The metric expansion of space is the increase of the distance between
two distant parts of the universe with time.[1] It is an intrinsic
expansion whereby the scale of space itself changes. It means that the
early universe did not expand "into" anything and does not require
space to exist "outside" the universe - instead space itself changed,
carrying the early universe with it as it grew. This is a completely
different kind of expansion than the expansions and explosions seen in
daily life. It also seems to be a property of the entire universe as a
whole rather than a phenomenon that applies just to one part of the
universe or can be observed from "outside" it.
Metric expansion is a key feature of
Big Bang
Big Bang cosmology, is modeled
mathematically with the Friedmann-Lemaître-Robertson-Walker metric
and is a generic property of the universe we inhabit. However, the
model is valid only on large scales (roughly the scale of galaxy
clusters and above), because gravitational attraction binds matter
together strongly enough that metric expansion cannot be observed at
this time, on a smaller scale. As such, the only galaxies receding
from one another as a result of metric expansion are those separated
by cosmologically relevant scales larger than the length scales
associated with the gravitational collapse that are possible in the
age of the universe given the matter density and average expansion
rate.
According to measurements, the universe's expansion rate was
decelerating until about 5 billion years ago due to the gravitational
attraction of the matter content of the universe, after which time the
expansion began accelerating. The source of this acceleration is
currently unknown. Physicists have postulated the existence of dark
energy, appearing as a cosmological constant in the simplest
gravitational models as a way to explain the acceleration. According
to the simplest extrapolation of the currently-favored cosmological
model (known as "ΛCDM"), this acceleration becomes more dominant into
the future. In June 2016,
NASA
NASA and
ESA
ESA scientists reported that the
universe was found to be expanding 5% to 9% faster than thought
earlier, based on studies using the Hubble
Space
Space Telescope.[2]
While special relativity prohibits objects from moving faster than
light with respect to a local reference frame where spacetime can be
treated as flat and unchanging, it does not apply to situations where
spacetime curvature or evolution in time become important. 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 "separation" is different
from that used in an inertial frame. This can be seen when observing
distant galaxies more than the
Hubble radius
Hubble radius away from us
(approximately 4.5 gigaparsecs or 14.7 billion light-years);
these galaxies have a recession speed that is faster than the speed of
light.
Light
Light that is emitted today from galaxies beyond the
cosmological event horizon, about 5 gigaparsecs or 16 billion
light-years, will never reach us, although we can still see the light
that these galaxies emitted in the past. Because of the high rate of
expansion, it is also possible for a distance between two objects to
be greater than the value calculated by multiplying the speed of light
by the age of the universe. These details are a frequent source of
confusion among amateurs and even professional physicists.[3] Due to
the non-intuitive nature of the subject and what has been described by
some as "careless" choices of wording, certain descriptions of the
metric expansion of space and the misconceptions to which such
descriptions can lead are an ongoing subject of discussion within
education and communication of scientific concepts.[4][5][6][7]
Contents
1 Cosmic inflation
2 Overview of metrics and comoving coordinates
2.1 Example: "Great Circle" metric for Earth's surface
2.2 Metric tensors
2.3 Comoving coordinates
3 Understanding the expansion of the universe
3.1 Measurement of expansion and change of rate of expansion
3.2 Measuring distances in expanding space
3.3
Topology
Topology of expanding space
3.4
Density
Density of universe during expansion
3.5 Effects of expansion on small scales
3.6 Metric expansion and speed of light
3.7 Scale factor
3.8 Other conceptual models of expansion
4 Theoretical basis and first evidence
4.1 Hubble's law
4.2
Cosmological constant
Cosmological constant and the Friedmann equations
4.3 Hubble's concerns over the rate of expansion
4.4 Inflation as an explanation for the expansion
4.5 Measuring distance in a metric space
5 Observational evidence
6 Notes
7 Printed references
8 External links
Cosmic inflation
Main articles: inflation (cosmology) and inflaton
Around 1930,
Edwin Hubble
Edwin Hubble discovered that light from remote galaxies
was redshifted; i.e. the more remote galaxies were, the more shifted
was the light coming from them. This observation was quickly
interpreted as galaxies being receding from earth. If earth is not in
some special, privileged, central position in the universe, then it
would mean all galaxies are moving apart, and the further away, the
faster they are moving away. It is now understood that the universe is
expanding, carrying the galaxies with it, and causing this
observation. Many other observations agree, and also lead to the same
conclusion. However, for many years it was not clear why or how the
universe might be expanding, or what it might signify.
Based on a huge amount of experimental observation and theoretical
work, it is now believed that the reason for the observation is that
space itself is expanding, and that it expanded very rapidly within
the first fraction of a second after the Big Bang. This kind of
expansion is known as the "metric expansion". In mathematics and
physics, a "metric" means a measure of distance, and the term implies
that the sense of distance within the universe is itself changing,
although at this time it is far too small an effect to see on less
than an intergalactic scale.
The modern explanation for the metric expansion of space was proposed
by physicist
Alan Guth
Alan Guth in 1979, while investigating the problem of why
no magnetic monopoles are seen today. 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 like
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.
No field has yet discovered what is responsible for the cosmic
inflation. However such a field, if found in the future, would be
scalar. The first similar scalar field proven to exist was only
discovered in 2012 - 2013 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.
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.
Overview of metrics and comoving coordinates
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Human
Human timeline and Life timeline
Main articles:
Metric (mathematics)
Metric (mathematics) and tensor
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
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. GPS,
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. 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 will also be expanding (extremely slowly). 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 or 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.
Example: "Great Circle" metric for Earth's surface
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
Earth is
two-dimensional, points on the surface of the
Earth
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
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
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.
Metric tensors
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 grows or shrinks 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.
Comoving coordinates
Main article: Comoving coordinates
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
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.
Understanding the expansion of the universe
Main article: Inflation (cosmology)
Measurement of expansion and change of rate of expansion
When an object is receding, its light gets stretched (redshifted)
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 occurred with the
creation of the Hubble diagram. Using standard candles with known
intrinsic brightness, the expansion of the universe has been measured
using redshift to derive Hubble's Constant: H0 = 67.15 ± 1.2
(km/s)/Mpc. For every million parsecs of distance from the observer,
the rate of expansion increases by about 67 kilometers per
second.[8][9][10]
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. Surprisingly, the deceleration
parameter was measured by two different groups to be less than zero
(actually, consistent with −1) which implied that today the Hubble
parameter is converging to a constant value as time goes on. Some
cosmologists have whimsically called the effect associated with the
"accelerating universe" the "cosmic jerk".[11] The 2011 Nobel Prize in
Physics
Physics was given for the discovery of this phenomenon.[12]
Measuring distances in expanding space
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Two views of an isometric embedding of part of the visible universe
over most of its history, showing how a light ray (red line) can
travel an effective distance of 28 billion light years (orange line)
in just 13 billion years of cosmological time. (Mathematical details)
At cosmological scales the present universe is geometrically flat,[13]
which is to say that the rules of
Euclidean geometry
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.
The images to the right show two views of spacetime diagrams that show
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 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
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
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. In particular, light always
travels locally at the speed c; in our 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 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
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
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
Earth was actually moving away from the
Earth
Earth when it was first emitted, in the sense that the metric distance
to the
Earth
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
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.
Topology
Topology of expanding space
A graphical representation of the expansion of the universe with the
inflationary epoch represented as the dramatic expansion of the metric
seen on the left. This diagram can be confusing because the expansion
of space looks like it is happening into an empty "nothingness".
However, this is a choice made for convenience of visualization: it is
not a part of the physical models which describe the expansion.
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.[14]
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
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.[15]
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.
Density
Density of universe during expansion
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.
Effects of expansion on small scales
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.
Animation of an expanding raisin bread model. As the bread doubles in
width (depth and length), the distances between raisins also double.
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
Hubble Flow is
changing as well as the masses of the objects to which we are being
gravitationally pulled. Currently, the
Local Group
Local Group is being
gravitationally pulled towards either the Shapley
Supercluster
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
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. As the
universe expands and the matter in it thins, the gravitational
attraction decreases (since it is proportional to the density), while
the cosmological repulsion increases; thus the ultimate fate of the
ΛCDM
ΛCDM universe is a near vacuum expanding at an ever-increasing rate
under the influence of the cosmological constant. 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
Milky Way do not expand and the
Andromeda galaxy is moving fast enough towards us that it will still
merge with the
Milky Way
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.
Metric expansion and speed of light
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].
While special relativity prohibits objects from moving faster than
light with respect to a local reference frame where spacetime can be
treated as flat and unchanging, it does not apply to situations where
spacetime curvature or evolution in time become important. 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
4.5 gigaparsecs or 14.7 billion light-years, away from us have a
recession speed that is faster than the speed of light. Visibility of
these objects depends on the exact expansion history of the universe.
Light
Light that is emitted today from galaxies beyond the cosmological
event horizon, about 5 gigaparsecs or 16 billion light-years,
will never reach us, although we can still see the light that these
galaxies emitted in the past.
Because of the high rate of expansion, it is also possible for a
distance between two objects to be greater than the value calculated
by multiplying the speed of light by the age of the universe. These
details are a frequent source of confusion among amateurs and even
professional physicists.[16] Due to the non-intuitive nature of the
subject and what has been described by some as "careless" choices of
wording, certain descriptions of the metric expansion of space and the
misconceptions to which such descriptions can lead are an ongoing
subject of discussion in the realm of pedagogy and communication of
scientific concepts.[4][5][6][7] In June 2016,
NASA
NASA and
ESA
ESA scientists
reported that the universe was found to be expanding 5% to 9% faster
than thought earlier, based on studies using the Hubble Space
Telescope.[2]
Scale factor
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 13.799 ± 0.021 billion
years ago. 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.
Other conceptual models of 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. If we stretch the rope in accordance
with the
ΛCDM
ΛCDM scale factor and think of the ant's speed as the speed
of light, then this analogy is numerically accurate — the ant's
position over time will match the path of the red line on the
embedding diagram above.
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.
Theoretical basis and first evidence
The expansion of the universe proceeds in all directions as determined
by the Hubble constant. However, the
Hubble constant
Hubble constant can change in the
past and in the future, dependent on the observed value of density
parameters (Ω). Before the discovery of dark energy, it was believed
that the universe was matter-dominated, and so Ω on this graph
corresponds to the ratio of the matter density to the critical density
(
Ω
m
displaystyle Omega _ m
).
Hubble's law
Technically, the metric expansion of space is a feature of many
solutions[which?] to the
Einstein field equations
Einstein field equations of general
relativity, and distance is measured using the Lorentz interval. 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).
Cosmological constant
Cosmological constant and the Friedmann equations
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 1922
Alexander Friedmann
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.[17] The
observations of
Edwin Hubble
Edwin Hubble in 1929 suggested that distant galaxies
were all apparently moving away from us, so that many scientists came
to accept that the universe was expanding.
Hubble's concerns over the rate of expansion
While the metric expansion of space appeared to be implied by Hubble's
1929 observations, Hubble disagreed with the expanding-universe
interpretation of the data:
[…] if redshift are not primarily due to velocity shift […] the
velocity-distance relation is linear, the distribution of the nebula
is uniform, there is no evidence of expansion, no trace of curvature,
no restriction of the time scale […] and we find ourselves in the
presence of one of the principles of nature that is still unknown to
us today […] whereas, if redshifts are velocity shifts which measure
the rate of expansion, the expanding models are definitely
inconsistent with the observations that have been made […] expanding
models are a forced interpretation of the observational results.
— E. Hubble, Ap. J., 84, 517, 1936 [18]
[If the redshifts are a Doppler shift …] the observations as they
stand lead to the anomaly of a closed universe, curiously small and
dense, and, it may be added, suspiciously young. 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.
— E. Hubble, Monthly Notices of the Royal Astronomical Society,
97, 506, 1937 [19]
Hubble's skepticism about the universe being too small, dense, and
young turned out to be based on an observational error. Later
investigations appeared to show that Hubble had confused distant H II
regions for Cepheid variables and the Cepheid variables themselves had
been inappropriately lumped together with low-luminosity RR Lyrae
stars causing calibration errors that led to a value of the Hubble
Constant of approximately 500 km/s/Mpc instead of the true value of
approximately 70 km/s/Mpc. 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 1950s, the new lower values for the
Hubble Constant
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.[20]
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.[21] In 2001, Dr. Wendy Freedman
determined space to expand at 72 kilometers per second per megaparsec
- roughly 3.3 million light years - meaning that as we move away from
Earth
Earth every 3.3 million light years is moving 72 kilometers a second
faster.[21] In the summer of 2016, another measurement reported a
value of 73 for the constant, thereby contradicting 2013 measurements
from the European Planck mission of slower expansion value of 67. The
discrepancy opened new questions concerning the nature of dark energy,
or of neutrinos.[21]
Inflation as an explanation for the expansion
Until the theoretical developments in the 1980s 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?" is now
answered by understanding the details of the inflation decay process
which occurred in the first 10−32 seconds of the existence of our
universe.[22] During inflation, the metric changed exponentially,
causing any volume of space that was smaller than an atom to grow to
around 100 million light years across in a time scale similar to the
time when inflation occurred (10−32 seconds).
Measuring distance in a metric space
A diagram depicting the expansion of the universe and the appearance
of galaxies moving away from a single galaxy. The phenomenon is
relative to the observer. Object t1 is a smaller expansion than t2.
Each section represents the movement of the red galaxies over the
white galaxies for comparison. The blue and green galaxies are markers
to show which galaxy is the same one (fixed center point) in the
subsequent box. t = time.
Main article: Comoving coordinates
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.
Observational evidence
Theoretical cosmologists developing models of the universe have drawn
upon a small number of reasonable assumptions in their work. These
workings have led to models in which the metric expansion of space is
a likely feature of the universe. Chief among the underlying
principles that result in models including metric expansion as a
feature are:
the
Cosmological Principle
Cosmological Principle which demands that the universe looks the
same way in all directions (isotropic) and has roughly the same smooth
mixture of material (homogeneous).
the
Copernican Principle
Copernican Principle which demands that no place in the universe
is preferred (that is, the universe has no "starting point").
Scientists have tested carefully whether these assumptions are valid
and borne out by observation. Observational cosmologists have
discovered evidence — very strong in some cases — that supports
these assumptions, and as a result, metric expansion of space is
considered by cosmologists to be an observed feature on the basis that
although we cannot see it directly, scientists have tested the
properties of the universe and observation provides compelling
confirmation.[23] Sources of this confidence and confirmation include:
Hubble demonstrated that all galaxies and distant astronomical objects
were moving away from us, as predicted by a universal expansion.[24]
Using the redshift of their electromagnetic spectra to determine the
distance and speed of remote objects in space, he showed that all
objects are moving away from us, and that their speed is proportional
to their distance, a feature of metric expansion. Further studies have
since shown the expansion to be highly isotropic and homogeneous, that
is, it does not seem to have a special point as a "center", but
appears universal and independent of any fixed central point.
In studies of large-scale structure of the cosmos taken from redshift
surveys a so-called "End of Greatness" was discovered at the largest
scales of the universe. Until these scales were surveyed, the universe
appeared "lumpy" with clumps of galaxy clusters and superclusters and
filaments which were anything but isotropic and homogeneous. This
lumpiness disappears into a smooth distribution of galaxies at the
largest scales.
The isotropic distribution across the sky of distant gamma-ray bursts
and supernovae is another confirmation of the Cosmological Principle.
The
Copernican Principle
Copernican Principle was not truly tested on a cosmological scale
until measurements of the effects of the cosmic microwave background
radiation on the dynamics of distant astrophysical systems were made.
A group of astronomers at the
European Southern Observatory
European Southern Observatory noticed,
by measuring the temperature of a distant intergalactic cloud in
thermal equilibrium with the cosmic microwave background, that the
radiation from the
Big Bang
Big Bang was demonstrably warmer at earlier
times.[25] Uniform cooling of the cosmic microwave background over
billions of years is strong and direct observational evidence for
metric expansion.
Taken together, these phenomena overwhelmingly support models that
rely on space expanding through a change in metric. Interestingly, it
was not until the discovery in the year 2000 of direct observational
evidence for the changing temperature of the cosmic microwave
background that more bizarre constructions could be ruled out. Until
that time, it was based purely on an assumption that the universe did
not behave as one with the
Milky Way
Milky Way sitting at the middle of a
fixed-metric with a universal explosion of galaxies in all directions
(as seen in, for example, an early model proposed by Milne). Yet
before this evidence, many rejected the Milne viewpoint based on the
mediocrity principle.
Notes
^ Overbye, Dennis (20 February 2017). "Cosmos Controversy: The
Universe
Universe Is Expanding, but How Fast?". New York Times. Retrieved 21
February 2017.
^ a b Radford, Tim (3 June 2016). "
Universe
Universe is expanding up to 9%
faster than we thought, say scientists". The Guardian. Retrieved 3
June 2016.
^ Tamara M. Davis and Charles H. Lineweaver, Expanding Confusion:
common misconceptions of cosmological horizons and the superluminal
expansion of the universe. astro-ph/0310808
^ a b Alan B. Whiting (2004). "The Expansion of Space: Free Particle
Motion and the Cosmological Redshift". arXiv:astro-ph/0404095 .
Bibcode:2004Obs...124..174W.
^ a b EF Bunn & DW Hogg (2008). "The kinematic origin of the
cosmological redshift". American Journal of Physics. 77: 688.
arXiv:0808.1081 . Bibcode:2009AmJPh..77..688B.
doi:10.1119/1.3129103.
^ a b Yu. V. Baryshev (2008). "Expanding Space: The Root of Conceptual
Problems of the Cosmological Physics". Practical Cosmology. 2:
20–30. arXiv:0810.0153 . Bibcode:2008pc2..conf...20B.
^ a b JA Peacock (2008). "A diatribe on expanding space".
arXiv:0809.4573 .
^ "Planck Mission Brings universe Into Sharp Focus". NASA. 2013-03-21.
Retrieved 2013-03-21.
^ "NASA's Hubble Rules Out One Alternative to Dark Energy". NASA.
2011-03-14. Retrieved 2011-03-27.
^ Riess, Adam G.; Lucas Macri; Stefano Casertano; Hubert Lampeitl;
Henry C. Ferguson; Alexei V. Filippenko; Saurabh W. Jha; Weidong Li;
Ryan Chornock (2011-04-01). "A 3% solution: determination of the
Hubble Constant
Hubble Constant with the
Hubble Space Telescope
Hubble Space Telescope and Wide Field Camera
3". The Astrophysical Journal. 730 (2): 119. arXiv:1103.2976 .
Bibcode:2011ApJ...730..119R. doi:10.1088/0004-637X/730/2/119.
^ Overbye, Dennis (11 October 2003). "A 'Cosmic Jerk' That Reversed
the universe". New York Times.
^ The Nobel Prize in
Physics
Physics 2011
^ Krauss, Lawrence M. (2012). A
Universe
Universe from Nothing. Free Press.
p. 82. ISBN 9781451624458.
^ Peebles, P. J. E. (1993). Principles of Physical Cosmology.
Princeton University Press. p. 73.
^ Rothstein, Dave (23 April 2003). "What is the universe expanding
into?". Ask an Astronomer. Retrieved 28 April 2017.
^ Tamara M. Davis and Charles H. Lineweaver, Expanding Confusion:
common misconceptions of cosmological horizons and the superluminal
expansion of the universe. astro-ph/0310808
^ Friedman, A: Über die Krümmung des Raumes, Z. Phys. 10 (1922),
377–386. (English translation in: Gen. Rel. Grav. 31 (1999),
1991–2000.)
^ Hubble, Edwin (1936). "Effects of Red Shifts on the Distribution of
Nebulae". The Astrophysical Journal. 84: 517.
Bibcode:1936ApJ....84..517H. doi:10.1086/143782.
^ Hubble, Edwin (1937). "Red-shifts and the distribution of nebulæ".
Monthly Notices of the Royal Astronomical Society. 97: 506.
Bibcode:1937MNRAS..97..506H. doi:10.1093/mnras/97.7.506.
^ Gingerich, Owen (1999). "A Brief History of Our View of the
Universe".
Publ. Astron. Soc. Pac. Astronomical Society of the
Pacific. 111 (757): 254–257. Bibcode:1999PASP..111..254G.
doi:10.1086/316324. JSTOR 10.1086/316324.
^ a b c Overbye, Dennis (2017-02-20). "Cosmos Controversy: The
Universe
Universe Is Expanding, but How Fast?". The New York Times.
ISSN 0362-4331. Retrieved 2017-06-29.
^ Interview with Alan Guth; THE INFLATIONARY UNIVERSE, [11.19.02] by
Edge.org. [1]
^ Bennett, Charles L. (27 April 2006). "
Cosmology
Cosmology from start to
finish". Nature. 440 (7088): 1126–1131. Bibcode:2006Natur.440.1126B.
doi:10.1038/nature04803. PMID 16641983.
^ Hubble, Edwin, "A Relation between
Distance
Distance and Radial Velocity
among Extra-Galactic Nebulae" (1929) Proceedings of the National
Academy of Sciences of the United States of America, Volume 15, Issue
3, pp. 168-173 (Full article, PDF)
^ Astronomers reported their measurement in a paper published in the
December 2000 issue of
Nature
Nature titled The microwave background
temperature at the redshift of 2.33771 which can be read here [2]. A
press release from the
European Southern Observatory
European Southern Observatory explains the
findings to the public.
Printed references
Eddington, Arthur. The Expanding Universe: Astronomy's 'Great Debate',
1900-1931. Press Syndicate of the University of Cambridge, 1933.
Liddle, Andrew R. and David H. Lyth. Cosmological Inflation and
Large-Scale Structure. Cambridge University Press, 2000.
Lineweaver, Charles H. and Tamara M. Davis, "Misconceptions about the
Big Bang", Scientific American, March 2005 (non-free content).
Mook, Delo E. and Thomas Vargish. Inside Relativity. Princeton
University Press, 1991.
External links
Swenson, Jim Answer to a question about the expanding universe
Felder, Gary, "The Expanding universe".
NASA's
WMAP
WMAP team offers an "Explanation of the universal expansion" at
a very elementary level
Hubble Tutorial from the University of Wisconsin
Physics
Physics Department
Expanding raisin bread from the University of Winnipeg: an
illustration, but no explanation
"Ant on a balloon" analogy to explain the expanding universe at "Ask
an Astronomer". (The astronomer who provides this explanation is not
specified.)
Researched Essay: "The Big Bang" - Proof that the
Universe
Universe is
Expanding
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