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111-532: Hubble's law is considered the first observational basis for the expansion of the universe , and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is known as the Hubble flow . It is described by the equation v = H 0 D , with H 0 the constant of proportionality—the Hubble constant —between

222-414: A − 3 {\displaystyle \rho \propto a^{-3}} , where a {\displaystyle a} is the scale factor . For ultrarelativistic particles ("radiation"), the energy density drops more sharply, as ρ ∝ a − 4 {\displaystyle \rho \propto a^{-4}} . This is because in addition to the volume dilution of

333-664: A Taylor series expansion: z = R ( t 0 ) R ( t e ) − 1 ≈ R ( t 0 ) R ( t 0 ) ( 1 + ( t e − t 0 ) H ( t 0 ) ) − 1 ≈ ( t 0 − t e ) H ( t 0 ) , {\displaystyle z={\frac {R(t_{0})}{R(t_{e})}}-1\approx {\frac {R(t_{0})}{R(t_{0})\left(1+(t_{e}-t_{0})H(t_{0})\right)}}-1\approx (t_{0}-t_{e})H(t_{0}),} If

444-548: A linear relationship between distance to galaxies and their recessional velocity . Edwin Hubble observationally confirmed Lundmark's and Lemaître's findings in 1929. Assuming the cosmological principle , these findings would imply that all galaxies are moving away from each other. Astronomer Walter Baade recalculated the size of the known universe in the 1940s, doubling the previous calculation made by Hubble in 1929. He announced this finding to considerable astonishment at

555-516: A redshift velocity , which is the recessional velocity that would produce the same redshift if it were caused by a linear Doppler effect (which, however, is not the case, as the velocities involved are too large to use a non-relativistic formula for Doppler shift). This redshift velocity can easily exceed the speed of light. In other words, to determine the redshift velocity v rs , the relation: v rs ≡ c z , {\displaystyle v_{\text{rs}}\equiv cz,}

666-463: A "Hubble diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer. A straight line of positive slope on this diagram is the visual depiction of Hubble's law. After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant , a term he had inserted into his equations of general relativity to coerce them into producing

777-485: A description in which space does not expand and objects simply move apart while under the influence of their mutual gravity. Although cosmic expansion is often framed as a consequence of general relativity , it is also predicted by Newtonian gravity . According to inflation theory , the universe suddenly expanded during the inflationary epoch (about 10 of a second after the Big Bang), and its volume increased by

888-446: A discussion of the significance of this): r HS = c H 0   . {\displaystyle r_{\text{HS}}={\frac {c}{H_{0}}}\ .} Since the Hubble "constant" is a constant only in space, not in time, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today. Current evidence suggests that

999-464: 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. The distance traveled is thus inherently ambiguous because of the changing scale of the universe. Nevertheless, there are two distances that appear to be physically meaningful:

1110-455: A factor of at least 10 (an expansion of distance by a factor of at least 10 in each of the three dimensions). This would be equivalent to expanding an object 1  nanometer across ( 10  m , about half the width of a molecule of DNA ) to one approximately 10.6  light-years across (about 10  m , or 62 trillion miles). Cosmic expansion subsequently decelerated to much slower rates, until around 9.8 billion years after

1221-404: A finite distance. The comoving distance that such particles can have covered over the age of the universe is known as the particle horizon , and the region of the universe that lies within our particle horizon is known as the observable universe . If the dark energy that is inferred to dominate the universe today is a cosmological constant, then the particle horizon converges to a finite value in

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1332-524: A galaxy is at distance D , and this distance changes with time at a rate d t D . We call this rate of recession the "recession velocity" v r : v r = d t D = d t R R D . {\displaystyle v_{\text{r}}=d_{t}D={\frac {d_{t}R}{R}}D.} We now define the Hubble constant as H ≡ d t R R , {\displaystyle H\equiv {\frac {d_{t}R}{R}},} and discover

1443-403: A low-impact journal. In the 1931 high-impact English translation of this article, a critical equation was changed by omitting reference to what is now known as the Hubble constant." It is now known that the alterations in the translated paper were carried out by Lemaître himself. Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe . In 1920,

1554-435: A non-zero Riemann curvature tensor in curvature of Riemannian manifolds . Euclidean "geometrically flat" space has a Riemann curvature tensor of zero. "Geometrically flat" space has three dimensions and is consistent with Euclidean space. However, spacetime has four dimensions; it is not flat according to Einstein's general theory of relativity. Einstein's theory postulates that "matter and energy curve spacetime, and there

1665-433: 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 that 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

1776-564: A separate galaxy with its own signature age and rate of nova occurrences. Curtis also noted the large radial velocities of spiral nebulae that suggested they could not be gravitationally bound to the Milky Way in a Kapteyn -model universe. In addition, he cited dark lanes present in other galaxies similar to the dust clouds found in Earth's own galaxy, explaining the zone of avoidance . Curtis stated that if van Maanen's observation of

1887-412: A smaller velocity than earlier ones. Redshift can be measured by determining the wavelength of a known transition, such as hydrogen α-lines for distant quasars, and finding the fractional shift compared to a stationary reference. Thus, redshift is a quantity unambiguous for experimental observation. The relation of redshift to recessional velocity is another matter. The redshift z is often described as

1998-436: A supernova brightness, which provides information about its distance, and the redshift z = ∆ λ / λ of its spectrum of radiation. Hubble correlated brightness and parameter z . Combining his measurements of galaxy distances with Vesto Slipher and Milton Humason 's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there

2109-406: Is a disagreement between this measurement and the supernova-based measurements, known as the Hubble tension . A third option proposed recently is to use information from gravitational wave events (especially those involving the merger of neutron stars , like GW170817 ), to measure the expansion rate. Such measurements do not yet have the precision to resolve the Hubble tension. In principle,

2220-540: Is accelerating in the present epoch. By assuming a cosmological model, e.g. the Lambda-CDM model , another possibility is to infer the present-day expansion rate from the sizes of the largest fluctuations seen in the cosmic microwave background . A higher expansion rate would imply a smaller characteristic size of CMB fluctuations, and vice versa. The Planck collaboration measured the expansion rate this way and determined H 0 = 67.4 ± 0.5 (km/s)/Mpc . There

2331-414: Is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted and is not established except for small redshifts. For distances D larger than the radius of the Hubble sphere r HS , objects recede at a rate faster than the speed of light ( See Uses of the proper distance for

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2442-443: Is enough matter and energy to provide for curvature." 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 may be at fundamental odds with the observed interaction between matter and spacetime seen in the universe. The images to the right show two views of spacetime diagrams that show

2553-442: Is essentially pressureless, with | p | ≪ ρ c 2 {\displaystyle |p|\ll \rho c^{2}} , while a gas of ultrarelativistic particles (such as a photon gas ) has positive pressure p = ρ c 2 / 3 {\displaystyle p=\rho c^{2}/3} . Negative-pressure fluids, like dark energy, are not experimentally confirmed, but

2664-424: 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

2775-534: Is known. The object's distance can then be inferred from the observed apparent brightness . Meanwhile, the recession speed is measured through the redshift. Hubble used this approach for his original measurement of the expansion rate, by measuring the brightness of Cepheid variable stars and the redshifts of their host galaxies. More recently, using Type Ia supernovae , the expansion rate was measured to be H 0   =   73.24 ± 1.74 (km/s)/Mpc . This means that for every million parsecs of distance from

2886-400: 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 13.787 ± 0.020 billion years ago . If the universe continues to expand forever, the scale factor will approach infinity in the future. It is also possible in principle for

2997-401: Is some reference time. If light is emitted from a galaxy at time t e and received by us at t 0 , it is redshifted due to the expansion of the universe, and this redshift z is simply: z = R ( t 0 ) R ( t e ) − 1. {\displaystyle z={\frac {R(t_{0})}{R(t_{\text{e}})}}-1.} Suppose

3108-584: Is the equation of state parameter . The energy density of such a fluid drops as Nonrelativistic matter has w = 0 {\displaystyle w=0} while radiation has w = 1 / 3 {\displaystyle w=1/3} . For an exotic fluid with negative pressure, like dark energy, the energy density drops more slowly; if w = − 1 {\displaystyle w=-1} it remains constant in time. If w < − 1 {\displaystyle w<-1} , corresponding to phantom energy ,

3219-417: Is the gravitational constant , ρ {\displaystyle \rho } is the energy density within the universe, p {\displaystyle p} is the pressure , c {\displaystyle c} is the speed of light , and Λ {\displaystyle \Lambda } is the cosmological constant. A positive energy density leads to deceleration of

3330-803: Is used. That is, there is no fundamental difference between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called Fizeau–Doppler formula z = λ o λ e − 1 = 1 + v c 1 − v c − 1 ≈ v c . {\displaystyle z={\frac {\lambda _{\text{o}}}{\lambda _{\text{e}}}}-1={\sqrt {\frac {1+{\frac {v}{c}}}{1-{\frac {v}{c}}}}}-1\approx {\frac {v}{c}}.} Here, λ o , λ e are

3441-564: The Big Bang and Steady State theories of cosmology. In 1927, two years before Hubble published his own article, the Belgian priest and astronomer Georges Lemaître was the first to publish research deriving what is now known as Hubble's law. According to the Canadian astronomer Sidney van den Bergh , "the 1927 discovery of the expansion of the universe by Lemaître was published in French in

Hubble's law - Misplaced Pages Continue

3552-590: The Pinwheel Galaxy rotating were correct, he himself would have been wrong about the scale of the Universe and that the Milky Way would fully encompass it. Later in the 1920s, Edwin Hubble showed that Andromeda was far outside the Milky Way by measuring Cepheid variable stars, proving that Curtis was correct. It is now known that the Milky Way is only one of as many as an estimated 200 billion ( 2 × 10 ) to 2 trillion ( 2 × 10 ) or more galaxies in

3663-850: The Shapley–Curtis Debate , was held on 26 April 1920 at the Smithsonian Museum of Natural History , between the astronomers Harlow Shapley and Heber Curtis . It concerned the nature of so-called spiral nebulae and the size of the Universe . Shapley believed that these nebulae were relatively small and lay within the outskirts of the Milky Way galaxy (then thought to be the entire Universe), while Curtis held that they were in fact independent galaxies, implying that they were exceedingly large and distant. The two scientists first presented independent technical papers about "The Scale of

3774-473: The Shapley–Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy, and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations. Edwin Hubble did most of his professional astronomical observing work at Mount Wilson Observatory , home to

3885-440: The equivalence principle of general relativity, the rules of special relativity are locally valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed  c ; in the diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels

3996-418: The large-scale structure of the universe . Around 3 billion years ago, at a time of about 11 billion years, dark energy is believed to have begun to dominate the energy density of the universe. This transition came about because dark energy does not dilute as the universe expands, instead maintaining a constant energy density. Similarly to inflation, dark energy drives accelerated expansion, such that

4107-404: The proportionality constant of Hubble's law. Georges Lemaître independently found a similar solution in his 1927 paper discussed in the following section. The Friedmann equations are derived by inserting the metric for a homogeneous and isotropic universe into Einstein's field equations for a fluid with a given density and pressure . This idea of an expanding spacetime would eventually lead to

4218-469: The speed of light in vacuum . Shapley also backed up his claims with the observation of a nova in the Andromeda "nebula" that had briefly outshone the entire nebula, constituting a seemingly impossible output of energy were Andromeda in fact a separate galaxy. Curtis, on the other hand, contended that Andromeda and other such "nebulae" were separate galaxies, or " island universes " (a term invented by

4329-439: The "proper distance" D to a galaxy (which can change over time, unlike the comoving distance ) and its speed of separation v , i.e. the derivative of proper distance with respect to the cosmic time coordinate. (See Comoving and proper distances § Uses of the proper distance for discussion of the subtleties of this definition of velocity. ) The Hubble constant is most frequently quoted in km / s / Mpc , which gives

4440-425: The 18th-century philosopher Immanuel Kant , who also argued that the "spiral nebulae" were extragalactic). He showed that there were more novae in Andromeda than in the Milky Way. From this, he could ask why there were more novae in one small section of the galaxy than the other sections of the galaxy, if Andromeda were not a separate galaxy but simply a nebula within Earth's galaxy. This led to supporting Andromeda as

4551-660: The 1952 meeting of the International Astronomical Union in Rome. For most of the second half of the 20th century, the value of the Hubble constant was estimated to be between 50 and 90 km⋅s ⋅ Mpc . On 13 January 1994, NASA formally announced a completion of its repairs related to the main mirror of the Hubble Space Telescope , allowing for sharper images and, consequently, more accurate analyses of its observations. Shortly after

Hubble's law - Misplaced Pages Continue

4662-495: The Big Bang (4 billion years ago) it began to gradually expand more quickly , and is still doing so. Physicists have postulated the existence of dark energy , appearing as a cosmological constant in the simplest gravitational models, as a way to explain this late-time acceleration. According to the simplest extrapolation of the currently favored cosmological model, the Lambda-CDM model , this acceleration becomes dominant in

4773-419: The Big Bang. During the matter-dominated epoch, cosmic expansion also decelerated, with the scale factor growing as the 2/3 power of the time ( a ∝ t 2 / 3 {\displaystyle a\propto t^{2/3}} ). Also, gravitational structure formation is most efficient when nonrelativistic matter dominates, and this epoch is responsible for the formation of galaxies and

4884-401: The Hubble horizon are not dynamical, because gravitational influences do not have time to propagate across them, while perturbations much smaller than the Hubble horizon are straightforwardly governed by Newtonian gravitational dynamics . An object's peculiar velocity is its velocity with respect to the comoving coordinate grid, i.e., with respect to the average expansion-associated motion of

4995-463: The Hubble law: v r = H D . {\displaystyle v_{\text{r}}=HD.} From this perspective, Hubble's law is a fundamental relation between (i) the recessional velocity associated with the expansion of the universe and (ii) the distance to an object; the connection between redshift and distance is a crutch used to connect Hubble's law with observations. This law can be related to redshift z approximately by making

5106-418: The Hubble rate H {\displaystyle H} quantifies the rate of expansion. H {\displaystyle H} is a function of cosmic time . The expansion of the universe can be understood as a consequence of an initial impulse (possibly due to inflation ), which sent the contents of the universe flying apart. The mutual gravitational attraction of the matter and radiation within

5217-489: The NASA/IPAC Extragalactic Database of Galaxy Distances, "Lundmark's extragalactic distance estimates were far more accurate than Hubble's, consistent with an expansion rate (Hubble constant) that was within 1% of the best measurements today." In 1927, Georges Lemaître independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented observational evidence for

5328-756: The Universe" during the day and then took part in a joint discussion that evening. Much of the lore of the Great Debate grew out of two papers published by Shapley and by Curtis in the May 1921 issue of the Bulletin of the National Research Council . The published papers each included counterarguments to the position advocated by the other scientist at the 1920 meeting. In the aftermath of the public debate, scientists have been able to verify individual pieces of evidence from both astronomers, but on

5439-457: The cosmic scale factor grew exponentially in time. In order to solve the horizon and flatness problems, inflation must have lasted long enough that the scale factor grew by at least a factor of e (about 10 ). The history of the universe after inflation but before a time of about 1 second is largely unknown. However, the universe is known to have been dominated by ultrarelativistic Standard Model particles, conventionally called radiation , by

5550-513: The cosmic expansion history can also be measured by studying how redshifts, distances, fluxes, angular positions, and angular sizes of astronomical objects change over the course of the time that they are being observed. These effects are too small to have yet been detected. However, changes in redshift or flux could be observed by the Square Kilometre Array or Extremely Large Telescope in the mid-2030s. At cosmological scales,

5661-487: The current rate of expansion it takes one billion years for an unbound structure to grow by 7%. Although widely attributed to Edwin Hubble , the notion of the universe expanding at a calculable rate was first derived from general relativity equations in 1922 by Alexander Friedmann . Friedmann published a set of equations, now known as the Friedmann equations , showing that the universe might be expanding, and presenting

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5772-456: The decay of particles' peculiar momenta, as discussed above. It can also be understood as adiabatic cooling . The temperature of ultrarelativistic fluids, often called "radiation" and including the cosmic microwave background , scales inversely with the scale factor (i.e. T ∝ a − 1 {\displaystyle T\propto a^{-1}} ). The temperature of nonrelativistic matter drops more sharply, scaling as

5883-528: The distance between 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 defined as the spatial dimension). The former distance is about 4 billion light-years, much smaller than ct , whereas the latter distance (shown by the orange line) is about 28 billion light-years, much larger than  ct . In other words, if space were not expanding today, it would take 28 billion years for light to travel between Earth and

5994-650: The distance is not too large, all other complications of the model become small corrections, and the time interval is simply the distance divided by the speed of light: z ≈ ( t 0 − t e ) H ( t 0 ) ≈ D c H ( t 0 ) , {\displaystyle z\approx (t_{0}-t_{\text{e}})H(t_{0})\approx {\frac {D}{c}}H(t_{0}),} or c z ≈ D H ( t 0 ) = v r . {\displaystyle cz\approx DH(t_{0})=v_{r}.} According to this approach,

6105-416: The energy density grows as the universe expands. Inflation is a period of accelerated expansion hypothesized to have occurred at a time of around 10 seconds. It would have been driven by the inflaton , a field that has a positive-energy false vacuum state. Inflation was originally proposed to explain the absence of exotic relics predicted by grand unified theories , such as magnetic monopoles , because

6216-405: 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. Thus any edges or exotic geometries or topologies would not be directly observable, since 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

6327-506: The existence of dark energy is inferred from astronomical observations. In an expanding universe, it is often useful to study the evolution of structure with the expansion of the universe factored out. This motivates the use of comoving coordinates , which are defined to grow proportionally with the scale factor. If an object is moving only with the Hubble flow of the expanding universe, with no other motion, then it remains stationary in comoving coordinates. The comoving coordinates are

6438-467: The expansion of the universe is accelerating ( see Accelerating universe ), meaning that for any given galaxy, the recession velocity dD/dt is increasing over time as the galaxy moves to greater and greater distances; however, the Hubble parameter is actually thought to be decreasing with time, meaning that if we were to look at some fixed distance D and watch a series of different galaxies pass that distance, later galaxies would pass that distance at

6549-430: The expansion speed if that were the case. Before Hubble, German astronomer Carl Wilhelm Wirtz had, in two publications dating 1922 and 1924, already deduced with his own data that galaxies that appeared smaller and dimmer had larger redshifts and thus that more distant galaxies recede faster from the observer. Then Georges Lemaître , in a 1927 article, independently derived that the universe might be expanding, observed

6660-469: The expansion, a ¨ < 0 {\displaystyle {\ddot {a}}<0} , and a positive pressure further decelerates expansion. On the other hand, sufficiently negative pressure with p < − ρ c 2 / 3 {\displaystyle p<-\rho c^{2}/3} leads to accelerated expansion, and the cosmological constant also accelerates expansion. Nonrelativistic matter

6771-401: The first few billion years of its travel time, also indicating that the expansion of space between Earth and the quasar at the early time was faster than the speed of light. None of this behavior originates from a special property of metric expansion, but rather from local principles of special relativity integrated over a curved surface. Over time, the space that makes up the universe

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6882-510: The first year observations of the Wilkinson Microwave Anisotropy Probe satellite (WMAP) further agreed with the estimated expansion rates for local galaxies, 72 ± 5 km⋅s ⋅Mpc . The universe at the largest scales is observed to be homogeneous (the same everywhere) and isotropic (the same in all directions), consistent with the cosmological principle . These constraints demand that any expansion of

6993-420: The future" over long distances. However, within general relativity , the shape of these comoving synchronous spatial surfaces is affected by gravity. Current observations are consistent with these spatial surfaces being geometrically flat (so that, for example, the angles of a triangle add up to 180 degrees). An expanding universe typically has a finite age. Light, and other particles, can have propagated only

7104-502: The future. In 1912–1914, Vesto Slipher discovered that light from remote galaxies was redshifted , a phenomenon later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used the Einstein field equations to provide theoretical evidence that the universe is expanding. Swedish astronomer Knut Lundmark was the first person to find observational evidence for expansion, in 1924. According to Ian Steer of

7215-519: The galaxy in Curtis's model, while Shapley correctly placed the Sun in the outer regions of the galaxy). It later became apparent that van Maanen's observations were incorrect—one cannot actually see the Pinwheel Galaxy rotate during a human lifespan . The format of the great debate has been used subsequently to argue the nature of fundamental questions in astronomy. In honor of the first "Great Debate",

7326-418: 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

7437-432: The infinite future. This implies that the amount of the universe that we will ever be able to observe is limited. Many systems exist whose light can never reach us, because there is a cosmic event horizon induced by the repulsive gravity of the dark energy. Within the study of the evolution of structure within the universe, a natural scale emerges, known as the Hubble horizon . Cosmological perturbations much larger than

7548-413: The inverse square of the scale factor (i.e. T ∝ a − 2 {\displaystyle T\propto a^{-2}} ). The contents of the universe dilute as it expands. The number of particles within a comoving volume remains fixed (on average), while the volume expands. For nonrelativistic matter, this implies that the energy density drops as ρ ∝

7659-409: The large-scale geometry of the universe according to the ΛCDM cosmological model. 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 700 million years after the Big Bang, while

7770-499: The main point of the existence of other galaxies, Curtis has been proven correct. Shapley presented the case that the Milky Way is the entirety of the Universe. He argued that " spiral nebulae " such as Andromeda were simply part of the Milky Way. He backed up this claim by appealing to their relative sizes—if Andromeda were not part of the Milky Way, then its distance must have been on the order of 10 light years —a span most contemporary astronomers would not accept. Shapley cited

7881-439: The most general principles to the nature of the universe yielded a dynamic solution that conflicted with the then-prevalent notion of a static universe . In 1912, Vesto M. Slipher measured the first Doppler shift of a " spiral nebula " (the obsolete term for spiral galaxies) and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at

7992-455: The observable Universe. Also, astronomers generally accept that the nova Shapley referred to in his arguments was in fact a supernova , which does indeed temporarily outshine the combined output of an entire galaxy. On other points, the results were mixed (the actual size of the Milky Way is in between the sizes proposed by Shapley and Curtis), or in favor of Shapley (the Sun was near the center of

8103-513: The observational basis for modern cosmology. The cosmological constant has regained attention in recent decades as a hypothetical explanation for dark energy . The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows: v = H 0 D {\displaystyle v=H_{0}\,D} where Hubble's law

8214-416: The observed and emitted wavelengths respectively. The "redshift velocity" v rs is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity. Next, the connection between redshift or redshift velocity and recessional velocity is discussed. Suppose R ( t ) is called the scale factor of the universe, and increases as

8325-491: The observer , on average. While objects cannot move faster than light , this limitation applies only with respect to local reference frames and does not limit the recession rates of cosmologically distant objects. Cosmic expansion is a key feature of Big Bang cosmology. It can be modeled mathematically with the Friedmann–Lemaître–Robertson–Walker metric (FLRW), where it corresponds to an increase in

8436-550: The observer, recessional velocity of objects at that distance increases by about 73 kilometres per second (160,000 mph). Supernovae are observable at such great distances that the light travel time therefrom can approach the age of the universe. Consequently, they can be used to measure not only the present-day expansion rate but also the expansion history. In work that was awarded the 2011 Nobel Prize in Physics , supernova observations were used to determine that cosmic expansion

8547-423: The particle count, the energy of each particle (including the rest mass energy ) also drops significantly due to the decay of peculiar momenta. In general, we can consider a perfect fluid with pressure p = w ρ {\displaystyle p=w\rho } , where ρ {\displaystyle \rho } is the energy density. The parameter w {\displaystyle w}

8658-435: The present era (less in the past and more in the future). The circular curling of the surface is an artifact of the embedding with no physical significance and is done for illustrative purposes; a flat universe does not curl back onto itself. (A similar effect can be seen in the tubular shape of the pseudosphere .) The brown line on the diagram is the worldline of Earth (or more precisely its location in space, even before it

8769-416: The present universe conforms to Euclidean space , what cosmologists describe as geometrically flat , to within experimental error. Consequently, the rules of Euclidean geometry associated with Euclid's fifth postulate hold in the present universe in 3D space. It is, however, possible that the geometry of past 3D space could have been highly curved. The curvature of space is often modeled using

8880-681: The proportionality between recessional velocity of, and distance to, distant bodies, and suggested an estimated value for the proportionality constant; this constant, when Edwin Hubble confirmed the existence of cosmic expansion and determined a more accurate value for it two years later, came to be known by his name as the Hubble constant. Hubble inferred the recession velocity of the objects from their redshifts , many of which were earlier measured and related to velocity by Vesto Slipher in 1917. Combining Slipher's velocities with Henrietta Swan Leavitt 's intergalactic distance calculations and methodology allowed Hubble to better calculate an expansion rate for

8991-418: 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. In fact, the light emitted towards Earth was actually moving away from Earth when it was first emitted; the metric distance to Earth increased with cosmological time for

9102-416: The rapid expansion would have diluted such relics. It was subsequently realized that the accelerated expansion would also solve the horizon problem and the flatness problem . Additionally, quantum fluctuations during inflation would have created initial variations in the density of the universe, which gravity later amplified to yield the observed spectrum of matter density variations . During inflation,

9213-443: The relation cz = v r is an approximation valid at low redshifts, to be replaced by a relation at large redshifts that is model-dependent. See velocity-redshift figure . Strictly speaking, neither v nor D in the formula are directly observable, because they are properties now of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it. Expansion of

9324-465: The repairs were made, Wendy Freedman 's 1994 Key Project analyzed the recession velocity of M100 from the core of the Virgo Cluster , offering a Hubble constant measurement of 80 ± 17 km⋅s ⋅Mpc . Later the same year, Adam Riess et al. used an empirical method of visual-band light-curve shapes to more finely estimate the luminosity of Type Ia supernovae . This further minimized

9435-567: The same place like going all the way around the surface of a balloon (or a planet like the Earth), is an observational question that is constrained as measurable or non-measurable by the universe's global geometry . At present, observations are consistent with the universe having infinite extent and being a simply connected space , though cosmological horizons limit our ability to distinguish between simple and more complicated proposals. The universe could be infinite in extent or it could be finite; but

9546-527: The same velocity as its own. More generally, the peculiar momenta of both relativistic and nonrelativistic particles decay in inverse proportion with the scale factor. For photons, this leads to the cosmological redshift . While the cosmological redshift is often explained as the stretching of photon wavelengths due to "expansion of space", it is more naturally viewed as a consequence of the Doppler effect . The universe cools as it expands. This follows from

9657-424: The scale factor grows exponentially in time. The most direct way to measure the expansion rate is to independently measure the recession velocities and the distances of distant objects, such as galaxies. The ratio between these quantities gives the Hubble rate, in accordance with Hubble's law. Typically, the distance is measured using a standard candle , which is an object or event for which the intrinsic brightness

9768-399: The scale of the spatial part of the universe's spacetime metric tensor (which governs the size and geometry of spacetime). Within this framework, the separation of objects over time is associated with the expansion of space itself. However, this is not a generally covariant description but rather only a choice of coordinates . Contrary to common misconception, it is equally valid to adopt

9879-620: The spatial coordinates in the FLRW metric . The universe is a four-dimensional spacetime, but within a universe that obeys the cosmological principle, there is a natural choice of three-dimensional spatial surface. These are the surfaces on which observers who are stationary in comoving coordinates agree on the age of the universe . In a universe governed by special relativity , such surfaces would be hyperboloids , because relativistic time dilation means that rapidly receding distant observers' clocks are slowed, so that spatial surfaces must bend "into

9990-406: The speed of a galaxy 1 megaparsec (3.09 × 10 km) away as 70 km/s . Simplifying the units of the generalized form reveals that H 0 specifies a frequency (SI unit: s ), leading the reciprocal of H 0 to be known as the Hubble time (14.4 billion years). The Hubble constant can also be stated as a relative rate of expansion. In this form H 0  = 7%/ Gyr , meaning that at

10101-399: The static solution he previously considered the correct state of the universe. The Einstein equations in their simplest form model either an expanding or contracting universe, so Einstein introduced the constant to counter expansion or contraction and lead to a static and flat universe. After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that

10212-474: The surrounding material. It is a measure of how a particle's motion deviates from the Hubble flow of the expanding universe. The peculiar velocities of nonrelativistic particles decay as the universe expands, in inverse proportion with the cosmic scale factor . This can be understood as a self-sorting effect. A particle that is moving in some direction gradually overtakes the Hubble flow of cosmic expansion in that direction, asymptotically approaching material with

10323-426: The systematic measurement errors of the Hubble constant, to 67 ± 7 km⋅s ⋅Mpc . Reiss's measurements on the recession velocity of the nearby Virgo Cluster more closely agree with subsequent and independent analyses of Cepheid variable calibrations of Type Ia supernova , which estimates a Hubble constant of 73 ± 7 km⋅s ⋅Mpc . In 2003, David Spergel 's analysis of the cosmic microwave background during

10434-421: The time it was highly controversial whether or not these nebulae were "island universes" outside the Milky Way galaxy. In 1922, Alexander Friedmann derived his Friedmann equations from Einstein field equations , showing that the universe might expand at a rate calculable by the equations. The parameter used by Friedmann is known today as the scale factor and can be considered as a scale invariant form of

10545-413: The time of neutrino decoupling at about 1 second. During radiation domination, cosmic expansion decelerated, with the scale factor growing proportionally with the square root of the time. Since radiation redshifts as the universe expands, eventually nonrelativistic matter came to dominate the energy density of the universe. This transition happened at a time of about 50 thousand years after

10656-413: The time through which various events take place. The expansion of space is in reference to this 3D 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 that in principle must be observed – as there are no constraints that can simply be reasoned out (in other words there cannot be any

10767-478: The universe The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it. To any observer in the universe, it appears that all but the nearest galaxies (which are bound to each other by gravity) move away at speeds that are proportional to their distance from

10878-414: The universe accord with Hubble's law , in which objects recede from each observer with velocities proportional to their positions with respect to that observer. That is, recession velocities v → {\displaystyle {\vec {v}}} scale with (observer-centered) positions x → {\displaystyle {\vec {x}}} according to where

10989-552: The universe expands in a manner that depends upon the cosmological model selected. Its meaning is that all measured proper distances D ( t ) between co-moving points increase proportionally to R . (The co-moving points are not moving relative to their local environments.) In other words: D ( t ) D ( t 0 ) = R ( t ) R ( t 0 ) , {\displaystyle {\frac {D(t)}{D(t_{0})}}={\frac {R(t)}{R(t_{0})}},} where t 0

11100-415: The universe gradually slows this expansion over time, but expansion nevertheless continues due to momentum left over from the initial impulse. Also, certain exotic relativistic fluids , such as dark energy and inflation, exert gravitational repulsion in the cosmological context, which accelerates the expansion of the universe. A cosmological constant also has this effect. Mathematically, the expansion of

11211-527: The universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" 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. Shapley%E2%80%93Curtis debate The Great Debate , also called

11322-462: 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 that does not require an answer, according to the theories that 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

11433-402: The universe is quantified by the scale factor , a {\displaystyle a} , which is proportional to the average separation between objects, such as galaxies. The scale factor is a function of time and is conventionally set to be a = 1 {\displaystyle a=1} at the present time. Because the universe is expanding, a {\displaystyle a}

11544-480: The universe is static his "greatest mistake". On its own, general relativity could predict the expansion of the universe, which (through observations such as the bending of light by large masses , or the precession of the orbit of Mercury ) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated. In 1931, Einstein went to Mount Wilson Observatory to thank Hubble for providing

11655-424: The universe to stop expanding and begin to contract, which corresponds to the scale factor decreasing in time. The scale factor a {\displaystyle a} is a parameter of the FLRW metric , and its time evolution is governed by the Friedmann equations . The second Friedmann equation, shows how the contents of the universe influence its expansion rate. Here, G {\displaystyle G}

11766-490: The universe. Though the Hubble constant H 0 is constant at any given moment in time, the Hubble parameter H , of which the Hubble constant is the current value, varies with time, so the term constant is sometimes thought of as somewhat of a misnomer. A decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of an expanding universe by using Einstein field equations of general relativity . Applying

11877-412: 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 that eventually dominates in this model. The purple grid lines mark cosmological time at intervals of one billion years from the Big Bang. The cyan grid lines mark comoving distance at intervals of one billion light-years in

11988-489: The work of Adriaan van Maanen , a well-respected astronomer of the time, as providing evidence supporting Shapley's argument. Van Maanen had claimed he had observed the Pinwheel Galaxy rotating, and that if the Pinwheel Galaxy were in fact a distinct galaxy and could be observed to be rotating on a timescale of years, its orbital velocity would be enormous and there would be a violation of the universal speed limit,

12099-511: The world's most powerful telescope at the time. His observations of Cepheid variable stars in "spiral nebulae" enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be called nebulae , and it was only gradually that the term galaxies replaced it. The parameters that appear in Hubble's law, velocities and distances, are not directly measured. In reality we determine, say,

12210-529: Was considerable scatter (now known to be caused by peculiar velocities —the 'Hubble flow' is used to refer to the region of space far enough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 (km/s)/Mpc (much higher than the currently accepted value due to errors in his distance calibrations; see cosmic distance ladder for details). Hubble's law can be easily depicted in

12321-443: Was formed). 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 Earth at the present day. The orange line shows the present-day distance between the quasar and Earth, about 28 billion light-years, which is a larger distance than the age of the universe multiplied by the speed of light,  ct . According to

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