Until a few hundred years ago, the Solar System and the Universe were equivalent in the minds of scientists, so the discovery that the Earth is not the center of the Solar System was an important step in the development of cosmology. Early in the 20th century Shapley established that the Solar System is far from the center of the Milky Way. So by the 1920's, the stage was set for the critical observational discoveries that led to the Big Bang model of the Universe.

The slope of the fitted line is 464 km/sec/Mpc, and is now known as the Hubble constant, H

1/HThus Hubble's value is equivalent to approximately 2 Gyr. Since this should be close to the age of the Universe, and we know (and it was known in 1929) that the age of the Earth is larger than 2 billion years, Hubble's value for H_{o}= (978 Gyr)/(H_{o}in km/sec/Mpc)

Hubble's data in 1929 is actually quite poor, since individual
galaxies have peculiar velocities of several hundred km/sec,
and Hubble's data only went out to 1200 km/sec. This has led
some people to propose
quadratic redshift-distance laws,
but the data shown below on Type Ia SNe from
Riess, Press and Kirshner (1996)

extend beyond 30,000 km/sec and provide a dramatic confirmation of the Hubble law,

v = dD/dt = H*DThe fitted line in this graph has a slope of 64 km/sec/Mpc. Since we measure the radial velocity using the Doppler shift, it is often called the

1 + z = lambda(observed)/lambda(emitted)where lambda is the wavelength of a line or feature in the spectrum of an object. We know from relativity that the redshift is given by

1 + z = sqrt((1+v/c)/(1-v/c)) so v = cz + ...

The subscript "o" in H_{o} (pronounced "aitch naught") indicates the
current value of a time variable quantity. Since the 1/H_{o} is
approximately the age of the Universe, the value of H depends on
time. Another quantity with a naught is t_{o}, the age of the
Universe.

The linear distance-redshift law found by Hubble is compatible with
a Copernican view of the Universe: our position is not a special one.
First note that the recession velocity is symmetric: if A sees B receding,
then B sees that A is receding, as shown in this diagram:

which is based on a sketch by Bob Kirshner. Then consider the following space-time diagram showing several nearby galaxies moving away from us from our point of view (galaxy A, the blue worldline) on the top and from galaxy B's (the green worldline) point of view on the bottom.

The diagrams from the two different points of view are identical except for the names of the galaxies. The v(sq) = D

Thus if we saw a quadratic velocity vs. distance law, then an observer in a different galaxy would see a different law -- and one that would be different in different directions. Thus if we saw v(sq), then B would see much higher radial velocities in the "plus" direction than in the "minus" direction. This effect would allow one to locate the "center of Universe" by finding the one place where the redshift-distance law was the same in all directions. Since we actually see the same redshift-distance law in all directions, either the redshift-distance law is linear or else we are at the center which is anti-Copernican.

The Hubble law generates a homologous expansion which does not change the shapes of objects, while other possible velocity-distance relations lead to distortions during expansion.

The Hubble law defines a special frame of reference at any
point in the Universe. An observer with a large motion with
respect to the Hubble flow would measure blueshifts in front
and large redshifts behind, instead of the same redshifts
proportional to distance in all directions.
Thus we can measure our motion relative to the Hubble flow,
which is also our motion relative to the observable
Universe. A *comoving*
observer is at rest in this special frame of reference. Our
Solar System is not quite comoving: we have a velocity of 370
km/sec relative to the observable Universe. The Local Group
of galaxies, which includes the Milky Way, appears to be moving
at 600 km/sec relative to the observable Universe.

Hubble also measured the number of galaxies in different directions
and at different brightness in the sky. He found approximately
the same number of faint galaxies in all directions, even though
there is a large excess of bright galaxies in the Northern part of
the sky. When a distribution is the same in all directions,
it is *isotropic*.
And when he looked for galaxies with fluxes brighter
than F/4 he saw approximately 8 times more galaxies than he
counted which were brighter than F. Since a flux 4 times smaller
implies a doubled distance, and hence a detection volume that
is 8 times larger, this indicated that the Universe is close
to *homogeneous* (having uniform density) on large scales.

The figure above shows a homogeneous but not isotropic pattern on the left and an isotropic but not homogeneous pattern on the right. If a figure is isotropic from more than 1 (2 if spherical) points, then it must also be homogeneous.

Of course the Universe is not really homogeneous and isotropic,
because it contains dense regions like the Earth. But it can still
be statistically homogeneous and isotropic, like this
24 kB simulated galaxy field, which is
homogeneous and isotropic after smoothing out small scale details.
Peacock and Dodds (1994, MNRAS, 267, 1020) have looked at the
fractional density fluctuations in the nearby Universe as a function of
the radius of a top-hat smoothing filter, and find:

Thus for 100 Mpc regions the Universe is smooth to within several percent. Redshift surveys of very large regions confirm this tendency toward smoothness on the largest scales, even though nearby galaxies show large inhomogeneities like the Virgo Cluster and the supergalactic plane.

The case for an isotropic and homogeneous Universe became much stronger
after Penzias and Wilson announced the discovery of the Cosmic Microwave
Background in 1965. They observed an excess flux at 7.5 cm wavelength
equivalent to the radiation from a blackbody with a temperature of
3.7+/-1 degrees Kelvin. [The Kelvin temperature scale has degrees of the
same size as the Celsius scale, but it is referenced at absolute zero,
so the freezing point of water is 273.15 K.]
A blackbody radiator is an object that absorbs any radiation that hits it,
and has a constant temperature.
Many groups have measured
the intensity of the CMB at different wavelengths. Currently the best
information on the spectrum of the CMB comes from the FIRAS instrument
on the
COBE
satellite, and it is shown below:

The x axis variable is the wavenumber or 1/[wavelength in cm]. The y axis variable is the power per unit area per unit frequency per unit solid angle in MegaJanskies per steradian. 1 Jansky is 10

The temperature of the CMB is almost the same all over the sky.
The figure below shows a map of the temperature on a scale where
0 K is black and 3 K is white.

Thus the microwave sky is extremely isotropic. These observations are combined into the Cosmological Principle:

Another piece of evidence in favor of the Big Bang is the abundance of the light elements, like hydrogen, deuterium (heavy hydrogen), helium and lithium. As the Universe expands, the photons of the CMB lose energy due to the redshift and the CMB becomes cooler. That means that the CMB temperature was higher in the past. When the Universe was only a few minutes old, the temperature was high enough to make the light elements by nuclear fusion. The theory of Big Bang Nucleosynthesis predicts that about 1/4 of the mass of the Universe should be helium, which is very close to what is observed. The abundance of deuterium is inversely related to the density of nucleons in the Universe, and the observed value of the deuterium abundance suggests that there is one nucleon for every 4 cubic meters of space in the the Universe.

The Cosmological Principle:

To say the Universe is homogeneous means that any measurable
property of the Universe is the same everywhere. This is only
approximately true, but it appears to be an excellent approximation
when one averages over large regions. Since the age of the
Universe is one of the measurable quantities, the homogeneity
of the Universe must be defined on a surface of constant proper
time since the Big Bang. Time dilation causes the proper time measured
by an observer to depend on the velocity of the observer, so we
specify that the time variable t in the Hubble law is the
proper time since the Big Bang *for comoving observers*.

With the correct interpretation of the variables, the Hubble law
(*v = HD*) is
true for all values of D, even very large ones which give v > c.
But one must be careful in interpreting the distance and velocity.
The distance in the Hubble law must be defined so that if A and B
are two distant galaxies seen by us in the same direction, and A and B
are not too far from each other, then the difference in distances from
us, D(A)-D(B), is the distance A would measure to B. But this
measurement must be made "now" -- so A must measure the distance to B
at the same proper time since the Big Bang as we see now.
Thus to determine D_{now} for a distant galaxy Z we would
find a chain of galaxies ABC...XYZ
along the path to Z, with each element of the chain close to its neighbors,
and then have each galaxy in the chain measure the distance to the next
galaxy at time t_{o} since the Big Bang.
The distance to Z, D(us to Z), is the sum of all these subintervals:

DAnd the velocity in the Hubble law is just the change of D_{now}= D(us to Z) = D(us to A) + D(A to B) + ... D(X to Y) + D(Y to Z)

but now showing the lightcones. Note how the lightcones must tip over along with the worldlines of the galaxies, showing that in these cosmological variables the speed of light is c

The time and distance used in the Hubble law are not the same as the
x and t used in special relativity, and this often leads to confusion.
In particular, galaxies that are far enough away from us necessarily
have velocities greater than the speed of light:

Worldlines of comoving observers are plotted and decorated with small, schematic lightcones. The red pear-shaped object is our past light cone. Notice that the red curve always has the same slope as the little light cones. In these variables, velocities greater than c are certainly possible, and since the open Universes are spatially infinite, they are actually required. But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get:

The grey hyperbolae show the surfaces of constant proper time since the Big Bang. When we flatten these out to make the previous space-time diagram, the worldlines of the galaxies get flatter and giving velocities v = dD

v = HNote that the redshift-velocity law is_{o}D_{now}D_{now}= (c/H_{o})ln(1+z) 1+z = exp(v/c)

1+z = sqrt[(1+v/c)/(1-v/c)]which only applies to special relativistic coordinates, not to cosmological coordinates.

While the Hubble law distance is in principle measurable, the need for
helpers all along the chain of galaxies out to a distant galaxy makes
its use quite impractical. Other distances can be defined and measured
more easily. One is the *angular size distance*, defined by

theta = size/Dwhere "size" is the transverse extent of an object and "theta" is the angle (in radians) that it subtends on the sky. For the zero density model, the special relativistic x is equal to the angular size distance, x = D_{A}so D_{A}= size/theta

Another important distance indicator is the flux received from an
object, and this defines the *luminosity distance*
D_{L} through

Flux = Luminosity/(4*pi*DA fourth distance is based on the light travel time: D_{L}^{2})

The predicted curve relating one distance indicator to another depends
on the cosmological model. The plot of redshift vs distance for Type Ia
supernovae shown earlier is really a plot of cz vs D_{L},
since fluxes
were used to determine the distances of the supernovae.
This data clearly rules out models that do not give a linear
cz vs D_{L}
relation for small cz.
Extension of these observations to more
distant supernovae
have started to allow us to measure the
curvature of the cz
vs D_{L} relation, and provide more valuable
information about the Universe.

The perfect fit of the CMB to a
blackbody allows us to determine the
D_{A} vs D_{L} relation.
Since the CMB is produced at great distance but still looks like a
blackbody, a distant blackbody must look like a blackbody (even though
the temperature will change due to the redshift).
The luminosity of blackbody is

L = 4*pi*Rwhere R is the radius, T^{2}*sigma*T_{em}^{4}

Tand the flux will be_{obs}= T_{em}/(1+z)

F = thetawhere the angular radius is related to the physical radius by^{2}*sigma*T_{obs}^{4}

theta = R/DCombining these equations gives_{A}

DModels that do not predict this relationship between D_{L}^{2}= L/(4*pi*F) = (4*pi*R^{2}*sigma*T_{em}^{4})/(4*pi*theta^{2}*sigma*T_{obs}^{4}) = D_{A}^{2}*(1+z)^{4}or D_{L}= D_{A}*(1+z)^{2}

Here is a
Javascript calculator that takes
H_{o},
Omega_{M},
the normalized
cosmological constant *lambda*
and the redshift z
and then computes all of the these distances.
Here are the technical formulae
for these distances.
The graphs below show these
distances vs. redshift for three models: the critical density matter
dominated Einstein - de Sitter model (EdS), the empty model, and the
accelerating Lambda CDM model (LCDM) that is the current concensus model.

Note that all the distances are very similar for small distances, with

Because the velocity or dD_{now}/dt is strictly proportional to
D_{now}, the
distance between any pair of comoving objects
grows by a factor (1+H*dt) during a time interval dt.
This means we can write the distance to any comoving observer as

Dwhere D_{G}(t) = a(t)*D_{G}(t_{o})

We can compute the dynamics of the Universe by considering an object
with distance D(t) = a(t) D_{o}. This distance and the corresponding
velocity dD/dt are measured with respect to us at the center of the
coordinate system. The gravitational acceleration due to the spherical
ball of matter with radius D(t) is g = -G*M/D(t)^{2} where the mass
is M = 4*pi*D(t)^{3}*rho(t)/3. Rho(t) is the density of matter which
depends only on the time since the Universe is homogeneous. The mass
contained within D(t) is independent of the time since the interior
matter has slower expansion velocity while the exterior matter has
higher expansion velocity and thus stays outside. The gravitational
effect of the external matter vanishes: the gravitational acceleration
inside a spherical shell is zero, and all the matter in the Universe
with distance from us greater than D(t) can be represented as union of
spherical shells. With a constant mass interior to D(t) producing the
acceleration of the edge, the problem reduces to the problem of a
body moving radially in the gravitational field of a point mass.
If the velocity is less than the escape velocity, the expansion
will stop and recollapse. If the velocity equals the
escape velocity
we have the critical case. This gives

v = H*D = v(esc) = sqrt(2*G*M/D) HFor rho less than or equal to the critical density rho(crit), the Universe expands forever, while for rho greater than rho(crit), the Universe will eventually stop expanding and recollapse. The value of rho(crit) for H^{2}*D^{2}= 2*(4*pi/3)*rho*D^{2}or rho(crit) = 3*H^{2}/(8*pi*G)

One consequence of general relativity is that the curvature of space
depends on the ratio of
rho to
rho(crit). We call this ratio
Omega = rho/rho(crit). For Omega less than 1, the Universe has
negatively curved or
hyperbolic geometry. For Omega = 1, the Universe has Euclidean
or flat geometry. For Omega greater than 1, the Universe has
positively curved or spherical geometry. We have already seen
that the zero density case has hyperbolic geometry, since the cosmic
time slices in the special relativistic coordinates were hyperboloids
in this model.

The figure above shows the three curvature cases plotted along side of the corresponding a(t)'s. These a(t) curves assume that the cosmological constant is zero, which is not the current standard model. Omega > 1 still corresponds to a spherical shape, but could expand forever even though the density is greater than the critical density because of the repulsive gravitational effect of the cosmological constant.

The age of the Universe
depends on Omega_{o} as well as H_{o}. For Omega=1,
the critical density case, the scale factor is

a(t) = (t/tand the age of the Universe is_{o})^{2/3}

twhile in the zero density case, Omega=0, and_{o}= (2/3)/H_{o}

a(t) = t/tIf Omega_{o}with t_{o}= 1/H_{o}

The figure above shows the scale factor vs time measured from the present for H

The value of H_{o}*t_{o}
is a dimensionless number that should be 1 if
the Universe is almost empty and 2/3 if the Universe has the critical
density. In 1994 Freedman *et al.* (Nature, 371, 757) found
H_{o} = 80 +/- 17 and
when combined with
t_{o} = 14.6 +/- 1.7 Gyr, we find that
H_{o}*t_{o} = 1.19 +/- 0.29.
At face value this favored the empty Universe
case, but a 2 standard deviation error in the downward direction would
take us to the critical density case. Since both the age of globular
clusters used above and the value of H_{o}
depend on the distance scale in
the same way, an underlying error in the distance scale could make a
large change
in H_{o}*t_{o}.
In fact, recent data from the
HIPPARCOS satellite
suggest that the Cepheid distance scale must be increased by 10%,
and also that the
age of globular clusters
must be reduced by 20%. If we take the latest
HST value for H_{o} = 72 +/- 8 (Freedman *et al.* 2001,
ApJ, 553, 47) and the latest globular cluster ages giving
t_{o} = 13.5 +/- 0.7 Gyr, we find that
H_{o}*t_{o} = 0.99 +/- 0.12 which is
consistent with an empty Universe, but also consistent with the
accelerating Universe that is the current standard model.

However, if Omega_{o} is sufficiently greater than 1,
the Universe will eventually
stop expanding, and then Omega will become infinite. If Omega_{o} is
less than 1, the Universe will expand forever and the density goes
down faster than the critical density so Omega gets smaller and smaller.
Thus Omega = 1 is an unstable stationary point unless the expansion of the
universe is accelerating, and it is quite
remarkable that Omega is anywhere close to 1 now.

The figure above shows a(t) for three models with three different densities at a time 1 nanosecond after the Big Bang. The black curve shows the critical density case with density = 447,225,917,218,507,401,284,016 gm/cc. Adding only 1 gm/cc to this 447 sextillion gm/cc causes the Big Crunch to be right now! Taking away 1 gm/cc gives a model with Omega that is too low for our observations. Thus the density 1 ns after the Big Bang was set to an accuracy of better than 1 part in 447 sextillion. Even earlier it was set to an accuracy better than 1 part in 10

The critical density model is shown in the space-time diagram below.

Note that the worldlines for galaxies are now curved due to the force of gravity causing the expansion to decelerate. In fact, each worldline is a constant factor times a(t) which is (t/t

The diagram above shows the space-time diagram drawn on a deck of cards, and the diagram below shows the deck pushed over to put it into A's point-of-view.

Note that this is not a Lorentz transformation, and that these coordinates are not the special relativistic coordinates for which a Lorentz transformation applies. The Galilean transformation which could be done by skewing cards in this way required that the edge of the deck remain straight, and in any case the Lorentz transformation can not be done on cards in this way because there is no absolute time. But in cosmological models we do have cosmic time, which is the proper time since the Big Bang measured by comoving observers, and it can be used to set up a deck of cards. The presence of gravity in this model leads to a curved spacetime that can not be plotted on a flat space-time diagram without distortion. If every coordinate system is a distorted representation of the Universe, we may as well use a convenient coordinate system and just keep track of the distortion by following the lightcones.

Sometimes it is convenient to "divide out" the expansion of the
Universe, and the space-time diagram shows the result of dividing the
spatial coordinate by a(t). Now the worldlines of galaxies are all
vertical lines.

This division has expanded our past line cone so much that we have to replot to show it all:

If we now "stretch" the time axis near the Big Bang we get the following space-time diagram which has straight line past lightcones:

This kind of space-time diagram is called a "conformal" space-time diagram, and while it is highly distorted it makes it easy to see where the light goes. This transformation we have done is analogous to the transformation from the side view of the Earth on the left below and the Mercator chart on the right.

Note that a constant SouthEast course is a straight line on the Mercator chart which is analogous to having straight line past lightcones on the conformal space-time diagram.

Also remember that the Omega_{o} = 1 spacetime is infinite in extent
so the conformal space-time diagram can go on far beyond our past
lightcone,

as shown above.

Other coordinates can be used as well. Plotting the spatial coordinate
as angle on polar graph paper makes the translation to a different
point-of-view easy. On the diagram below,

an Omega

The conformal space-time diagram is a good tool use for describing the
meaning of CMB anisotropy observations. The Universe was opaque before
protons and electrons combined to form hydrogen atoms when the
temperature fell to about 3,000 K at a redshift of 1+z = 1090. After
this time the photons of the CMB have traveled freely through the
transparent Universe we see today. Thus the temperature of the CMB at a
given spot on the sky had to be determined by the time the hydrogen
atoms formed, usually called "recombination" even though it was the
first time so "combination" would be a better name.
Since the wavelengths in the CMB scale the same way that intergalaxy
distances do during the expansion of the Universe, we know that
a(t) had to be 0.0009 at recombination.
For the Omega_{o} = 1 model this implies that
t/t_{o} = 0.00003 so for t_{o} about 14 Gyr the time is about
380,000 years after the Big Bang. This is such a small fraction of the
current age that the "stretching" of the time axis when making a
conformal space-time diagram is very useful to magnify this part of the
history of the Universe.

The conformal space-time diagram above has exaggerated this part even further by taking the redshift of recombination to be 1+z = 144, which occurs at the blue horizontal line. The yellow regions are the past lightcones of the events which are on our past lightcone at recombination. Any event that influences the temperature of the CMB that we see on the left side of the sky must be within the left-hand yellow region. Any event that affects the temperature of the CMB on the right side of the sky must be within the right-hand yellow region. These regions have no events in common, but the two temperatures are equal to better than 1 part in 10,000. How is this possible? This is known as the "horizon" problem in cosmology.

The "inflationary scenario", developed by Starobinsky and by Guth,
offers a solution to the flatness-oldness problem and the
horizon problem. The
inflationary scenario invokes a
vacuum
energy density. We normally think of the vacuum as empty and
massless, and we can determine that the density of the vacuum is
less than 1E-30 gm/cc now. But in quantum field theory, the vacuum
is not empty, but rather filled with virtual particles:

The space-time diagram above shows virtual particle-antiparticle pairs forming out of nothing and then annihilating back into nothing. For particles of mass m, one expects about one virtual particle in each cubical volume with sides given by the Compton wavelength of the particle, h/mc, where h is Planck's constant. Thus the expected density of the vacuum is rho = m

The inflationary scenario proposes that the vacuum energy was
very large during a brief period early in the history of the
Universe. When the Universe is dominated by a vacuum energy
density the scale factor grows exponentially,
a(t) = exp(H(t_{o}-t)). The Hubble constant really is constant
during this epoch so it doesn't need the "naught".
If the inflationary epoch lasts long enough the exponential
function gets very large. This makes a(t) very large,
and thus makes the radius of curvature of the Universe
very large. The diagram below shows our
horizon superimposed
on a very large radius sphere on top, or a smaller sphere on
the bottom. Since we can only see as far as our horizon,
for the inflationary case on top the large radius sphere
looks almost flat to us.

This solves the flatness-oldness problem as long as the exponential growth during the inflationary epoch continues for at least 100 doublings. Inflation also solves the horizon problem, because the future lightcone of an event that happens before inflation is expanded to a huge region by the growth during inflation.

This space-time diagram shows the inflationary epoch tinted green, and the future lightcones of two events in red. The early event has a future lightcone that covers a huge area, that can easily encompass all of our horizon. Thus we can explain why the temperature of the microwave background is so uniform across the sky.

Of course the Universe is not really homogeneous, since it contains
dense regions like galaxies and people. These dense regions should
affect the temperature of the microwave background.
Sachs and Wolfe (1967, ApJ, 147, 73) derived the effect of the
gravitational potential perturbations on the CMB. The
gravitational potential,
phi = -GM/r, will be negative in dense lumps, and positive in
less dense regions. Photons lose energy when they climb out of
the gravitational potential wells of the lumps:

This conformal space-time diagram above shows lumps as gray vertical bars, the epoch before recombination as the hatched region, and the gravitational potential as the color-coded curve phi(x). Where our past lightcone intersects the surface of recombination, we see a temperature perturbed by dT/T = phi/(3*c

The map above is from COBE and is much better than Conklin's 2 standard deviation detection. The red part of the sky is hotter by (v/c)*T

The map above shows cosmic anisotropy (and detector noise) after the dipole pattern and the radiation from the Milky Way have been subtracted out. The anisotropy in this map has an RMS value of 30 microK, and if it is converted into a gravitational potential using Sachs and Wolfe's result and that potential is then expressed as a height assuming a constant acceleration of gravity equal to the gravity on the Earth, we get a height of twice the distance from the Earth to the Sun. The "mountains and valleys" of the Universe are really quite large.

Inflation predicts a certain statistical pattern in the anisotropy.
The quantum fluctuations normally affect very small regions of space,
but the huge exponential expansion during the inflationary epoch
makes these tiny regions observable.

The space-time diagram on the left above shows the future lightcones of quantum fluctuation events. The top of this diagram is really a volume which intersects our past lightcone making the sky. The future lightcones of events become circles on the sky. Events early in the inflationary epoch make large circles on the sky, as shown in the bottom map on the right. Later events make smaller circles as shown in the middle map, but there are more of them so the sky coverage is the same as before. Even later events make many small circles which again give the same sky coverage as seen on the top map.

An animated GIF file showing the spatial part of the above space-time diagram
as a function of time is available
here [1.2 MB].

The pattern formed by adding all of the effects from events of all ages is known as "equal power on all scales", and it agrees with the COBE data.

Having found that the observed pattern of anisotropy is consistent
with inflation, we can also ask whether the amplitude implies
gravitational forces large enough to produce the observed clustering
of galaxies.

The conformal space-time diagram above shows the phi(x) at recombination determined by COBE's dT data, and the worldlines of galaxies which are perturbed by the gravitational forces produced by the gradient of the potential. Matter flows "downhill" away from peaks of the potential (red spots on the COBE map), producing voids in the current distribution of galaxies, while valleys in the potential (blue spots) are where the clusters of galaxies form.

COBE was not able to see spots as small as clusters or even superclusters of galaxies, but if we use "equal power on all scales" to extrapolate the COBE data to smaller scales, we find that the gravitational forces are large enough to produce the observed clustering, but only if these forces are not opposed by other forces. If the all the matter in the Universe is made out of the ordinary chemical elements, then there was a very effective opposing force before recombination, because the free electrons which are now bound into atoms were very effective at scattering the photons of the cosmic background. We can therefore conclude that most of the matter in the Universe is "dark matter" that does not emit, absorb or scatter light. Furthermore, observations of distant supernovae have shown that most of the energy density of the Universe is a vacuum energy density (a "dark energy") like Einstein's cosmological constant that causes an accelerating expansion of the Universe. These strange conclusions have been greatly strengthened by temperature anisotropy data at smaller angular scales which was be provided by the Wilkinson Microwave Anisotropy Probe (WMAP) in 2003.

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© 1996-2017 Edward L. Wright. Last modified 21 Jul 2017