed by the pre-Socratic philosophers. 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 apparently different materials of the world (wood, metal, etc.) are all different forms of a single material, the arche. The first to do so was Thales, who called this material Water. Following him, Anaximenes called it Air, and posited that there must be attractive and repulsive forces that cause the arche to condense or dissociate into different forms. Empedocles proposed that multiple fundamental materials were necessary to explain the diversity of the universe, and proposed that all four classical elements (Earth, Air, Fire and Water) existed, albeit in different combinations and forms. This four-element theory was adopted by many of the subsequent philosophers. Some philosophers before Empedocles advocated less material things for the arche; Heraclitus argued for a Logos, Pythagoras believed that all things were composed of numbers, whereas Thales' student, Anaximander, proposed that everything was composed of a chaotic substance known as apeiron, roughly corresponding to the modern concept of a quantum foam. Various modifications of the apeiron theory were proposed, most notably that of Anaxagoras, which proposed that the various matter is the world was spun off from a rapidly rotating apeiron, set in motion by the principle of Nous (Mind). Still other philosophers — most notably Leucippus and Democritus — proposed that the universe was composed of indivisible atoms moving through empty space, a vacuum; Aristotle opposed this view ("Nature abhors a vacuum") on the grounds that resistance to motion increases with density; hence, empty space should offer no resistance to motion, leading to the possibility of infinite speed.

Although Heraclitus argued for eternal change, his rough 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 το εν (The One). Parmenides' theory seemed implausible to many Greeks, but his student Zeno of Elea challenged them with several famous paradoxes. Aristotle resolved these paradoxes by developing the notion of an infinitely divisible continuum, and applying it to space and time.

[edit] Astronomical models

Hand-colored version of the Flammarion woodcut, depicting the Aristotelian conception of the universe that preceded the models of Copernicus and Thomas Digges.

Main article: History of astronomy

More practical Greek philosophers were concerned with developing models of the universe that would account for the observed motion of the stars and planets. The first coherent model was proposed by Eudoxus of Cnidos. According to this model, space and time are infinite and eternal, but the distribution of matter is confined to certain rotating concentric spheres. This model was refined by Kallippos and Aristotle, and brought to its highest level by Ptolemy. The success of this model is due to the mathematical fact that any function (such as the position of a planet) can be decomposed into a set of Fourier modes.

Model of the Copernican universe by Thomas Digges in 1576, with the amendment that the stars are no longer confined to a sphere, but spread uniformly throughout the space surrounding the planets.

The Aristotelian model was accepted for roughly two millennia, until Copernicus proposed that the astronomical data could be explained better if the sun were placed at the center of the universe, rather than the earth. This allowed the stars to placed uniformly through the (infinite) space surrounding the planets, as first proposed by Thomas Digges and considered by Isaac Newton.

The Newtonian cosmology, however, had several paradoxes that were resolved only with the development of general relativity. The first of these was that it assumed that space and time were infinite, and that the stars in the universe had existed for an infinite time; however, since stars are constantly radiating energy, a finite star seems inconsistent with the radiation of infinite energy. Secondly, Johannes Kepler noted that the assumption of an infinite space filled uniformly with stars would lead to the prediction that the nightime sky would be as bright as the sun itself; this became known as Olber's paradox in the 19th century. Third, Newton himself showed 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 by the Jeans instability criterion. One solution to these latter two paradoxes is the Charlier universe, in which the matter is arranged in a fractal way so that it has a neglgibly small overall density.

The modern era of physical cosmology began in 1917, when Albert Einstein first applied his theory of general relativity to model the structure and dynamics of the universe. This theory and its implications will be discussed in more detail below, in the "Space and Time" section.

[edit] Theoretical models

Of the four fundamental interactions, gravity is dominant at cosmological length scales; that is, the other three forces are believed to play a negligible role in determining structures at the level of planets, stars, galaxies and larger-scale structures. The effects of the two nuclear interactions, the weak and strong nuclear forces, are mainly confined to sub-atomic length scales, because their strengths decrease very rapidly with distance. In principle, electromagnetism could be significant, being equally as long-ranged as gravity; however, the effects of positive and negative charges tend to cancel one another, leaving only a small residue. By contrast, all matter and energy gravitate, causing gravity's effects to be cumulative.

[edit] General relativity

Main articles: Introduction to general relativity and General relativity

Given gravity's predominance in shaping cosmological structures, accurate predictions of the universe's past and future require an accurate theory of gravitation. The best available theory is general relativity, which has passed all experimental tests hitherto. However, such experiments have not been carried out on cosmological length scales so, in principle, general relativity might be inaccurate. Nevertheless, its cosmological predictions appear to be consistent with observations, so there is no compelling reason to adopt another theory.

General relativity consists of a set of equations (the Einstein field equations) that must be solved from the distribution of mass-energy and momentum throughout the universe. Since these are unknown in exact detail, cosmological models have been based on the cosmological principle, which states that the universe is homogeneous and isotropic. In effect, the various galaxies making up the universe are replaced by a fine uniform dust distributed equally throughout the universe. Assuming the cosmological principle makes it easy to solve the Einstein equations and predict the past and future of the universe on cosmological time scales.

[edit] Special relativity and space-time

Main articles: Introduction to special relativity and Special relativity

The universe has at least three spatial and one temporal (time) dimension. It was long thought that the spatial and temporal dimensions were different in nature and independent of one another. However, according to the theory of special relativity, spatial and temporal separations are interconvertible (within limits) by changing one's reference frame.

Only its length s is intrinsic to the rod (shown in black); the coordinate differences Δx, Δy, etc. depend on the frame of reference (in blue and red).

To understand this interconversion, it is helpful to consider the analogous interconversion of spatial separations along the three spatial dimensions. Consider the two endpoints of a rod of length l. The length can be determined from the differences in the three coordinates Δx, Δy and Δz of the two endpoints in a given reference frame

l² = Δx² + Δy² + Δz²

using the Pythagorean theorem. In a rotated reference frame, the coordinate differences will differ, although they naturally give the same length

l² = Δξ² + Δη² + Δζ²

Thus, the coordinates differences are not intrinsic to the rod, but reflect the reference frame used to describe it; by contrast, the length l is intrinsic. The coordinate differences can be changed freely without affecting the rod, merely by rotating one's reference frame.

The analogy in spacetime is called the interval between two events; an event is defined as a point in spacetime, a specific position in space and a specific moment in time. The spacetime interval between two events is given by

where c is the speed of light. Thus, by changing one's reference frame, one can change a spatial and time separation (l₁, Δt₁) into another (l₂, Δt₂), as long as the change maintains the spacetime interval s. Such a change in reference frame can be obtained by changing one's motion; a moving frame will measure different lengths and times from those measured in a stationary reference frame.

[edit] Solving Einstein's equations

See also: Big Bang and Ultimate fate of the universe

In non-Cartesian (non-square) or curved coordinate systems, the Pythagorean theorem holds only on infinitesimal length scales and must be augmented with a more general metric tensor g^μν, which can vary from place to place and which describes the local geometry in the particular coordinate system. However, assuming the cosmological principle, every point in space is like every other point; hence, the metric tensor must be the same everywhere. That leads to a single form for the metric tensor, called the Friedmann-Lemaître-Robertson-Walker metric

where (r, θ, φ) correspond to a spherical coordinate system. This metric has only two undetermined parameters: an overall length scale R that can vary with time, and a curvature index k that can be only zero, one or -1, corresponding to flat Euclidean geometry, or spaces of positive or negative curvature. In cosmology, solving for the history of the universe is done by calculating R as a function of time, given k and the value of the cosmological constant Λ, which is a (small) parameter in Einstein's field equations. The equation describing how R varies with time is known as the Friedmann equation, after its inventor, Alexander Friedmann.

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. Since this equilibrium is unstable and since the universe is known to be inhomogeneous on smaller scales, R must change, according to general relativity. When R changes, all the spatial distances in the universe change in tandem; there is an overall expansion or contraction of space itself. The accounts for the observation that galaxies appear to be flying apart; space is being created between them. 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 13.7 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 goes to zero and matter and energy became infinitely dense. It may seem that this conclusion is uncertain since it seems based on the assumptions of homogeneity and isotropy (the cosmological principle) and that only the gravitational interaction matters. However, the Penrose-Hawking singularity theorems show that a singularity should exist for very general conditions. According to the equations, R should grow 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.

Third, the curvature index k determines the sign of the mean curvature of spacetime averaged over length scales greater than a billion light years. If k=1, the curvature is positive and the universe has a finite volume. Such universes are often visualized as a three-dimensional sphere S³ embedded in a four-dimensional space. Conversely, if k is zero or negative, the universe may have infinite volume, depending on its overall topology. 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 that is indeed a possibility when k does not equal 1. For comparison, an infinite plane has zero curvature but infinite area, whereas an infinite cylinder is finite in one direction and a torus in finite in both. A toroidal universe could behave like a normal universe with periodic boundary conditions, as seen in some video games; a traveller crossing an outer "boundary" of space going outwards would reappear instantly at another point on the boundary moving inwards.

The ultimate fate of the universe is still unknown, since it depends critically on the curvature index k and the cosmological constant Λ. If the universe is sufficiently dense, k equals +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 is insufficiently dense, k equals 0 or -1 and the universe will expand forever, cooling off and eventually becoming inhospitable for all life, as the stars die and all matter coalesces into black holes (the Big Freeze and the heat death of the universe). As noted above, recent data suggests that the expansion of the universe is not decreasing as originally expected, but accelerating; if this continues indefinitely, the universe will eventually rip itself to shreds (the Big Rip). Experimentally, the universe has an overall density that is very close to the critical value between recollapse and eternal expansion; more careful astronomical observations are needed to decide the question.

[edit] Prevailing Big Bang model

Main articles: Big Bang, Timeline of the Big Bang, Nucleosynthesis, and Lambda-CDM model

The prevailing Big Bang model accounts for many of the experimental observations described above, such as the correlation of distance and redshift of galaxies, the universal ratio of hydrogen:helium atoms, and the ubiquitous, isotropic microwave radiation background. As noted above, the redshift arises from the metric expansion of space; as the space itself expands, the wavelength of a photon traveling through space likewise increases, decreasing its energy. The longer a photon has been traveling, the more expansion it has undergone; hence, older photons from more distant galaxies are the most red-shifted. Determining the correlation between distance and redshift is an important problem in experimental physical cosmology.

Other experimental observations can be explained by combining the overall expansion of space with nuclear and atomic physics. As the universe expands, the energy density of the electromagnetic radiation decreases more quickly than does that of matter, since the energy of a photon decreases with its wavelength. Thus, although the energy density of the universe is now dominated by matter, it was once dominated by radiation; poetically speaking, all was light. As the universe expanded, its energy density decreased and it became cooler; as it did so, the elementary particles of matter could associate stably into ever larger combinations. Thus, in the early part of the matter-dominated era, stable protons and neutrons formed, which then associated into atomic nuclei. At this stage, the matter in the universe was mainly a hot, dense plasma of negative electrons, neutral neutrinos and positive nuclei. Nuclear reactions among the nuclei led to the present abundances of the lighter nuclei, particularly hydrogen, deuterium, and helium. Eventually, the electrons and nuclei combined to form stable atoms, which are transparent to most wavelengths of radiation; at this point, the radiation decoupled from the matter, forming the ubiquitous, isotropic background of microwave radiation observed today.

Other observations are not definitively answered by known physics. It is believed that the Universe was created with a slight imbalance of matter over antimatter, owing to the CP violation observed by particle physicists. The matter and antimatter mainly annihilated each other, producing the present matter-dominated universe. Several lines of evidence also suggest that a rapid cosmic inflation of the universe occurred very early in its history (roughly 10^-35 seconds after its creation). Recent observations also suggest that the cosmological constant Λ is not zero and that the net mass-energy content of the universe is dominated by a hitherto mysterious dark energy and dark matter.

[edit] Alternative cosmologies

Main article: Non-standard cosmology

Despite its experimental verification, some scientists find the theory of general relativity implausible and have suggested alternatives. Such theories can only be considered scientific if they offer testable predictions that differ from those of general relativity. The main scientific alternative is the Brans-Dicke theory, which augments general relativity with a scalar field that determines the local value of the gravitational constant G. Other, more radical suggestions include the variable G cosmologies (in which the universe's physical constants vary with the age or size of the universe), the tired light hypothesis of Zwicky, and the plasma cosmology theory. The validity of most such theories seems unlikely, given the available data.

The steady-state theory of cosmology was popular in the 1950s; according to this theory, the universe has been the same at all times, as well as being homogeneous and isotropic (the perfect cosmological principle). This theory predicts that the conservation of energy is violated, albeit very slightly. This theory made admirably precise predictions, which have since been disproven by experimental observations.

[edit] Multiverse

Main articles: Multiverse, Many-worlds hypothesis, Bubble universe theory, and Parallel universe (fiction)

Some speculative theories have proposed that this universe is but one of a set of disconnected universes, collectively denoted as the multiverse.^[3][16] By definition, there is no possible way for anything in one universe to affect another; if two "universes" could affect one another, they would be part of a single universe. Thus, although some fictional characters travel between "parallel fictional "universes", this is a loose usage of the term "universe".

There are two scientific senses in which multiple can occur. First, disconnected spacetime continua may exist; presumably, all forms of matter and energy are confined to one universe and cannot "tunnel" between them. An example of such a theory is the chaotic inflation model of the early universe.^[17] Second, according to the many-worlds hypothesis, a parallel universe is born with every quantum measurement; the universe "forks" into parallel copies, each one corresponding to a different outcome of the quantum measurement. Authors have explored this concept in some fiction, most notably Jorge Borges' short story The Garden of Forking Paths. However, both senses of the term "multiverse" are speculative and may be considered unscientific; the fact that universes cannot interact makes it impossible to test experimentally in this universe whether another universe exists.

[edit] See also

[edit] Notes and references

[edit] Further reading

• Rindberg W (1977). Essential Relativity: Special, General, and Cosmological. New York: Springer Verlag, pp. 193–244. ISBN 0-387-10090-3. 

• Weinberg S (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: John Wiley and Sons, pp. 407–633. ISBN 0-471-92567-5. 

• Gal-Or, B (1983). Cosmology, Physics and Philosophy. New York: Springer Verlag. ISBN 978-0387905815. 

[edit] External links

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