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

- What is the evidence for the Big Bang?
- What is this "anti-gravity"? [The cosmological constant]
- Why do we think that the expansion of the Universe is accelerating?
- How old is the Universe?
- If the Universe is only 10 billion years old, why isn't the most distant object we can see 5 billion light years away?
- If the Universe is only 10 billion years old, how can we see objects that are now 30 billion light years away?
- 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?
- What about the oscillating Universe?
- What is the dark matter?
- What is the value of the Hubble constant?
- What can a layperson do in cosmology?
- Ask your own question!

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.

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 do 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 10 billion
years. In that time light travels 10 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 5 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: 5 billion years at an average time 7.5 billion
years after the Big Bang, which gives 5 billion light
years that have grown by a factor of 1/(0.75)^{2/3} =
1.21, plus another 5 billion light years at an average
time 2.5 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*10 = 15.9 billion light years, while with two
intervals we get 5*(1.21+2.52) = 18.7 billion light
years. With 8192 intervals we get 29.3 billion light
years. In the limit of very many time intervals we get
30 billion light years.

Another way of seeing this is to consider a photon and a galaxy 30
billion light years away from us now, 10 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 (10.1/10)^{2/3} = 1.0066, so the galaxy will be
1.0066*30 = 30.2 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 = 30.3 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.

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

Determining the age of the oldest stars requires a knowledge of their luminosity, which depends on their distance. This leads to a 25% 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 is within the current margin of error. In fact, in 1997 improved distances from the HIPPARCOS satellite suggested that this discrepancy has vanished.

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)
*
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 = [WL(obs)-WL(em)]/WL(em)where WL(em) is the emitted wavelength of a line, which is known from laboratory measurements, and WL(obs) is the observed wavelength of the line. In an expanding Universe, distant objects are redshifted, with

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.

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 4 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.

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.

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. Planets are going
around the Sun is 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*.

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.

Or you can ask Dr. Science :)

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

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, Jonathan Dursi's tutorial on dark matter, and the Center for Particle Astrophysics on dark matter.

Dr. Science on dark matter :).

This is the question that professional astronomers ask the most frequently,
and the answer is:

- 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.

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

© 1996-2000 Edward L. Wright. Last modified 20-Jul-2000