Tutorial : Part 1 | Part 2 | Part 3 | Part 4 | Age | Distances | Bibliography | Relativity

- What is the currently most accepted model for the Universe?
- What is the evidence for the Big Bang?
- What happened during the Big Bang?
- What is this "anti-gravity"? [The cosmological constant]
- Why do we think that the expansion of the Universe is accelerating?
- What is quintessence?
- How old is the Universe?
- If the Universe is only 14 billion years old, why isn't the most distant object we can see 7 billion light years away?
- If the Universe is only 14 billion years old, how can we see objects that are now 47 billion light years away?
- Is the Universe really infinite or just really big?
- How can the Universe be infinite if it was all concentrated into a point at the Big Bang?
- How can the oldest stars in the Universe be older than the Universe?
- Can objects move away from us faster than the speed of light?
- What is the redshift?
- Are quasars really at the large distances indicated by their redshifts?
- What about objects with discordant redshifts, like Stephan's Quintet?
- Has the time dilation of distant source light curves predicted by the Big Bang been observed?
- Are galaxies really moving away from us or is space just expanding?
- Why doesn't the Solar System expand if the whole Universe is expanding?
- Is the Universe expanding or is it just that our definitions of length and time are changing?
- Why haven't the CMBR photons outrun the galaxies in the Big Bang?
- Where was the center of the Big Bang?
- What is meant by a flat Universe?
- Is the Big Bang a Black Hole?
- What is the Universe expanding into?
- What came before the Big Bang?
- Doug Scott's Cosmic Microwave Background Radiation (CMBR) FAQ
- Can the CMBR be redshifted starlight?
- Why is the sky dark at night?
- Will the Universe expand forever or recollapse?
- Does entropy prevent a Big Crunch?
- What about the oscillating Universe?
- What is the dark matter?
- What about MOND?
- What is the value of the Hubble constant?
- What can a layperson do in cosmology?
- When will the next WMAP data release occur?
- Ask your own question!

The current best fit model is a flat ΛCDM Big Bang model where the expansion of the Universe is accelerating, and the age of the Universe is 13.7 billion years.

The evidence for the Big Bang comes from many pieces of
observational data
that are consistent with the Big Bang. None of these *prove* the
Big Bang, since scientific theories are not proven. Many of these facts
are consistent with the Big Bang and some other cosmological models,
but taken together these observations show that the Big Bang is the
best current model for the Universe. These observations include:

- The darkness of the night sky - Olbers' paradox.
- The Hubble Law - the linear distance vs redshift law. The data are now very good.
- Homogeneity - fair data showing that our location in the Universe is not special.
- Isotropy - very strong data showing that the sky looks the same in all directions to 1 part in 100,000.
- Time dilation in supernova light curves.

- Radio source and quasar counts vs. flux. These show that the Universe has evolved.
- Existence of the blackbody CMB. This shows that the Universe has evolved from a dense, isothermal state.
- Variation of
T
_{CMB}with redshift. This is a direct observation of the evolution of the Universe. - Deuterium,
^{3}He,^{4}He, and^{7}Li abundances. These light isotopes are all well fit by predicted reactions occurring in the First Three Minutes.

The evidence for an accelerating expansion comes from observations of the
brightness of distant supernovae.
We observe the redshift of a supernova
which tells us by what the factor the Universe has expanded since the
supernova exploded.
This factor is *(1+z)*, where *z* is the redshift.
But in order to determine the expected brightness
of the supernova, we need to know its distance now.
If the expansion of the Universe is accelerating
due to a cosmological constant,
then the expansion was slower in the past,
and thus the time required to expand by a given factor
is longer, and the distance NOW is larger.
But if the expansion is decelerating, it was faster in the past
and the distance NOW is smaller. Thus for an accelerating expansion the
supernovae at high redshifts will appear to be fainter than they would
for a decelerating expansion because their
current distances are larger.
Note that these distances are all proportional to the age of the
Universe [or 1/H_{o}],
but this dependence cancels out when the brightness of a nearby supernova at
*z* close to 0.1 is compared to a distant supernova with *z*
close to 1.

Quintessence, or the fifth essence, is a fifth element beyond the standard earth, air, fire and water of ancient chemistry. Steinhardt and colleagues have adopted quintessence as the name for a particular model for the vacuum energy which causes the accelerating expansion of the Universe. A search of astro-ph on the LANL preprint server arXiv for "quintessence" in the abstract hits over 600 articles of which the oldest dates from 1998.

This question makes some hidden assumptions about space and time which
are not consistent with all definitions of distance and time.
One assumes that all the galaxies left from a single point at the Big
Bang, and the most distant one traveled away from us for half the age of
the Universe at almost the speed of light, and then emitted light which
came back to us at the speed of light. By assuming constant velocities,
we must ignore gravity, so this would only happen in a nearly empty
Universe. In the empty Universe, one of the many possible definitions
of distance does agree with the assumptions in this question: the
*angular size distance*, and it does reach a maximum value of
the speed of light times one half the age of the Universe.
See
Part 2 of the cosmology tutorial for a discussion of the other kinds
of distances which go to infinity in the empty Universe model since
this gives an unbounded Universe.

When talking about the distance of a moving object, we mean the spatial separation NOW, with the positions of both objects specified at the current time. In an expanding Universe this distance NOW is larger than the speed of light times the light travel time due to the increase of separations between objects as the Universe expands. This is not due to any change in the units of space and time, but just caused by things being farther apart now than they used to be.

What is the distance NOW to the most distant thing we can
see? Let's take the age of the Universe to be 14 billion
years. In that time light travels 14 billion light
years, and some people stop here. But the distance has
grown since the light traveled. The average time when
the light was traveling was 7 billion years ago. For the
critical density case,
the scale factor for the Universe goes like
the 2/3 power of the time since the Big Bang, so the
Universe has grown by a factor of 2^{2/3} = 1.59 since
the midpoint of the light's trip. But the size of the
Universe changes continuously, so we should divide the
light's trip into short intervals. First take two
intervals: 7 billion years at an average time 10.5 billion
years after the Big Bang, which gives 7 billion light
years that have grown by a factor of 1/(0.75)^{2/3} =
1.21, plus another 7 billion light years at an average
time 3.5 billion years after the Big Bang, which has grown
by a factor of 4^{2/3} = 2.52. Thus with 1 interval we
got 1.59*14 = 22.3 billion light years, while with two
intervals we get 7*(1.21+2.52) = 26.1 billion light
years. With 8192 intervals we get 41 billion light
years. In the limit of very many time intervals we get
42 billion light years. With calculus this whole paragraph
reduces to this.

Another way of seeing this is to consider a photon and a galaxy 42
billion light years away from us now, 14 billion years after the Big
Bang. The distance of this photon satisfies D = 3ct.
If we wait for 0.1 billion years, the Universe will grow by a
factor of (14.1/14)^{2/3} = 1.0048, so the galaxy will be
1.0048*42 = 42.2 billion light years away. But the light will have
traveled 0.1 billion light years further than the galaxy
*because it moves at the speed of light relative to the matter in its
vicinity*
and will thus be at D = 42.3 billion light years, so D = 3ct is still
satisfied.

If the Universe does not have the critical density then the distance is different, and for the low densities that are more likely the distance NOW to the most distant object we can see is bigger than 3 times the speed of light times the age of the Universe. The current best fit model which has an accelerating expansion gives a maximum distance we can see of 47 billion light years.

We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. The negatively curved space is also infinite in volume even though it is curved. So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.

Of course the Universe has to be older than the oldest stars in it. So this question basically asks: which estimate is wrong -

- The age of the Universe
- The age of the oldest stars
- Both

The estimated age of the Universe has been increased by the observations
of an accelerated expansion of the Universe. The current best value is
*13.74 +/- 0.11* billion years from a fit of
9 years of WMAP data to a flat
Universe, or *13.750 +/- 0.088* billion years for a fit to
WMAP+BAO+H_{0} data.

Determining the age of the oldest stars requires a knowledge of their luminosity, which depends on their distance. This leads to a 10% uncertainty in the ages of the oldest stars due to the difficulty in determining distances.

Thus the discrepancy between the age of the oldest things in the Universe and the age inferred from the expansion rate was always within the margin of error. In fact, in 1997 improved distances from the HIPPARCOS satellite suggested that the oldest stars were younger, and the WMAP results in 2003 suggest that the Universe is older, so the discrepancy has disappeared.

Again, this is a question that depends on which of the
many distance definitions one uses.
However, if we assume that the distance of an object at time *t*
is the distance from our position at time
*t* to the object's position at time *t*
measured by a set of observers moving with
the expansion of the Universe, and all making their observations when
they see the Universe as having age *t*, then the velocity
(change in *D* per change in *t*) can definitely be larger
than the speed of light. This is not a contradiction of special
relativity because this distance is not the
same as the spatial distance used in SR, and the age of the Universe is
not the same as the time used in SR.
In the special case of the empty Universe, where one can show
the model in both special relativistic and
cosmological coordinates, the velocity defined by
change in cosmological distance per unit cosmic time is given by
*
v = c ln(1+z),
*
where *z* is the redshift,
which clearly goes to *infinity* as the redshift goes to
infinity, and is larger than c for *z > 1.718*.
For the critical density Universe, this velocity is given
by
*
v = 2c[1-(1+z) ^{-0.5}]
*
which is larger than c for

The redshift of an object is the amount by which the spectral lines in the source are shifted to the red. That is, the wavelengths get longer. To be precise, the redshift is given by

z = [λwhere λ_{obs}-λ_{em}]/λ_{em}

The short answer is

Stockton (1978, ApJ, 223, 747) observed faint galaxies near in the sky to bright quasars at moderate redshifts. He chose quasars with moderate redshifts so he would still be able to see galaxies at the redshift of the quasar. He found that a good fraction of the redshifts of the faint galaxies agreed with the redshifts of the quasars. In other words, quasars are associated with galaxies that have the same redshift as the quasar and have just the brightness expected if the quasars are at their cosmological distances. Thus at least some quasars are at the distance indicated by their redshifts, and this includes some of the most luminous quasars: for example 3C273. Thus the simple answer selected by Occam's razor is that all quasars are at the distances indicated by their redshifts.

A further argument in favor of cosmological redshifts for quasars is the essentially perfect rank ordering implied by the fact that quasar absorption line system always have redshifts less than or equal to the quasar emission line redshift. In gravitational lens systems, the redshift of the lens is always less than the redshift of the lensed object. Thus intervening systems like lensing galaxies or absorbing clouds, which obviously have smaller distances than the quasars, also have smaller redshifts.

The statistical arguments advanced by Arp and others in favor of anomalous quasar redshifts are often incorrect.

One famous example of objects with different redshifts appearing in the same part of the sky is Stephan's Quintet. But the low redshift galaxy (in the lower left) is obviously more resolved into stars and looks "bumpier". By the surface brightness fluctuation method of distance determination, this bumpiness means that the low redshift galaxy is indeed much closer to us than the other four members of the quintet.

This time dilation is a consequence of the standard interpretation of the redshift: a supernova that takes 20 days to decay will appear to take 40 days to decay when observed at redshift z=1. The time dilation has been observed, with 5 different published measurements of this effect in supernova light curves. These papers are:

- Leibundgut etal, 1996, ApJL, 466, L21-L24
- Goldhaber etal, in Thermonuclear Supernovae (NATO ASI), eds. R. Canal, P. Ruiz-LaPuente, and J. Isern.
- Riess etal, 1997, AJ, 114, 722.
- Perlmutter etal, 1998, Nature, 391, 51.
- Goldhaber etal, 2001, ApJ, 558, 359.

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways.

In the absence of the cosmological constant, an object released at rest
with respect to us does not then fly away from us to join the Hubble
flow. Instead, it falls toward us, and then joins the Hubble flow on
the other side of the sky, as discussed by
Davis, Lineweaver
& Webb (2003, AJP, 71, 358).
In what are arguably the most reasonable coordinates,
the cosmic time *t* and the distance *D(t)* measured
entirely at the cosmic time *t*, the acceleration is given
by *g = -GM(r<D)/D ^{2}* where

Also see the Relativity FAQ answer to this question.

This question is best answered in the coordinate system where the
galaxies change their positions. The galaxies are receding from us
because they started out receding from us, and the force of gravity just
causes an acceleration that causes them to slow down, or speed up in the
case of an accelerating expansion. Planets are going
around the Sun in fixed size orbits because they are bound to the Sun.
Everything is just moving under the influence of Newton's laws
(with very slight modifications due to relativity).
[Illustration]
For the technically minded,
Cooperstock
*et al.* computes that the influence of the cosmological
expansion on the Earth's orbit around the Sun amounts to
a growth by only one part in a septillion over the age of the Solar System.
This effect is caused by the cosmological background density within the
Solar System going down as the Universe expands, which may or may not happen
depending on the nature of the dark matter.
The mass loss of the Sun due to its luminosity and the Solar wind leads to
a much larger [but still tiny] growth of the Earth's orbit which has nothing
to do with the expansion of the Universe.
Even on the much larger (million light year) scale of clusters of
galaxies, the effect of the expansion of the Universe is 10 million
times smaller than the gravitational binding of the cluster.

Also see the Relativity FAQ answer to this question.

The definitions of length and time are not changing in the standard model. The second is still 9192631770 cycles of a Cesium atomic clock and the meter is still the distance light travels in 9192631770/299792458 cycles of a Cesium atomic clock.

The Universe appears to be homogeneous and isotropic, and there are only
three possible geometries that are homogeneous and isotropic as shown in
Part 3. A flat space has
Euclidean geometry,
where the sum of the angles in a triangle is 180^{o}.
A curved space has
non-Euclidean geometry.
In a
positively curved, or hyperspherical space, the sum of the angles in a
triangle is bigger than 180^{o}, and this angle excess gives the
area of the triangle divided by the square of the radius of the surface.
In a negatively curved or
hyperbolic space, the sum of the angles in a triangle is less than
180^{o}.
When
Gauss
invented
this non-Euclidean geometry he actually tried
measuring a large triangle, but he got an angle sum of 180^{o}
because the radius of the Universe is very large (if not infinite) so
the angle excess or deficit has to be tiny for any triangle we can measure.
If the radius is infinite, then the Universe is flat.

Bolyai developed this geometry and published it, whereupon Gauss
wrote to Bolyai's father: "To praise it would amount to praising myself.
For the entire content of the work ... coincides
almost exactly with my own meditations which have occupied my mind for
the past thirty or thirty-five years."
And
Lobachevsky had published very similar work in the obscure *Kazan
Messenger*.

The Big Bang is really nothing like a black hole. The Big Bang is a singularity extending through all space at a single instant, while a black hole is a singularity extending through all time at a single point. For more, see the sci.physics FAQ.

This question is based on the ever popular misconception that
the Universe is some curved object embedded in a higher dimensional
space, and that the Universe is expanding into this space.
This misconception is probably fostered by the
balloon analogy which shows a 2-D spherical
model of the Universe expanding in a 3-D space. While it is possible
to think of the Universe this way, it is not necessary, *and there
is nothing whatsoever that we have measured or can measure that will
show us anything about the larger space.* Everything that we
measure is within the Universe, and we see no edge or boundary or center
of expansion. Thus the Universe is not expanding into *anything*
that we can see, and this is not a profitable thing to think about.
Just as Dali's Corpus Hypercubicus is just a 2-D picture of a 3-D object that represents
the surface of a 4-D cube,
remember that the balloon analogy is just a 2-D picture of a 3-D
situation that is supposed to help you think about a curved 3-D space,
but it does not mean that there is really a 4-D space that the Universe
is expanding into.

- The distances between objects are all increasing, so the distance between any pair of raisins increases by an amount proportional to the distance.
- The edge of the loaf pushes out into previously unoccupied space. Note the distance between any pair of points on the edge increases by an amount proportional to the distance.

The standard Big Bang model is *singular* at the time of the Big Bang,
*t = 0*. This means that one cannot even define time, since spacetime
is singular.
In some models like the chaotic or perpetual inflation favored by
Linde, the Big Bang is just one of many inflating bubbles in a spacetime
foam. But there is no possibility of getting information from outside
our own one bubble. Thus I conclude that:
"Whereof one cannot speak, thereof one must be silent."

From Bruce Margon and Craig Hogan at the Univ. of Washington

The issue of entropy in the Universe is subtle and not entirely settled. Theorists are still trying to work out what happens to the entropy of matter that falls into a black hole, a problem which involves both quantum mechanics and strong gravity. When a successful theory of quantum gravity is worked out, it should explain why the Universe came out of the Big Bang singularity with a very large entropy, and what happens to the entropy of the Universe if it recollapses.

Entropy is related to the number of ways a system can be in a given state or condition. Thus a shuffled deck of cards has a higher entropy than a new deck with all the suits in order. Adding energy to a system usually opens up more states, and increases the entropy. The temperature of a system is defined such that kT is the amount of energy needed to increase the number of available states by a factor of e = 2.71828... where k is Boltzmann's constant. Transferring heat from a hot piece of a system to a cold piece increases the number of ways to arrange the cold part by a larger factor than the decrease in the number of ways to arrange the hot piece. Thus the normal flow of heat from hot to cold causes an increase in the number of ways the whole system can be arranged which is then an increase in the total entropy of the whole system.

Entropy need not always increase in open systems. Energy could be used to make entropy decrease for a particular system. Your refrigerator does this by removing heat from the interior, if you consider the interior of your refrigerator to be a separate system. Of course, if you consider both the internal and external portions of the refrigerator then there is a net increase of entropy due to the inefficiency of the refrigerator.

Since entropy is a statistical concept, short term fluctuations in small systems can allow entropy to decrease.

Entropy remains constant in a system with a uniform temperature that has no heat added or subtracted from it. This is thought to be more or less the case for the Universe or for any representative piece of the Universe that expands or contracts in the same way the Universe does. Except for the contribution from black holes, the vast majority of the entropy of the Universe is in the cosmic microwave background radiation because the vast majority of particles in the Universe are the photons of the CMB. As the Universe expands, the temperature of the radiation drops to maintain constant entropy. If the Universe were to collapse at some point, the radiation would heat back up to maintain constant entropy. When the Universe expanded the radiation started out in thermal equilibrium with the matter and then de-coupled. In the collapse the radiation and the matter would once again come into thermal equilibrium. Whatever happened with the dynamics of the matter in the interim would be reflected in the final thermal equilibrium with the radiation. The final entropy of the Universe as it approaches the Big Crunch singularity would be larger than the initial entropy of the Universe because of the heat added by nuclear fusion in stars, so a recollapse does not involve a decrease in entropy.

Black holes probably contribute much more entropy than all the
particles and photons put together.
Egan & Lineweaver (2009)
estimate S/k = 10^{104.5} in the observable Universe,
primarily from the Bekenstein entropy of super massive black
holes.

When astronomers add up the masses and luminosities of the stars near
the Sun, they find that there are about 3 solar masses for every 1 solar
luminosity. When they measure the total mass of clusters of galaxies
and compare that to the total luminosity of the clusters, they find
about 300 solar masses for every solar luminosity. Evidently most of
the mass in the Universe is dark. If the Universe has the critical
density then there are about 1000 solar masses for every solar
luminosity, so an even greater fraction of the Universe is dark matter.
But the theory of
Big
Bang nucleosynthesis says that the density of
ordinary matter (*anything made from atoms*) can be at most 10% of
the critical density, so the majority of the Universe does not emit
light, does not scatter light, does not absorb light, and is not even
made out of atoms. It can only be "seen" by its gravitational effects.
This "non-baryonic"
dark matter can be neutrinos, if they have small
masses instead of being massless, or it can be WIMPs (Weakly Interacting
Massive Particles), or it could be primordial black holes. My nominee
for the "least likely to be caught" award goes to hypothetical stable
Planck mass remnants of primordial black holes that have evaporated due
to Hawking radiation. The Hawking radiation from the not-yet evaporated
primordial black holes may be detectable by future
gamma ray telescopes,
but the 20 microgram remnants would be very hard to detect.

Also see the Relativity FAQ answer to this question, the Cryogenic Dark Matter Search (CDMS) home page, and Martin White on dark matter.

This is the question that professional astronomers ask the most frequently.
For many decades the Sandage [*H _{o} = 50*] and
de Vaucouleurs [

- Stay in school! There is a lot to learn about the Universe.
- Keep taking math and science courses!

*The book of nature lies continuously open before our eyes (I speak of the Universe) but it can't be understood without first learning to understand the language and characters in which it is written. It is written in mathematical language, and its characters are geometrical figures.*- Galileo Galilei

That was true 400 years ago and it is much more true today! - If you are out of school, check out the bibliography.
- Tell your Congressman and Senators to support astrophysics research at NASA, NSF, and DOE.

The data release on 21 Dec 2012 included all 9 years of data. The hourglass has been retired. There will be no further releases.

Tutorial : Part 1 | Part 2 | Part 3 | Part 4 | Age | Distances | Bibliography | Relativity

© 1996-2013 Edward L. Wright. Last modified 24 May 2013