Copernican heliocentrism

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https://en.wikipedia.org/wiki/Copernican_heliocentrism 

 

Heliocentric model from Nicolaus Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres)

Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. This model positioned the Sun at the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths, modified by epicycles, and at uniform speeds. The Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, which had placed Earth at the center of the Universe.

Although he had circulated an outline of his own heliocentric theory to colleagues sometime before 1514, he did not decide to publish it until he was urged to do so later by his pupil Rheticus. Copernicus's challenge was to present a practical alternative to the Ptolemaic model by more elegantly and accurately determining the length of a solar year while preserving the metaphysical implications of a mathematically ordered cosmos. Thus, his heliocentric model retained several of the Ptolemaic elements, causing inaccuracies, such as the planets' circular orbits, epicycles, and uniform speeds, while at the same time using ideas such as:-

• The Earth is one of several planets revolving around a stationary sun in a determined order.
• The Earth has three motions: daily rotation, annual revolution, and annual tilting of its axis.
• Retrograde motion of the planets is explained by the Earth's motion.
• The distance from the Earth to the Sun is small compared to the distance from the Sun to the stars.

Heliocentrism before Copernicus

Main articles: Heliocentrism and Heliocentrism § Ancient_and_medieval_astronomy

Antiquity

Philolaus (4th century BCE) was one of the first to hypothesize movement of the Earth, probably inspired by Pythagoras' theories about a spherical, moving globe.

Aristarchus of Samos, in the 3rd century BCE, proposed what was, so far as is known, the first serious model of a heliocentric Solar System, having developed some Heraclides Ponticus' theories (speaking of a "revolution of the Earth on its axis" every 24 hours). Though his original text has been lost, a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work in which Aristarchus advanced the 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 Floor, and that the sphere of the 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.

— The Sand Reckoner

It is a common misconception that the heliocentric view was rejected by the contemporaries of Aristarchus. This is due to Gilles Ménage's translation of a passage from Plutarch's On the Apparent Face in the Orb of the Moon. Plutarch reported that Cleanthes (a contemporary of Aristarchus and head of the Stoics) as a worshiper of the Sun and opponent to the heliocentric model, was jokingly told by Aristarchus that he should be charged with impiety. Gilles Ménage, shortly after the trials of Galileo and Giordano Bruno, amended an accusative (identifying the object of the verb) with a nominative (the subject of the sentence), and vice versa, so that the impiety accusation fell over the heliocentric sustainer. The resulting misconception of an isolated and persecuted Aristarchus is still transmitted today.

In 499 CE, the Indian astronomer and mathematician Aryabhata propounded a planetary model that explicitly incorporated Earth's rotation about its axis, which he explains as the cause of what appears to be an apparent westward motion of the stars. He also believed that the orbits of planets are elliptical. Aryabhata's followers were particularly strong in South India, where his principles of the diurnal rotation of Earth, among others, were followed and a number of secondary works were based on them.

Middle Ages

Islamic astronomers

Several Islamic astronomers questioned the Earth's apparent immobility, and centrality within the universe. Some accepted that the Earth rotates around its axis, such as Abu Sa'id al-Sijzi (died circa 1020). who invented an astrolabe based on a belief held by some of his contemporaries "that the motion we see is due to the Earth's movement and not to that of the sky". That others besides al-Sijzi held this view is further confirmed by a reference from an Arabic work in the 13th century which states: "According to the geometers [or engineers] (muhandisīn), the earth is in constant circular motion, and what appears to be the motion of the heavens is actually due to the motion of the earth and not the stars".

In the 12th century, Nur ad-Din al-Bitruji proposed a complete alternative to the Ptolemaic system (although not heliocentric). He declared the Ptolemaic system as an imaginary model, successful at predicting planetary positions, but not real or physical. Al-Btiruji's alternative system spread through most of Europe during the 13th century.

Mathematical techniques developed in the 13th to 14th centuries by the Arab and Persian astronomers Mo'ayyeduddin al-Urdi, Nasir al-Din al-Tusi, and Ibn al-Shatir (died circa 1375) for geocentric models of planetary motions closely resemble some of the techniques used later by Copernicus in his heliocentric models.

European astronomers

Ptolemaic system

Main article: Geocentric model

 

Line art drawing of Ptolemaic system

The prevailing astronomical model of the cosmos in Europe in the 1,400 years leading up to the 16th century was the Ptolemaic System, a geocentric model created by the Roman citizen Claudius Ptolemy in his Almagest, dating from about 150 CE. Throughout the Middle Ages it was spoken of as the authoritative text on astronomy, although its author remained a little understood figure frequently mistaken as one of the Ptolemaic rulers of Egypt. The Ptolemaic system drew on many previous theories that viewed Earth as a stationary center of the universe. Stars were embedded in a large outer sphere which rotated relatively rapidly, while the planets dwelt in smaller spheres between—a separate one for each planet. To account for apparent anomalies in this view, such as the apparent retrograde motion of the planets, a system of deferents and epicycles was used. The planet was said to revolve in a small circle (the epicycle) about a center, which itself revolved in a larger circle (the deferent) about a center on or near the Earth.

A complementary theory to Ptolemy's employed homocentric spheres: the spheres within which the planets rotated could themselves rotate somewhat. This theory predated Ptolemy (it was first devised by Eudoxus of Cnidus; by the time of Copernicus it was associated with Averroes). Also popular with astronomers were variations such as eccentrics—by which the rotational axis was offset and not completely at the center. The planets were also made to have exhibit irregular motions that deviated from a uniform and circular path. The eccentrics of the planets motions were analyzed to have made reverse motions over periods of observations. This retrograde motion created the foundation for why these particular pathways became known as epicycles.

Ptolemy's unique contribution to this theory was the equant—a point about which the center of a planet's epicycle moved with uniform angular velocity, but which was offset from the center of its deferent. This violated one of the fundamental principles of Aristotelian cosmology—namely, that the motions of the planets should be explained in terms of uniform circular motion, and was considered a serious defect by many medieval astronomers. In Copernicus' day, the most up-to-date version of the Ptolemaic system was that of Peurbach (1423–1461) and Regiomontanus (1436–1476).

Post-Ptolemy

Since the 13th century, European scholars were well aware of problems with Ptolemaic astronomy. The debate was precipitated by the reception by Averroes' criticism of Ptolemy, and it was again revived by the recovery of Ptolemy's text and its translation into Latin in the mid-15th century. Otto E. Neugebauer in 1957 argued that the debate in 15th-century Latin scholarship must also have been informed by the criticism of Ptolemy produced after Averroes, by the Ilkhanid-era (13th to 14th centuries) Persian school of astronomy associated with the Maragheh observatory (especially the works of Al-Urdi, Al-Tusi and Ibn al-Shatir).

The state of the question as received by Copernicus is summarized in the Theoricae novae planetarum by Georg von Peuerbach, compiled from lecture notes by Peuerbach's student Regiomontanus in 1454, but not printed until 1472. Peuerbach attempts to give a new, mathematically more elegant presentation of Ptolemy's system, but he does not arrive at heliocentrism. Regiomontanus was the teacher of Domenico Maria Novara da Ferrara, who was in turn the teacher of Copernicus. There is a possibility that Regiomontanus already arrived at a theory of heliocentrism before his death in 1476, as he paid particular attention to the heliocentric theory of Aristarchus in a late work, and mentions the "motion of the Earth" in a letter.

Copernican theory

Further information: Nicolaus Copernicus

Copernicus' major work, De revolutionibus orbium coelestium - On the Revolutions of the Heavenly Spheres (first edition 1543 in Nuremberg, second edition 1566 in Basel), was a compendium of six books published during the year of his death, though he had arrived at his theory several decades earlier. The work marks the beginning of the shift away from a geocentric (and anthropocentric) universe with the Earth at its center.

Copernicus held that the Earth is another planet revolving around the fixed Sun once a year, and turning on its axis once a day. But while Copernicus put the Sun at the center of the celestial spheres, he did not put it at the exact center of the universe, but near it. Copernicus' system used only uniform circular motions, correcting what was seen by many as the chief inelegance in Ptolemy's system.

The Copernican model replaced Ptolemy's equant circles with more epicycles. 1,500 years of Ptolemy's model help create a more accurate estimate of the planets motions for Copernicus. This is the main reason that Copernicus' system had even more epicycles than Ptolemy's. The more epicycles proved to have more accurate measurements of how the planets were truly positioned, "although not enough to get excited about". The Copernican system can be summarized in several propositions, as Copernicus himself did in his early Commentariolus that he handed only to friends, probably in the 1510s. The "little commentary" was never printed. Its existence was only known indirectly until a copy was discovered in Stockholm around 1880, and another in Vienna a few years later.

The major features of Copernican theory are:

1. Heavenly motions are uniform, eternal, and circular or compounded of several circles (epicycles).
2. The center of the universe is near the Sun.
3. Around the Sun, in order, are Mercury, Venus, the Earth and Moon, Mars, Jupiter, Saturn, and the fixed stars.
4. The Earth has three motions: daily rotation, annual revolution, and annual tilting of its axis.
5. Retrograde motion of the planets is explained by the Earth's motion, which in short was also influenced by planets and other celestial bodies around Earth.
6. The distance from the Earth to the Sun is small compared to the distance to the stars.

Inspiration came to Copernicus not from observation of the planets, but from reading two authors, Cicero and Plutarch. In Cicero's writings, Copernicus found an account of the theory of Hicetas. Plutarch provided an account of the Pythagoreans Heraclides Ponticus, Philolaus, and Ecphantes. These authors had proposed a moving Earth, which did not revolve around a central Sun. Copernicus cited Aristarchus and Philolaus in an early manuscript of his book which survives, stating: "Philolaus believed in the mobility of the earth, and some even say that Aristarchus of Samos was of that opinion". For unknown reasons (although possibly out of reluctance to quote pre-Christian sources), Copernicus did not include this passage in the publication of his book.

Nicolai Copernicito Torinensis De Revolutionibus Orbium Coelestium, Libri VI (On the Revolutions of the Heavenly Spheres, in six books) (title page of 2nd edition, Basel, 1566)

Copernicus used what is now known as the Urdi lemma and the Tusi couple in the same planetary models as found in Arabic sources. Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the Commentariolus was found in an earlier work by Ibn al-Shatir (died circa 1375) of Damascus. Ibn al-Shatir's lunar and Mercury models are also identical to those of Copernicus. This has led some scholars to argue that Copernicus must have had access to some yet to be identified work on the ideas of those earlier astronomers. However, no likely candidate for this conjectured work has come to light, and other scholars have argued that Copernicus could well have developed these ideas independently of the late Islamic tradition. Nevertheless, Copernicus cited some of the Islamic astronomers whose theories and observations he used in De Revolutionibus, namely al-Battani, Thabit ibn Qurra, al-Zarqali, Averroes, and al-Bitruji.

De revolutionibus orbium coelestium

When Copernicus' compendium was published, it contained an unauthorized, anonymous preface by a friend of Copernicus, the Lutheran theologian Andreas Osiander. This cleric stated that Copernicus wrote his heliocentric account of the Earth's movement as a mathematical hypothesis, not as an account that contained truth or even probability. Since Copernicus' hypothesis was believed to contradict the Old Testament account of the Sun's movement around the Earth (Joshua 10:12-13), this was apparently written to soften any religious backlash against the book. However, there is no evidence that Copernicus himself considered the heliocentric model as merely mathematically convenient, separate from reality.

Copernicus' actual compendium began with a letter from his (by then deceased) friend Nikolaus von Schönberg, Cardinal Archbishop of Capua, urging Copernicus to publish his theory. Then, in a lengthy introduction, Copernicus dedicated the book to Pope Paul III, explaining his ostensible motive in writing the book as relating to the inability of earlier astronomers to agree on an adequate theory of the planets, and noting that if his system increased the accuracy of astronomical predictions it would allow the Church to develop a more accurate calendar. At that time, a reform of the Julian Calendar was considered necessary and was one of the major reasons for the Church's interest in astronomy.

The work itself is divided into six books:

1. The first is a general vision of the heliocentric theory, and a summarized exposition of his idea of the World.
2. The second is mainly theoretical, presenting the principles of spherical astronomy and a list of stars (as a basis for the arguments developed in the subsequent books).
3. The third is mainly dedicated to the apparent motions of the Sun and to related phenomena.
4. The fourth is a description of the Moon and its orbital motions.
5. The fifth is a concrete exposition of the new system, including planetary longitude.
6. The sixth is further concrete exposition of the new system, including planetary latitude.

Early criticisms

Statue of Copernicus next to Cracow University's Collegium Novum

From publication until about 1700, few astronomers were convinced by the Copernican system, though the work was relatively widely circulated (around 500 copies of the first and second editions have survived, which is a large number by the scientific standards of the time). Few of Copernicus' contemporaries were ready to concede that the Earth actually moved. Even forty-five years after the publication of De Revolutionibus, the astronomer Tycho Brahe went so far as to construct a cosmology precisely equivalent to that of Copernicus, but with the Earth held fixed in the center of the celestial sphere instead of the Sun. It was another generation before a community of practicing astronomers appeared who accepted heliocentric cosmology.

For his contemporaries, the ideas presented by Copernicus were not markedly easier to use than the geocentric theory and did not produce more accurate predictions of planetary positions. Copernicus was aware of this and could not present any observational "proof", relying instead on arguments about what would be a more complete and elegant system. The Copernican model appeared to be contrary to common sense and to contradict the Bible.

Tycho Brahe's arguments against Copernicus are illustrative of the physical, theological, and even astronomical grounds on which heliocentric cosmology was rejected. Tycho, arguably the most accomplished astronomer of his time, appreciated the elegance of the Copernican system, but objected to the idea of a moving Earth on the basis of physics, astronomy, and religion. The Aristotelian physics of the time (modern Newtonian physics was still a century away) offered no physical explanation for the motion of a massive body like Earth, but could easily explain the motion of heavenly bodies by postulating that they were made of a different sort of substance called aether that moved naturally. So Tycho said that the Copernican system “... expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy. On no point does it offend the principle of mathematics. Yet it ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches, and a triple motion at that.” Thus many astronomers accepted some aspects of Copernicus's theory at the expense of others.

Copernican Revolution

The Copernican Revolution, a paradigm shift from the Ptolemaic model of the heavens, which described the cosmos as having Earth as a stationary body at the center of the universe, to the heliocentric model with the Sun at the center of the Solar System, spanned over a century, beginning with the publication of Copernus' De revolutionibus orbium coelestium and ending with the work of Isaac Newton. While not warmly received by his contemporaries, his model did have a large influence on later scientists such as Galileo and Johannes Kepler, who adopted, championed and (especially in Kepler's case) sought to improve it. However, in the years following publication of de Revolutionibus, for leading astronomers such as Erasmus Reinhold, the key attraction of Copernicus's ideas was that they reinstated the idea of uniform circular motion for the planets.

During the 17th century, several further discoveries eventually led to the wider acceptance of heliocentrism:

• Kepler in 1609 introduced the idea in his Astronomia nova that the orbits of the planets were elliptical rather than circular, while retaining the heliocentric concept.
• Using the newly invented telescope, in 1610 Galileo discovered the four large moons of Jupiter (evidence that the Solar System contained bodies that did not orbit Earth), the phases of Venus (the first observational evidence not properly explained by the Ptolemaic theory) and the rotation of the Sun about a fixed axis as indicated by the apparent annual variation in the motion of sunspots;
• With a telescope, Giovanni Zupi saw the phases of Mercury in 1639;
• Isaac Newton in 1687 proposed universal gravity and the inverse-square law of gravitational attraction to explain Kepler's elliptical planetary orbits.

Modern views

Substantially correct

From a modern point of view, the Copernican model has a number of advantages. It accurately predicts the relative distances of the planets from the Sun, although this meant abandoning the cherished Aristotelian idea that there is no empty space between the planetary spheres. Copernicus also gave a clear account of the cause of the seasons: that the Earth's axis is not perpendicular to the plane of its orbit. In addition, Copernicus's theory provided a strikingly simple explanation for the apparent retrograde motions of the planets—namely as parallactic displacements resulting from the Earth's motion around the Sun—an important consideration in Johannes Kepler's conviction that the theory was substantially correct. In the heliocentric model the planets' apparent retrograde motions' occurring at opposition to the Sun are a natural consequence of their heliocentric orbits. In the geocentric model, however, these are explained by the ad hoc use of epicycles, whose revolutions are mysteriously tied to that of the Sun's.

Modern historiography

Whether Copernicus' propositions were "revolutionary" or "conservative" has been a topic of debate in the historiography of science. In his book The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959), Arthur Koestler attempted to deconstruct the Copernican "revolution" by portraying Copernicus as a coward who was reluctant to publish his work due to a crippling fear of ridicule. Thomas Kuhn argued that Copernicus only transferred "some properties to the Sun's many astronomical functions previously attributed to the earth." Historians have since argued that Kuhn underestimated what was "revolutionary" about Copernicus' work, and emphasized the difficulty Copernicus would have had in putting forward a new astronomical theory relying alone on simplicity in geometry, given that he had no experimental evidence.

 

Observable universe

From Wikipedia, the free encyclopedia

 

 

Observable universe

Visualization of the whole observable universe. The scale is such that the fine grains represent collections of large numbers of superclusters. The Virgo Supercluster—home of Milky Way—is marked at the center, but is too small to be seen.
Diameter	8.8×1026 m or 880 Ym (28.5 Gpc or 93 Gly)
Volume	3.566×1080 m3
Mass (ordinary matter)	1.5×1053 kg
Density (of total energy)	9.9×10−27 kg/m3 (equivalent to 6 protons per cubic meter of space)
Age	13.799±0.021 billion years
Average temperature	2.72548 K
Contents	Ordinary (baryonic) matter (4.9%) Dark matter (26.8%) Dark energy (68.3%)

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 has recently been estimated at only several hundred billion based on new 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 has a spherical volume (a ball) 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.

The word observable in this sense does not refer to the capability of modern technology to detect light or other information from an object, or whether there is anything to be detected. It refers to the physical limit created by the speed of light itself. No signal can travel faster than light, hence there is a maximum distance (called the particle horizon) beyond which nothing can be detected, as the signals could not have reached us yet. Sometimes astrophysicists distinguish between the visible universe, which includes only signals emitted since recombination (when hydrogen atoms were formed from protons and electrons and photons were emitted)—and the observable universe, which includes signals since the beginning of the cosmological expansion (the Big Bang in traditional physical cosmology, the end of the inflationary epoch in modern cosmology).

According to calculations, the current comoving distance—proper distance, which takes into account that the universe has expanded since the light was emitted—to particles from which the cosmic microwave background radiation (CMBR) was emitted, which represents the radius of the visible universe, is about 14.0 billion parsecs (about 45.7 billion light-years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light-years), about 2% larger. The radius of the observable universe is therefore estimated to be about 46.5 billion light-years and its diameter about 28.5 gigaparsecs (93 billion light-years, or 8.8×10²⁶ metres or 2.89×10²⁷ feet), which equals 880 yottametres. Using the critical density and the diameter of the observable universe, the total mass of ordinary matter in the universe can be calculated to be about 1.5 × 10⁵³ kg. In November 2018, astronomers reported that the extragalactic background light (EBL) amounted to 4 × 10⁸⁴ photons.

As the universe's expansion is accelerating, all currently observable objects, outside our local supercluster, will eventually appear to freeze in time, while emitting progressively redder and fainter light. For instance, objects with the current redshift z from 5 to 10 will remain observable for no more than 4–6 billion years. In addition, light emitted by objects currently situated beyond a certain comoving distance (currently about 19 billion parsecs) will never reach Earth.

The universe versus the observable universe

The size of the whole universe is unknown, and it might be infinite in extent. Some parts of the universe are too far away for the light emitted since the Big Bang to have had enough time to reach Earth or space-based instruments, and therefore lie outside the observable universe. In the future, light from distant galaxies will have had more time to travel, so additional regions will become observable. However, owing to Hubble's law, regions sufficiently distant from the Earth are expanding away from it faster than the speed of light (special relativity prevents nearby objects in the same local region from moving faster than the speed of light with respect to each other, but there is no such constraint for distant objects when the space between them is expanding; see uses of the proper distance for a discussion) and furthermore the expansion rate appears to be accelerating owing to dark energy.

Assuming dark energy remains constant (an unchanging cosmological constant), so that the expansion rate of the universe continues to accelerate, there is a "future visibility limit" beyond which objects will never enter our observable universe at any time in the infinite future, because light emitted by objects outside that limit could never reach the Earth. (A subtlety is that, because the Hubble parameter is decreasing with time, there can be cases where a galaxy that is receding from the Earth just a bit faster than light does emit a signal that reaches the Earth eventually.) This future visibility limit is calculated at a comoving distance of 19 billion parsecs (62 billion light-years), assuming the universe will keep expanding forever, which implies the number of galaxies that we can ever theoretically observe in the infinite future (leaving aside the issue that some may be impossible to observe in practice due to redshift, as discussed in the following paragraph) is only larger than the number currently observable by a factor of 2.36.^{[note 2]}

Artist's logarithmic scale conception of the observable universe with the Solar System at the center, inner and outer planets, Kuiper belt, Oort cloud, Alpha Centauri, Perseus Arm, Milky Way galaxy, Andromeda Galaxy, nearby galaxies, Cosmic web, Cosmic microwave radiation and the Big Bang's invisible plasma on the edge. Celestial bodies appear enlarged to appreciate their shapes.

Though, in principle, more galaxies will become observable in the future, in practice, an increasing number of galaxies will become extremely redshifted due to ongoing expansion; so much so that they will seem to disappear from view and become invisible. An additional subtlety is that a galaxy at a given comoving distance is defined to lie within the "observable universe" if we can receive signals emitted by the galaxy at any age in its past history (say, a signal sent from the galaxy only 500 million years after the Big Bang), but because of the universe's expansion, there may be some later age at which a signal sent from the same galaxy can never reach the Earth at any point in the infinite future (so, for example, we might never see what the galaxy looked like 10 billion years after the Big Bang), even though it remains at the same comoving distance (comoving distance is defined to be constant with time—unlike proper distance, which is used to define recession velocity due to the expansion of space), which is less than the comoving radius of the observable universe. This fact can be used to define a type of cosmic event horizon whose distance from the Earth changes over time. For example, the current distance to this horizon is about 16 billion light-years, meaning that a signal from an event happening at present can eventually reach the Earth in the future if the event is less than 16 billion light-years away, but the signal will never reach the Earth if the event is more than 16 billion light-years away.

Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe". This can be justified on the grounds that we can never know anything by direct experimentation about any part of the universe that is causally disconnected from the Earth, although many credible theories require a total universe much larger than the observable universe. No evidence exists to suggest that the boundary of the observable universe constitutes a boundary on the universe as a whole, nor do any of the mainstream cosmological models propose that the universe has any physical boundary in the first place, though some models propose it could be finite but unbounded, like a higher-dimensional analogue of the 2D surface of a sphere that is finite in area but has no edge.

It is plausible that the galaxies within our observable universe represent only a minuscule fraction of the galaxies in the universe. According to the theory of cosmic inflation initially introduced by its founders, Alan Guth and D. Kazanas, if it is assumed that inflation began about 10⁻³⁷ seconds after the Big Bang, then with the plausible assumption that the size of the universe before the inflation occurred was approximately equal to the speed of light times its age, that would suggest that at present the entire universe's size is at least 3 × 10²³ (1.5 × 10³⁴ light-years) times the radius of the observable universe.

If the universe is finite but unbounded, it is also possible that the universe is smaller than the observable universe. In this case, what we take to be very distant galaxies may actually be duplicate images of nearby galaxies, formed by light that has circumnavigated the universe. It is difficult to test this hypothesis experimentally because different images of a galaxy would show different eras in its history, and consequently might appear quite different. Bielewicz et al. claim to establish a lower bound of 27.9 gigaparsecs (91 billion light-years) on the diameter of the last scattering surface (since this is only a lower bound, since the whole universe is possibly much larger, even infinite). This value is based on matching-circle analysis of the WMAP 7 year data. This approach has been disputed.

Size

Hubble Ultra-Deep Field image of a region of the observable universe (equivalent sky area size shown in bottom left corner), near the constellation Fornax. Each spot is a galaxy, consisting of billions of stars. The light from the smallest, most redshifted galaxies originated nearly 14 billion years ago.

The comoving distance from Earth to the edge of the observable universe is about 14.26 gigaparsecs (46.5 billion light-years or 4.40×10²⁶ m) in any direction. The observable universe is thus a sphere with a diameter of about 28.5 gigaparsecs (93 billion light-years or 8.8×10²⁶ m). Assuming that space is roughly flat (in the sense of being a Euclidean space), this size corresponds to a comoving volume of about 1.22×10⁴ Gpc³ (4.22×10⁵ Gly³ or 3.57×10⁸⁰ m³).

The figures quoted above are distances now (in cosmological time), not distances at the time the light was emitted. For example, the cosmic microwave background radiation that we see right now was emitted at the time of photon decoupling, estimated to have occurred about 380,000 years after the Big Bang, which occurred around 13.8 billion years ago. This radiation was emitted by matter that has, in the intervening time, mostly condensed into galaxies, and those galaxies are now calculated to be about 46 billion light-years from us. To estimate the distance to that matter at the time the light was emitted, we may first note that according to the Friedmann–Lemaître–Robertson–Walker metric, which is used to model the expanding universe, if at the present time we receive light with a redshift of z, then the scale factor at the time the light was originally emitted is given by

${\displaystyle \!a(t)={\frac {1}{1+z}}}$.

WMAP nine-year results combined with other measurements give the redshift of photon decoupling as z = 1091.64±0.47, which implies that the scale factor at the time of photon decoupling would be 1⁄1092.64. So if the matter that originally emitted the oldest cosmic microwave background (CMBR) photons has a present distance of 46 billion light-years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years.

The light-travel distance to the edge of the observable universe is the age of the Universe divided by the speed of light, 13.8 billion light years. This is the distance that a photon emitted shortly after the Big Bang, such as one from the cosmic microwave background, has travelled to reach observers on Earth. Because spacetime is curved, corresponding to the expansion of space, this distance does not correspond to the true distance at any moment in time.

Large-scale structure

Galaxy clusters, like RXC J0142.9+4438, are the nodes of the cosmic web that permeates the entire Universe.

 

Play media

Video of a cosmological simulation of the local universe, showing large-scale structure of clusters of galaxies and dark matter

Sky surveys and mappings of the various wavelength bands of electromagnetic radiation (in particular 21-cm emission) have yielded much information on the content and character of the universe's structure. The organization of structure appears to follow a hierarchical model with organization up to the scale of superclusters and filaments. Larger than this (at scales between 30 and 200 megaparsecs), there seems to be no continued structure, a phenomenon that has been referred to as the End of Greatness.

Walls, filaments, nodes, and voids

Map of the cosmic web generated from a slime mould-inspired algorithm

 

DTFE reconstruction of the inner parts of the 2dF Galaxy Redshift Survey

The organization of structure arguably begins at the stellar level, though most cosmologists rarely address astrophysics on that scale. Stars are organized into galaxies, which in turn form galaxy groups, galaxy clusters, superclusters, sheets, walls and filaments, which are separated by immense voids, creating a vast foam-like structure sometimes called the "cosmic web". Prior to 1989, it was commonly assumed that virialized galaxy clusters were the largest structures in existence, and that they were distributed more or less uniformly throughout the universe in every direction. However, since the early 1980s, more and more structures have been discovered. In 1983, Adrian Webster identified the Webster LQG, a large quasar group consisting of 5 quasars. The discovery was the first identification of a large-scale structure, and has expanded the information about the known grouping of matter in the universe.

In 1987, Robert Brent Tully identified the Pisces–Cetus Supercluster Complex, the galaxy filament in which the Milky Way resides. It is about 1 billion light-years across. That same year, an unusually large region with a much lower than average distribution of galaxies was discovered, the Giant Void, which measures 1.3 billion light-years across. Based on redshift survey data, in 1989 Margaret Geller and John Huchra discovered the "Great Wall", a sheet of galaxies more than 500 million light-years long and 200 million light-years wide, but only 15 million light-years thick. The existence of this structure escaped notice for so long because it requires locating the position of galaxies in three dimensions, which involves combining location information about the galaxies with distance information from redshifts. Two years later, astronomers Roger G. Clowes and Luis E. Campusano discovered the Clowes–Campusano LQG, a large quasar group measuring two billion light-years at its widest point which was the largest known structure in the universe at the time of its announcement. In April 2003, another large-scale structure was discovered, the Sloan Great Wall. In August 2007, a possible supervoid was detected in the constellation Eridanus. It coincides with the 'CMB cold spot', a cold region in the microwave sky that is highly improbable under the currently favored cosmological model. This supervoid could cause the cold spot, but to do so it would have to be improbably big, possibly a billion light-years across, almost as big as the Giant Void mentioned above.

Unsolved problem in physics:

The largest structures in the universe are larger than expected. Are these actual structures or random density fluctuations?

(more unsolved problems in physics)

Computer simulated image of an area of space more than 50 million light-years across, presenting a possible large-scale distribution of light sources in the universe—precise relative contributions of galaxies and quasars are unclear.

Another large-scale structure is the SSA22 Protocluster, a collection of galaxies and enormous gas bubbles that measures about 200 million light-years across.

In 2011, a large quasar group was discovered, U1.11, measuring about 2.5 billion light-years across. On January 11, 2013, another large quasar group, the Huge-LQG, was discovered, which was measured to be four billion light-years across, the largest known structure in the universe at that time. In November 2013, astronomers discovered the Hercules–Corona Borealis Great Wall, an even bigger structure twice as large as the former. It was defined by the mapping of gamma-ray bursts.

In 2021, the American Astronomical Society announced the detection of the Giant Arc; a crescent-shaped string of galaxies that span 3.3 billion light years in length, located 9.2 billion light years from Earth in the constellation Boötes from observations captured by the Sloan Digital Sky Survey.

End of Greatness

The End of Greatness is an observational scale discovered at roughly 100 Mpc (roughly 300 million light-years) where the lumpiness seen in the large-scale structure of the universe is homogenized and isotropized in accordance with the Cosmological Principle. At this scale, no pseudo-random fractalness is apparent. The superclusters and filaments seen in smaller surveys are randomized to the extent that the smooth distribution of the universe is visually apparent. It was not until the redshift surveys of the 1990s were completed that this scale could accurately be observed.

Observations

"Panoramic view of the entire near-infrared sky reveals the distribution of galaxies beyond the Milky Way. The image is derived from the 2MASS Extended Source Catalog (XSC)—more than 1.5 million galaxies, and the Point Source Catalog (PSC)—nearly 0.5 billion Milky Way stars. The galaxies are color-coded by 'redshift' obtained from the UGC, CfA, Tully NBGC, LCRS, 2dF, 6dFGS, and SDSS surveys (and from various observations compiled by the NASA Extragalactic Database), or photo-metrically deduced from the K band (2.2 μm). Blue are the nearest sources (z < 0.01); green are at moderate distances (0.01 < z < 0.04) and red are the most distant sources that 2MASS resolves (0.04 < z < 0.1). The map is projected with an equal area Aitoff in the Galactic system (Milky Way at center)."

Another indicator of large-scale structure is the 'Lyman-alpha forest'. This is a collection of absorption lines that appear in the spectra of light from quasars, which are interpreted as indicating the existence of huge thin sheets of intergalactic (mostly hydrogen) gas. These sheets appear to collapse into filaments, which can feed galaxies as they grow where filaments either cross or are overdense. An early direct evidence for this cosmic web of gas was the 2019 detection, by astronomers from the RIKEN Cluster for Pioneering Research in Japan and Durham University in the U.K., of light from the very brightest part of this web, surrounding and illuminated by a cluster of forming galaxies, acting as cosmic flashlights for intercluster medium hydrogen fluorescence via Lyman-alpha emissions.

In 2021, an international team, headed by Roland Bacon from the Centre de Recherche Astrophysique de Lyon, reported the first observation of diffuse extended Lyman-alpha emission from redshift 3.1 to 4.5 that traced several cosmic web filaments on scales of 2.5−4 cMpc, in filamentary environments outside massive structures typical of web nodes.

Some caution is required in describing structures on a cosmic scale because things are often different from how they appear. Gravitational lensing (bending of light by gravitation) can make an image appear to originate in a different direction from its real source. This is caused when foreground objects (such as galaxies) curve surrounding spacetime (as predicted by general relativity), and deflect passing light rays. Rather usefully, strong gravitational lensing can sometimes magnify distant galaxies, making them easier to detect. Weak lensing (gravitational shear) by the intervening universe in general also subtly changes the observed large-scale structure.

The large-scale structure of the universe also looks different if one only uses redshift to measure distances to galaxies. For example, galaxies behind a galaxy cluster are attracted to it, and so fall towards it, and so are slightly blueshifted (compared to how they would be if there were no cluster) On the near side, things are slightly redshifted. Thus, the environment of the cluster looks somewhat squashed if using redshifts to measure distance. An opposite effect works on the galaxies already within a cluster: the galaxies have some random motion around the cluster center, and when these random motions are converted to redshifts, the cluster appears elongated. This creates a "finger of God"—the illusion of a long chain of galaxies pointed at the Earth.

Cosmography of Earth's cosmic neighborhood

At the centre of the Hydra-Centaurus Supercluster, a gravitational anomaly called the Great Attractor affects the motion of galaxies over a region hundreds of millions of light-years across. These galaxies are all redshifted, in accordance with Hubble's law. This indicates that they are receding from us and from each other, but the variations in their redshift are sufficient to reveal the existence of a concentration of mass equivalent to tens of thousands of galaxies.

The Great Attractor, discovered in 1986, lies at a distance of between 150 million and 250 million light-years (250 million is the most recent estimate), in the direction of the Hydra and Centaurus constellations. In its vicinity there is a preponderance of large old galaxies, many of which are colliding with their neighbours, or radiating large amounts of radio waves.

In 1987, astronomer R. Brent Tully of the University of Hawaii's Institute of Astronomy identified what he called the Pisces–Cetus Supercluster Complex, a structure one billion light-years long and 150 million light-years across in which, he claimed, the Local Supercluster was embedded.

Mass of ordinary matter

The mass of the observable universe is often quoted as 10⁵⁰ tonnes or 10⁵³ kg. In this context, mass refers to ordinary matter and includes the interstellar medium (ISM) and the intergalactic medium (IGM). However, it excludes dark matter and dark energy. This quoted value for the mass of ordinary matter in the universe can be estimated based on critical density. The calculations are for the observable universe only as the volume of the whole is unknown and may be infinite.

Estimates based on critical density

Critical density is the energy density for which the universe is flat. If there is no dark energy, it is also the density for which the expansion of the universe is poised between continued expansion and collapse. From the Friedmann equations, the value for ${\displaystyle \rho _{c}}$ critical density, is:

${\displaystyle \rho _{c}={\frac {3H^{2}}{8\pi G}},}$

where G is the gravitational constant and H = H₀ is the present value of the Hubble constant. The value for H₀, due to the European Space Agency's Planck Telescope, is H₀ = 67.15 kilometres per second per megaparsec. This gives a critical density of 0.85×10⁻²⁶ kg/m³ (commonly quoted as about 5 hydrogen atoms per cubic metre). This density includes four significant types of energy/mass: ordinary matter (4.8%), neutrinos (0.1%), cold dark matter (26.8%), and dark energy (68.3%). Although neutrinos are Standard Model particles, they are listed separately because they are ultra-relativistic and hence behave like radiation rather than like matter. The density of ordinary matter, as measured by Planck, is 4.8% of the total critical density or 4.08×10⁻²⁸ kg/m³. To convert this density to mass we must multiply by volume, a value based on the radius of the "observable universe". Since the universe has been expanding for 13.8 billion years, the comoving distance (radius) is now about 46.6 billion light-years. Thus, volume (4/3πr³) equals 3.58×10⁸⁰ m³ and the mass of ordinary matter equals density (4.08×10⁻²⁸ kg/m³) times volume (3.58×10⁸⁰ m³) or 1.46×10⁵³ kg.

Matter content—number of atoms

Main article: Abundance of the chemical elements

Assuming the mass of ordinary matter is about 1.45×10⁵³ kg as discussed above, and assuming all atoms are hydrogen atoms (which are about 74% of all atoms in our galaxy by mass, see Abundance of the chemical elements), the estimated total number of atoms in the observable universe is obtained by dividing the mass of ordinary matter by the mass of a hydrogen atom (1.45×10⁵³ kg divided by 1.67×10⁻²⁷ kg). The result is approximately 10⁸⁰ hydrogen atoms, also known as the Eddington number.

Most distant objects

Main article: List of the most distant astronomical objects

The most distant astronomical object identified (as at 2016) is a galaxy classified GN-z11. In 2009, a gamma ray burst, GRB 090423, was found to have a redshift of 8.2, which indicates that the collapsing star that caused it exploded when the universe was only 630 million years old. The burst happened approximately 13 billion years ago, so a distance of about 13 billion light-years was widely quoted in the media (or sometimes a more precise figure of 13.035 billion light-years), though this would be the "light travel distance" rather than the "proper distance" used in both Hubble's law and in defining the size of the observable universe (cosmologist Ned Wright argues against the common use of light travel distance in astronomical press releases on this page, and at the bottom of the page offers online calculators that can be used to calculate the current proper distance to a distant object in a flat universe based on either the redshift z or the light travel time). The proper distance for a redshift of 8.2 would be about 9.2 Gpc, or about 30 billion light-years. Another record-holder for most distant object is a galaxy observed through and located beyond Abell 2218, also with a light travel distance of approximately 13 billion light-years from Earth, with observations from the Hubble telescope indicating a redshift between 6.6 and 7.1, and observations from Keck telescopes indicating a redshift towards the upper end of this range, around 7. The galaxy's light now observable on Earth would have begun to emanate from its source about 750 million years after the Big Bang.

Horizons

Main article: List of cosmological horizons

The limit of observability in our universe is set by a set of cosmological horizons which limit—based on various physical constraints—the extent to which we can obtain information about various events in the universe. The most famous horizon is the particle horizon which sets a limit on the precise distance that can be seen due to the finite age of the universe. Additional horizons are associated with the possible future extent of observations (larger than the particle horizon owing to the expansion of space), an "optical horizon" at the surface of last scattering, and associated horizons with the surface of last scattering for neutrinos and gravitational waves.

Steady-state model

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Steady-state_model

In cosmology, the steady-state model is an alternative to the Big Bang theory of evolution of the universe. In the steady-state model, the density of matter in the expanding universe remains unchanged due to a continuous creation of matter, thus adhering to the perfect cosmological principle, a principle that asserts that the observable universe is practically the same at any time and any place.

While the steady-state model enjoyed some minority support in the scientific mainstream until the mid-20th century, it is now rejected by the vast majority of cosmologists, astrophysicists and astronomers, as the observational evidence points to a hot Big Bang cosmology with a finite age of the universe, which the steady-state model does not predict.

History

In the 13th century, Siger of Brabant authored the thesis The Eternity of the World, which argued that there was no first man, and no first specimen of any particular: the physical universe is thus without any first beginning, and therefore eternal. Siger's views were condemned by the pope in 1277.

Cosmological expansion was originally discovered through observations by Edwin Hubble. Theoretical calculations also showed that the static universe as modeled by Einstein (1917) was unstable. The modern Big Bang theory is one in which the universe has a finite age and has evolved over time through cooling, expansion, and the formation of structures through gravitational collapse.

The steady-state model asserts that although the universe is expanding, it nevertheless does not change its appearance over time (the perfect cosmological principle); the universe has no beginning and no end. This required that matter be continually created in order to keep the universe's density from decreasing. Influential papers on steady-state cosmologies were published by Hermann Bondi, Thomas Gold, and Fred Hoyle in 1948. Similar models had been proposed earlier by William Duncan MacMillan, among others.

It is now known that Albert Einstein considered a steady-state model of the expanding universe, as indicated in a 1931 manuscript, many years before Hoyle, Bondi and Gold. However, he quickly abandoned the idea.

Observational tests

Counts of radio sources

See also: Source counts

Problems with the steady-state model began to emerge in the 1950s and 60s, when observations began to support the idea that the universe was in fact changing: bright radio sources (quasars and radio galaxies) were found only at large distances (therefore could have existed only in the distant past), not in closer galaxies. Whereas the Big Bang theory predicted as much, the steady-state model predicted that such objects would be found throughout the universe, including close to our own galaxy. By 1961, statistical tests based on radio-source surveys had ruled out the steady-state model in the minds of most cosmologists, although some proponents of the steady state insisted that the radio data were suspect.

Cosmic microwave background

For most cosmologists, the definitive refutation of the steady-state model came with the discovery of the cosmic microwave background radiation in 1964, which was predicted by the Big Bang theory. The steady-state model explained microwave background radiation as the result of light from ancient stars that has been scattered by galactic dust. However, the cosmic microwave background level is very even in all directions, making it difficult to explain how it could be generated by numerous point sources, and the microwave background radiation shows no evidence of characteristics such as polarization that are normally associated with scattering. Furthermore, its spectrum is so close to that of an ideal black body that it could hardly be formed by the superposition of contributions from a multitude of dust clumps at different temperatures as well as at different redshifts. Steven Weinberg wrote in 1972,

The steady state model does not appear to agree with the observed d_L versus z relation or with source counts ... In a sense, this disagreement is a credit to the model; alone among all cosmologies, the steady state model makes such definite predictions that it can be disproved even with the limited observational evidence at our disposal. The steady state model is so attractive that many of its adherents still retain hope that the evidence against it will eventually disappear as observations improve. However, if the cosmic microwave radiation ... is really black-body radiation, it will be difficult to doubt that the universe has evolved from a hotter denser early stage.

Since this discovery, the Big Bang theory has been considered to provide the best explanation of the origin of the universe. In most astrophysical publications, the Big Bang is implicitly accepted and is used as the basis of more complete theories.

Quasi-steady state

Quasi-steady-state cosmology (QSS) was proposed in 1993 by Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar as a new incarnation of the steady-state ideas meant to explain additional features unaccounted for in the initial proposal. The model suggests pockets of creation occurring over time within the universe, sometimes referred to as minibangs, mini-creation events, or little bangs. After the observation of an accelerating universe, further modifications of the model were made. The Planck particle is a hypothetical black hole whose Schwarzschild radius is approximately the same as its Compton wavelength; the evaporation of such a particle has been evoked as the source of light elements in an expanding steady-state universe.

Astrophysicist and cosmologist Ned Wright has pointed out flaws in the model. These first comments were soon rebutted by the proponents. Wright and other mainstream cosmologists reviewing QSS have pointed out new flaws and discrepancies with observations left unexplained by proponents.

Cosmological principle

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Cosmological_principle 

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.

Definition

Astronomer William Keel explains:

The cosmological principle is usually stated formally as 'Viewed on a sufficiently large scale, the properties of the universe are the same for all observers.' This amounts to the strongly philosophical statement that the part of the universe which we can see is a fair sample, and that the same physical laws apply throughout. In essence, this in a sense says that the universe is knowable and is playing fair with scientists.

The cosmological principle depends on a definition of "observer," and contains an implicit qualification and two testable consequences.

"Observers" means any observer at any location in the universe, not simply any human observer at any location on Earth: as Andrew Liddle puts it, "the cosmological principle [means that] the universe looks the same whoever and wherever you are."

The qualification is that variation in physical structures can be overlooked, provided this does not imperil the uniformity of conclusions drawn from observation: the Sun is different from the Earth, our galaxy is different from a black hole, some galaxies advance toward rather than recede from us, and the universe has a "foamy" texture of galaxy clusters and voids, but none of these different structures appears to violate the basic laws of physics.

The two testable structural consequences of the cosmological principle are homogeneity and isotropy. Homogeneity means that the same observational evidence is available to observers at different locations in the universe ("the part of the universe which we can see is a fair sample"). Isotropy means that the same observational evidence is available by looking in any direction in the universe ("the same physical laws apply throughout"). The principles are distinct but closely related, because a universe that appears isotropic from any two (for a spherical geometry, three) locations must also be homogeneous.

Origin

The cosmological principle is first clearly asserted in the Philosophiæ Naturalis Principia Mathematica (1687) of Isaac Newton. In contrast to earlier classical or medieval cosmologies, in which Earth rested at the center of universe, Newton conceptualized the Earth as a sphere in orbital motion around the Sun within an empty space that extended uniformly in all directions to immeasurably large distances. He then showed, through a series of mathematical proofs on detailed observational data of the motions of planets and comets, that their motions could be explained by a single principle of "universal gravitation" that applied as well to the orbits of the Galilean moons around Jupiter, the Moon around the Earth, the Earth around the Sun, and to falling bodies on Earth. That is, he asserted the equivalent material nature of all bodies within the Solar System, the identical nature of the Sun and distant stars and thus the uniform extension of the physical laws of motion to a great distance beyond the observational location of Earth itself.

Implications

Observations show that more distant galaxies are closer together and have lower content of chemical elements heavier than lithium. Applying the cosmological principle, this suggests that heavier elements were not created in the Big Bang but were produced by nucleosynthesis in giant stars and expelled across a series of supernovae explosions and new star formation from the supernovae remnants, which means heavier elements would accumulate over time. Another observation is that the furthest galaxies (earlier time) are often more fragmentary, interacting and unusually shaped than local galaxies (recent time), suggesting evolution in galaxy structure as well.

A related implication of the cosmological principle is that the largest discrete structures in the universe are in mechanical equilibrium. Homogeneity and isotropy of matter at the largest scales would suggest that the largest discrete structures are parts of a single indiscrete form, like the crumbs which make up the interior of a cake. At extreme cosmological distances, the property of mechanical equilibrium in surfaces lateral to the line of sight can be empirically tested; however, under the assumption of the cosmological principle, it cannot be detected parallel to the line of sight.

Cosmologists agree that in accordance with observations of distant galaxies, a universe must be non-static if it follows the cosmological principle. In 1923, Alexander Friedmann set out a variant of Albert Einstein's equations of general relativity that describe the dynamics of a homogeneous isotropic universe. Independently, Georges Lemaître derived in 1927 the equations of an expanding universe from the General Relativity equations. Thus, a non-static universe is also implied, independent of observations of distant galaxies, as the result of applying the cosmological principle to general relativity.

Criticism

Karl Popper criticized the cosmological principle on the grounds that it makes "our lack of knowledge a principle of knowing something". He summarized his position as:

the “cosmological principles” were, I fear, dogmas that should not have been proposed.

Observations

Although the universe is inhomogeneous at smaller scales, it is statistically homogeneous on scales larger than 250 million light years. The cosmic microwave background is isotropic, that is to say that its intensity is about the same whichever direction we look at.

However, recent findings have called this view into question. Data from the Planck Mission shows hemispheric bias in 2 respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies are, in fact, statistically significant and can no longer be ignored.

Inconsistencies

The cosmological principle implies that at a sufficiently large scale, the universe is homogeneous. Based on N-body simulations in a ΛCDM universe, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260/h Mpc or more.

A number of observations have been reported to be in conflict with predictions of maximal structure sizes:

• The Clowes–Campusano LQG, discovered in 1991, has a length of 580 Mpc, and is marginally larger than the consistent scale.
• The Sloan Great Wall, discovered in 2003, has a length of 423 Mpc, which is only just consistent with the cosmological principle.
• U1.11, a large quasar group discovered in 2011, has a length of 780 Mpc, and is two times larger than the upper limit of the homogeneity scale.
• The Huge-LQG, discovered in 2012, is three times longer than, and twice as wide as is predicted possible according to these current models, and so challenges our understanding of the universe on large scales.
• In November 2013, a new structure 10 billion light years away measuring 2000–3000 Mpc (more than seven times that of the SGW) has been discovered, the Hercules–Corona Borealis Great Wall, putting further doubt on the validity of the cosmological principle.
• In June 2021, the Giant Arc was discovered, a structure spanning approximately 1000 Mpc. It is located 2820 MPc away and consists of galaxies, galactic clusters, gas, and dust.

However, as pointed out by Seshadri Nadathur in 2013, the existence of structures larger than the homogeneous scale (260/h Mpc by Yadav's estimation) does not necessarily violate the cosmological principle.

While the isotropy of the universe around Earth is confirmed at high significance by studies of the cosmic microwave background temperature maps, its homogeneity over cosmological scales is still a matter of debate.

Cosmic Dipole

As stated above, it is true that the cosmic microwave background provides a snapshot of an isotropic and homogeneous universe. Nevertheless, what is often not advertised is that there is a dipole anisotropy in the cosmic microwave background. The amplitude of the dipole exceeds the amplitudes of the other temperature fluctuations, and for this reason, it is subtracted on the assumption that it is a Doppler effect, or simply due to relative motion. In recent years this assumption has been tested and current results suggest our motion with respect to distant radio galaxies  and quasars  differs from our motion with respect to the cosmic microwave background. The same conclusion has been reached in recent studies of the Hubble diagram of Type Ia supernovae and quasars. This contradicts the cosmological principle and challenges the assumption that the CMB dipole is simply due to relative motion.

This potential misinterpretation of the CMB dipole is hinted at through a number of other observations. First, even within the cosmic microwave background, there are curious directional alignments and an anomalous parity asymmetry  that may have an origin in the CMB dipole. Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations, scaling relations in galaxy clusters, strong lensing time delay, Type Ia supernovae, and quasars & gamma-ray bursts as standard candles. The fact that all these independent observables, based on different physics, are tracking the CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole.

Perfect cosmological principle

The perfect cosmological principle is an extension of the cosmological principle, and states that the universe is homogeneous and isotropic in space and time. In this view the universe looks the same everywhere (on the large scale), the same as it always has and always will. The perfect cosmological principle underpins Steady State theory and emerges from chaotic inflation theory.