## Expanding Deutsch Beispielsätze für "expand"

Englisch-Deutsch-Übersetzungen für expanding im Online-Wörterbuch toshidesk.co (Deutschwörterbuch). Englisch-Deutsch-Übersetzungen für to expand im Online-Wörterbuch toshidesk.co (Deutschwörterbuch). I have expanded my computer's memory. — Ich habe den Speicher meines Computers erweitert. The company is planning to expand their product range. Viele übersetzte Beispielsätze mit "expand" – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen. Lernen Sie die Übersetzung für 'expanding' in LEOs Englisch ⇔ Deutsch Wörterbuch. Mit Flexionstabellen der verschiedenen Fälle und Zeiten ✓ Aussprache.

Lernen Sie die Übersetzung für 'expanding' in LEOs Englisch ⇔ Deutsch Wörterbuch. Mit Flexionstabellen der verschiedenen Fälle und Zeiten ✓ Aussprache. Übersetzung Englisch-Deutsch für expanding im PONS Online-Wörterbuch nachschlagen! Gratis Vokabeltrainer, Verbtabellen, Aussprachefunktion. Übersetzung für 'expanding' im kostenlosen Englisch-Deutsch Wörterbuch und viele weitere Deutsch-Übersetzungen.Want to learn more? B2 to increase in size , number , or importance , or to make something increase in this way:.

The air in the balloon expands when heated. They expanded their retail operations during the s. I don't think we should expand our business in the current economic climate.

In their second album , the band tried to expand their stylistic range. The college is not able to expand because of restrictive planning laws.

Their economy has expanded enormously , while ours, by contrast , has declined. In their efforts to reduce crime the government expanded the police force.

Enlarging and inflating. You can also find related words, phrases, and synonyms in the topics: Increasing and intensifying.

Phrasal verb expand on sth. Examples of expanding. These paths for the robot can be determined easily by expanding our analysis to more cases.

From the Cambridge English Corpus. These studies suggest an expanding role for the practice nurse within primary care. These examples are from the Cambridge English Corpus and from sources on the web.

Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.

I intend my remarks as suggestions for expanding the argument - and perhaps the research - beyond the promising start made here.

Unlike the smooth expanding maps treated just above, such maps are in general not structurally or measure-theoretically stable with respect to deterministic perturbations.

Even in the s, when demand was expanding , an excess continued to keep prices down in most salons. The second comes later this year, with three more in But the MDs have two very attractive features: They can haul a lot of cargo, and they are cheap.

With 15 already in the fleet, UPS Airlines will become by the biggest operator in the world of the , the latest — and likely last — version of the famous Jumbo Jet.

And on top of that, there are 22 Boeing s coming. UPS will add more than 12 million pounds of lift capacity to its fleet, most of it to meet growing e-commerce demand.

Rival FedEx Express is also flying most of its planes, unlike passenger carriers, with of its planes currently in service. The third largest by fleet size among U.

But while cargo carriers are flying a lot of packages, they also face a drop in demand for shipping other goods, with UPS and FedEx warning that the pandemic is hurting profits.

Both companies reported declining net income in the first quarter of the year. But the world economy is shrinking, and that will hurt cargo carriers too.

The growth of e-commerce is fueling the growth of another all-cargo airline, one which threatens to take a big piece of the air deliveries of packages bought online: Amazon Air.

Nevertheless, we can single out two distances which appear to be physically meaningful: the distance between the Earth and the quasar when the light was emitted, and the distance between them in the present era taking a slice of the cone along the dimension that we've declared to be the spatial dimension.

The former distance is about 4 billion light years, much smaller than ct because the universe expanded as the light traveled the distance, the light had to "run against the treadmill" and therefore went farther than the initial separation between the Earth and the quasar.

The latter distance shown by the orange line is about 28 billion light years, much larger than ct. If expansion could be instantaneously stopped today, it would take 28 billion years for light to travel between the Earth and the quasar while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.

The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away, and, in fact, the light emitted towards the Earth was actually moving away from the Earth when it was first emitted, in the sense that the metric distance to the Earth increased with cosmological time for the first few billion years of its travel time, and also indicating that the expansion of space between the Earth and the quasar at the early time was faster than the speed of light.

None of this surprising behavior originates from a special property of metric expansion, but simply from local principles of special relativity integrated over a curved surface.

Over time , the space that makes up the universe is expanding. The words ' space ' and ' universe ', sometimes used interchangeably, have distinct meanings in this context.

Here 'space' is a mathematical concept that stands for the three-dimensional manifold into which our respective positions are embedded while 'universe' refers to everything that exists including the matter and energy in space, the extra-dimensions that may be wrapped up in various strings , and the time through which various events take place.

The expansion of space is in reference to this 3-D manifold only; that is, the description involves no structures such as extra dimensions or an exterior universe.

The ultimate topology of space is a posteriori — something which in principle must be observed — as there are no constraints that can simply be reasoned out in other words there can not be any a priori constraints on how the space in which we live is connected or whether it wraps around on itself as a compact space.

Though certain cosmological models such as Gödel's universe even permit bizarre worldlines which intersect with themselves, ultimately the question as to whether we are in something like a " Pac-Man universe" where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon or a planet like the Earth is an observational question which is constrained as measurable or non-measurable by the universe's global geometry.

At present, observations are consistent with the universe being infinite in extent and simply connected, though we are limited in distinguishing between simple and more complicated proposals by cosmological horizons.

The universe could be infinite in extent or it could be finite; but the evidence that leads to the inflationary model of the early universe also implies that the "total universe" is much larger than the observable universe , and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe, if they exist, are still allowed.

For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.

Regardless of the overall shape of the universe, the question of what the universe is expanding into is one which does not require an answer according to the theories which describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse.

All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on.

This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur.

The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect.

There is no reason to believe there is anything "outside" of the expanding universe into which the universe expands. Even if the overall spatial extent is infinite and thus the universe cannot get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing.

As an infinite space grows, it remains infinite. Despite being extremely dense when very young and during part of its early expansion - far denser than is usually required to form a black hole - the universe did not re-collapse into a black hole.

This is because commonly-used calculations for gravitational collapse are usually based upon objects of relatively constant size, such as stars , and do not apply to rapidly expanding space such as the Big Bang.

The expansion of space is sometimes described as a force which acts to push objects apart. Though this is an accurate description of the effect of the cosmological constant , it is not an accurate picture of the phenomenon of expansion in general.

For much of the universe's history the expansion has been due mainly to inertia. The matter in the very early universe was flying apart for unknown reasons most likely as a result of cosmic inflation and has simply continued to do so, though at an ever-decreasing [ citation needed ] rate due to the attractive effect of gravity.

In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so.

There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum; the former is simply a large-scale extrapolation of the latter.

Once objects are bound by gravity, they no longer recede from each other. Thus, the Andromeda galaxy, which is bound to the Milky Way galaxy, is actually falling towards us and is not expanding away.

Within the Local Group , the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place.

Once one goes beyond the Local Group, the inertial expansion is measurable, though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the " Hubble Flow " and end up as bound, non-expanding objects up to the scales of superclusters of galaxies.

We can predict such future events by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled.

Currently, the Local Group is being gravitationally pulled towards either the Shapley Supercluster or the " Great Attractor " with which, if dark energy were not acting, we would eventually merge and no longer see expand away from us after such a time.

A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the FLRW geometry , the same geometry which describes the expansion of the universe as a whole and was also the basis for the simpler Milne universe which ignores the effects of gravity.

In particular, general relativity predicts that light will move at the speed c with respect to the local motion of the exploding matter, a phenomenon analogous to frame dragging.

The situation changes somewhat with the introduction of dark energy or a cosmological constant. A cosmological constant due to a vacuum energy density has the effect of adding a repulsive force between objects which is proportional not inversely proportional to distance.

Unlike inertia it actively "pulls" on objects which have clumped together under the influence of gravity, and even on individual atoms.

However, this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state which is slightly undetectably larger than it would otherwise have been.

However, the only locally visible effect of the accelerating expansion is the disappearance by runaway redshift of distant galaxies; gravitationally bound objects like the Milky Way do not expand and the Andromeda galaxy is moving fast enough towards us that it will still merge with the Milky Way in 3 billion years time, and it is also likely that the merged supergalaxy that forms will eventually fall in and merge with the nearby Virgo Cluster.

However, galaxies lying farther away from this will recede away at ever-increasing speed and be redshifted out of our range of visibility.

At the end of the early universe's inflationary period , all the matter and energy in the universe was set on an inertial trajectory consistent with the equivalence principle and Einstein's general theory of relativity and this is when the precise and regular form of the universe's expansion had its origin that is, matter in the universe is separating because it was separating in the past due to the inflaton field [ citation needed ].

These situations are described by general relativity , which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "distance" here is somewhat different from that used in an inertial frame.

The definition of distance used here is the summation or integration of local comoving distances , all done at constant local proper time.

For example, galaxies that are more than the Hubble radius , approximately 4. Visibility of these objects depends on the exact expansion history of the universe.

At a fundamental level, the expansion of the universe is a property of spatial measurement on the largest measurable scales of our universe.

The distances between cosmologically relevant points increases as time passes leading to observable effects outlined below.

This feature of the universe can be characterized by a single parameter that is called the scale factor which is a function of time and a single value for all of space at any instant if the scale factor were a function of space, this would violate the cosmological principle.

By convention, the scale factor is set to be unity at the present time and, because the universe is expanding, is smaller in the past and larger in the future.

Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero; our current understanding of cosmology sets this time at If the universe continues to expand forever, the scale factor will approach infinity in the future.

In principle, there is no reason that the expansion of the universe must be monotonic and there are models where at some time in the future the scale factor decreases with an attendant contraction of space rather than an expansion.

The expansion of space is often illustrated with conceptual models which show only the size of space at a particular time, leaving the dimension of time implicit.

In the " ant on a rubber rope model" one imagines an ant idealized as pointlike crawling at a constant speed on a perfectly elastic rope which is constantly stretching.

In the "rubber sheet model" one replaces the rope with a flat two-dimensional rubber sheet which expands uniformly in all directions.

The addition of a second spatial dimension raises the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet.

In the "balloon model" the flat sheet is replaced by a spherical balloon which is inflated from an initial size of zero representing the big bang.

A balloon has positive Gaussian curvature while observations suggest that the real universe is spatially flat, but this inconsistency can be eliminated by making the balloon very large so that it is locally flat to within the limits of observation.

This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon.

In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time. In the "raisin bread model" one imagines a loaf of raisin bread expanding in the oven.

The loaf space expands as a whole, but the raisins gravitationally bound objects do not expand; they merely grow farther away from each other.

Technically, the metric expansion of space is a feature of many solutions [ which? This explains observations which indicate that galaxies that are more distant from us are receding faster than galaxies that are closer to us see Hubble's law.

The first general relativistic models predicted that a universe which was dynamical and contained ordinary gravitational matter would contract rather than expand.

Einstein's first proposal for a solution to this problem involved adding a cosmological constant into his theories to balance out the contraction, in order to obtain a static universe solution.

But in Alexander Friedmann derived a set of equations known as the Friedmann equations , showing that the universe might expand and presenting the expansion speed in this case.

While the metric expansion of space appeared to be implied by Hubble's observations, Hubble disagreed with the expanding-universe interpretation of the data:.

On the other hand, if redshifts are not Doppler effects, these anomalies disappear and the region observed appears as a small, homogeneous, but insignificant portion of a universe extended indefinitely both in space and time.

Hubble's skepticism about the universe being too small, dense, and young turned out to be based on an observational error. The higher value meant that an expanding universe would have an age of 2 billion years younger than the Age of the Earth and extrapolating the observed number density of galaxies to a rapidly expanding universe implied a mass density that was too high by a similar factor, enough to force the universe into a peculiar closed geometry which also implied an impending Big Crunch that would occur on a similar time-scale.

After fixing these errors in the s, the new lower values for the Hubble Constant accorded with the expectations of an older universe and the density parameter was found to be fairly close to a geometrically flat universe.

However, recent measurements of the distances and velocities of faraway galaxies revealed a 9 percent discrepancy in the value of the Hubble constant, implying a universe that seems expanding too fast compared to previous measurements.

Wendy Freedman determined space to expand at 72 kilometers per second per megaparsec - roughly 3. The discrepancy opened new questions concerning the nature of dark energy, or of neutrinos.

Until the theoretical developments in the s no one had an explanation for why this seemed to be the case, but with the development of models of cosmic inflation , the expansion of the universe became a general feature resulting from vacuum decay.

Accordingly, the question "why is the universe expanding? In expanding space, distance is a dynamic quantity which changes with time.

There are several different ways of defining distance in cosmology, known as distance measures , but a common method used amongst modern astronomers is comoving distance.

The metric only defines the distance between nearby so-called "local" points. In order to define the distance between arbitrarily distant points, one must specify both the points and a specific curve known as a " spacetime interval " connecting them.

The distance between the points can then be found by finding the length of this connecting curve through the three dimensions of space.

Comoving distance defines this connecting curve to be a curve of constant cosmological time. Operationally, comoving distances cannot be directly measured by a single Earth-bound observer.

To determine the distance of distant objects, astronomers generally measure luminosity of standard candles , or the redshift factor 'z' of distant galaxies, and then convert these measurements into distances based on some particular model of spacetime, such as the Lambda-CDM model.

It is, indeed, by making such observations that it was determined that there is no evidence for any 'slowing down' of the expansion in the current epoch.

Theoretical cosmologists developing models of the universe have drawn upon a small number of reasonable assumptions in their work.

Übersetzung Englisch-Deutsch für expanding im PONS Online-Wörterbuch nachschlagen! Gratis Vokabeltrainer, Verbtabellen, Aussprachefunktion. Übersetzung im Kontext von „expanding“ in Englisch-Deutsch von Reverso Context: self-expanding, rapidly expanding, expanding agent, expanding said. Übersetzung für 'expand' im kostenlosen Englisch-Deutsch Wörterbuch von LANGENSCHEIDT – mit Beispielen, Synonymen und Aussprache. Übersetzung für 'expanding' im kostenlosen Englisch-Deutsch Wörterbuch und viele weitere Deutsch-Übersetzungen. [1] toshidesk.co Englisch-Englisches Wörterbuch, Thesaurus und Enzyklopädie „expand“: [1] PONS Englisch-Deutsch, Stichwort: „expand“: [1] dict.cc Englisch-. Akk https://toshidesk.co/online-internet-casino/beste-spielothek-in-moosau-finden.php v The company is expanding worldwide.**Expanding Deutsch**the Users node by collapsing and expanding it. Read article gefällt Ihnen das Online Wörterbuch? Anstelle go here bislang favorisierten Fokussierung auf die Einzelinteressen der jeweiligen Berufsgruppe und dem Versuch, die [ The environment for German banks is likely to remain challenging in Following the considerable write-downs already taken, uncertainty will probably remain at least into the second half of the year about whether and to what extent additional value adjustments will be required in the wake of the subprime crisis In addition, raising funds on the markets is likely to remain difficult and involve higher costs This ongoing uncertainty could in turn continue to disrupt the functioning of certain segments of the market German banks could potentially be faced with challenges stemming from the. We are confident that we have the right long-term strategy Important elements of "Move" are read article realignment of the Company structure with a focus on our core competencies, and the [ Akk näher ausführen v. Stark zulegen konnte der Bereich Übrige

*Expanding Deutsch*und Aktivitäten. Von der Richtigkeit unserer Langfriststrategie sind wir fest überzeugt Wichtige Bestandteile von "Move" sind der Umbau der Unternehmensstruktur mit Fokussierung auf unsere Kernkompetenzen und das Streben nach. Akk ausweiten v. Beispiele für die Übersetzung expandierenden ansehen Beispiele mit Übereinstimmungen. We are using the following form field to detect spammers. Daher möchte ich nicht im einzelnen die Etappen darlegen, denn Sie kennen sie bestens. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness. The addition of a MiГџ Pro spatial SensationslГјstern raises the possibility of showing

**Expanding Deutsch**perturbations of the spatial geometry by local curvature in the sheet. So it is not seen as problematic read article a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered [ citation needed ]. Please give an overall site rating:. Fourth of July barbecue food safety: Grilling your burgers wrong could kill you this Independence Day. Luckin Coffee Source.

## Expanding Deutsch Beispiele aus dem Internet (nicht von der PONS Redaktion geprüft)

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## Expanding Deutsch Video

With 15 already in the fleet, UPS Airlines will become by the biggest operator in the world of the , the latest — and likely last — version of the famous Jumbo Jet.

And on top of that, there are 22 Boeing s coming. UPS will add more than 12 million pounds of lift capacity to its fleet, most of it to meet growing e-commerce demand.

Rival FedEx Express is also flying most of its planes, unlike passenger carriers, with of its planes currently in service.

The third largest by fleet size among U. But while cargo carriers are flying a lot of packages, they also face a drop in demand for shipping other goods, with UPS and FedEx warning that the pandemic is hurting profits.

Both companies reported declining net income in the first quarter of the year. But the world economy is shrinking, and that will hurt cargo carriers too.

The growth of e-commerce is fueling the growth of another all-cargo airline, one which threatens to take a big piece of the air deliveries of packages bought online: Amazon Air.

Amazon made half of its own deliveries last year, meaning the big cargo airlines are doing fewer of them even as e-commerce booms.

Retail sales in the U. That compares with less than two a day in the previous quarter. Trading has been halted for more than a month.

Luckin delayed its annual results last month, saying it was unable to prepare the financial report due to the coronavirus pandemic.

That raised questions about how long its cash flow can continue supporting its breakneck expansion, especially as Chinese consumer demand stays sluggish because of the outbreak.

Getting the company back on track may be a daunting challenge. Luckin has released only two quarters of results, the most recent in November, when it reported better-than-expected revenue and said it planned to break even this year, even as its net loss widened.

Last month, its offices in China were raided by authorities as part of a multi-agency investigation into its finances, Bloomberg News reported.

For more articles like this, please visit us at bloomberg. Fourth of July barbecue food safety: Grilling your burgers wrong could kill you this Independence Day.

Guth found in his investigation that if the universe contained a field that has a positive-energy false vacuum state, then according to general relativity it would generate an exponential expansion of space.

It was very quickly realized that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look as it does today, the universe would have to have started from very finely tuned , or "special" initial conditions at the Big Bang.

Inflation theory largely resolves these problems as well, thus making a universe like ours much more likely in the context of Big Bang theory.

Thus, he puts forward his scenario of the evolution of the Universe: conformal cyclic cosmology. No field responsible for cosmic inflation has been discovered.

However such a field, if found in the future, would be scalar. The first similar scalar field proven to exist was only discovered in - and is still being researched.

So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered [ citation needed ].

The proposed field and its quanta the subatomic particles related to it have been named inflaton. If this field did not exist, scientists would have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred, and is still occurring much more slowly today.

To understand the metric expansion of the universe, it is helpful to discuss briefly what a metric is, and how metric expansion works.

A metric defines the concept of distance , by stating in mathematical terms how distances between two nearby points in space are measured, in terms of the coordinate system.

Coordinate systems locate points in a space of whatever number of dimensions by assigning unique positions on a grid, known as coordinates , to each point.

Latitude and longitude , and x-y graphs are common examples of coordinates. A metric is a formula which describes how a number known as "distance" is to be measured between two points.

It may seem obvious that distance is measured by a straight line, but in many cases it is not. For example, long haul aircraft travel along a curve known as a " great circle " and not a straight line, because that is a better metric for air travel.

A straight line would go through the earth. Another example is planning a car journey, where one might want the shortest journey in terms of travel time - in that case a straight line is a poor choice of metric because the shortest distance by road is not normally a straight line, and even the path nearest to a straight line will not necessarily be the quickest.

A final example is the internet , where even for nearby towns, the quickest route for data can be via major connections that go across the country and back again.

In this case the metric used will be the shortest time that data takes to travel between two points on the network. In cosmology, we cannot use a ruler to measure metric expansion, because our ruler internal forces easily overcome the extremely slow expansion of space leaving the ruler intact.

Also any objects on or near earth that we might measure are being held together or pushed apart by several forces which are far larger in their effects.

So even if we could measure the tiny expansion that is still happening, we would not notice the change on a small scale or in everyday life.

On a large intergalactic scale, we can use other tests of distance and these do show that space is expanding, even if a ruler on earth could not measure it.

The metric expansion of space is described using the mathematics of metric tensors. The coordinate system we use is called " comoving coordinates ", a type of coordinate system which takes account of time as well as space and the speed of light , and allows us to incorporate the effects of both general and special relativity.

For example, consider the measurement of distance between two places on the surface of the Earth. This is a simple, familiar example of spherical geometry.

Because the surface of the Earth is two-dimensional, points on the surface of the Earth can be specified by two coordinates — for example, the latitude and longitude.

Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example latitude and longitude , or X-Y-Z Cartesian coordinates.

Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too.

On the curved surface of the Earth, we can see this effect in long-haul airline flights where the distance between two points is measured based upon a great circle , rather than the straight line one might plot on a two-dimensional map of the Earth's surface.

In general, such shortest-distance paths are called " geodesics ". In Euclidean geometry , the geodesic is a straight line, while in non-Euclidean geometry such as on the Earth's surface, this is not the case.

Indeed, even the shortest-distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth.

The difference between the straight line path and the shortest-distance great circle path is due to the curvature of the Earth's surface.

While there is always an effect due to this curvature, at short distances the effect is small enough to be unnoticeable.

On plane maps, great circles of the Earth are mostly not shown as straight lines. Indeed, there is a seldom-used map projection , namely the gnomonic projection , where all great circles are shown as straight lines, but in this projection, the distance scale varies very much in different areas.

There is no map projection in which the distance between any two points on Earth, measured along the great circle geodesics, is directly proportional to their distance on the map; such accuracy is possible only with a globe.

In differential geometry , the backbone mathematics for general relativity , a metric tensor can be defined which precisely characterizes the space being described by explaining the way distances should be measured in every possible direction.

General relativity necessarily invokes a metric in four dimensions one of time, three of space because, in general, different reference frames will experience different intervals of time and space depending on the inertial frame.

This means that the metric tensor in general relativity relates precisely how two events in spacetime are separated.

A metric expansion occurs when the metric tensor changes with time and, specifically, whenever the spatial part of the metric gets larger as time goes forward.

This kind of expansion is different from all kinds of expansions and explosions commonly seen in nature in no small part because times and distances are not the same in all reference frames, but are instead subject to change.

A useful visualization is to approach the subject rather than objects in a fixed "space" moving apart into "emptiness", as space itself growing between objects without any acceleration of the objects themselves.

The space between objects shrinks or grows as the various geodesics converge or diverge. Because this expansion is caused by relative changes in the distance-defining metric, this expansion and the resultant movement apart of objects is not restricted by the speed of light upper bound of special relativity.

Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.

Theory and observations suggest that very early in the history of the universe, there was an inflationary phase where the metric changed very rapidly, and that the remaining time-dependence of this metric is what we observe as the so-called Hubble expansion , the moving apart of all gravitationally unbound objects in the universe.

The expanding universe is therefore a fundamental feature of the universe we inhabit — a universe fundamentally different from the static universe Albert Einstein first considered when he developed his gravitational theory.

In expanding space, proper distances are dynamical quantities which change with time. An easy way to correct for this is to use comoving coordinates which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion.

In comoving coordinates, the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravity and electromagnetic radiation.

Any time-evolution however must be accounted for by taking into account the Hubble law expansion in the appropriate equations in addition to any other effects that may be operating gravity , dark energy , or curvature , for example.

Cosmological simulations that run through significant fractions of the universe's history therefore must include such effects in order to make applicable predictions for observational cosmology.

In principle, the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again, but in practice, standard rulers are not easy to find on cosmological scales and the timescales over which a measurable expansion would be visible are too great to be observable even by multiple generations of humans.

The expansion of space is measured indirectly. The theory of relativity predicts phenomena associated with the expansion, notably the redshift -versus-distance relationship known as Hubble's Law ; functional forms for cosmological distance measurements that differ from what would be expected if space were not expanding; and an observable change in the matter and energy density of the universe seen at different lookback times.

The first measurement of the expansion of space came with Hubble's realization of the velocity vs. On the other hand, by assuming a cosmological model, e.

Lambda-CDM model , one can infer the Hubble constant from the size of the largest fluctuations seen in the Cosmic Microwave Background. A higher Hubble constant would imply a smaller characteristic size of CMB fluctuations, and vice versa.

The Hubble parameter is not thought to be constant through time. There are dynamical forces acting on the particles in the universe which affect the expansion rate.

It was earlier expected that the Hubble parameter would be decreasing as time went on due to the influence of gravitational interactions in the universe, and thus there is an additional observable quantity in the universe called the deceleration parameter which cosmologists expected to be directly related to the matter density of the universe.

Some cosmologists have whimsically called the effect associated with the "accelerating universe" the "cosmic jerk ". In October , scientists presented a new third way two earlier methods, one based on redshifts and another on the cosmic distance ladder , gave results that do not agree , using information from gravitational wave events especially those involving the merger of neutron stars , like GW , of determining the Hubble Constant , essential in establishing the rate of expansion of the universe.

At cosmological scales the present universe is geometrically flat, [20] which is to say that the rules of Euclidean geometry associated with Euclid's fifth postulate hold, though in the past spacetime could have been highly curved.

In part to accommodate such different geometries, the expansion of the universe is inherently general relativistic ; it cannot be modeled with special relativity alone, though such models exist, they are at fundamental odds with the observed interaction between matter and spacetime seen in our universe.

Two of the dimensions of space are omitted, leaving one dimension of space the dimension that grows as the cone gets larger and one of time the dimension that proceeds "up" the cone's surface.

The narrow circular end of the diagram corresponds to a cosmological time of million years after the big bang while the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion as a splaying outward of the spacetime, a feature which eventually dominates in this model.

The purple grid lines mark off cosmological time at intervals of one billion years from the big bang.

The cyan grid lines mark off comoving distance at intervals of one billion light years in the present era less in the past and more in the future.

Note that the circular curling of the surface is an artifact of the embedding with no physical significance and is done purely to make the illustration viewable; space does not actually curl around on itself.

A similar effect can be seen in the tubular shape of the pseudosphere. The brown line on the diagram is the worldline of the Earth or, at earlier times, of the matter which condensed to form the Earth.

The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day.

The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years, which is, notably, a larger distance than the age of the universe multiplied by the speed of light: ct.

According to the equivalence principle of general relativity, the rules of special relativity are locally valid in small regions of spacetime that are approximately flat.

It does not follow, however, that light travels a distance ct in a time t , as the red worldline illustrates. While it always moves locally at c , its time in transit about 13 billion years is not related to the distance traveled in any simple way since the universe expands as the light beam traverses space and time.

In fact the distance traveled is inherently ambiguous because of the changing scale of the universe. Nevertheless, we can single out two distances which appear to be physically meaningful: the distance between the Earth and the quasar when the light was emitted, and the distance between them in the present era taking a slice of the cone along the dimension that we've declared to be the spatial dimension.

The former distance is about 4 billion light years, much smaller than ct because the universe expanded as the light traveled the distance, the light had to "run against the treadmill" and therefore went farther than the initial separation between the Earth and the quasar.

The latter distance shown by the orange line is about 28 billion light years, much larger than ct. If expansion could be instantaneously stopped today, it would take 28 billion years for light to travel between the Earth and the quasar while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.

The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away, and, in fact, the light emitted towards the Earth was actually moving away from the Earth when it was first emitted, in the sense that the metric distance to the Earth increased with cosmological time for the first few billion years of its travel time, and also indicating that the expansion of space between the Earth and the quasar at the early time was faster than the speed of light.

None of this surprising behavior originates from a special property of metric expansion, but simply from local principles of special relativity integrated over a curved surface.

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