the cosmic microwave background (CMB)
what it is
Discovered accidentally in 1964 by Penzias and Wilson (Nobel
Prize, 1978), the CMB is a remnant of the hot, dense phase of the
universe
that followed the Big Bang. For several hundred thousand years
after
the Big Bang, the universe was hot enough for its matter (predominantly
hydrogen) to remain ionized, and therefore opaque (like the bulk of the
sun) to radiation. During this period, matter and light were in
thermal equilibrium
and the radiation is therefore expected to obey the classic blackbody
laws (Planck, Wien, Stefan).
The existence of the CMB is regarded as one of three experimental
pillars
that point to a Big Bang start to the universe. (The other two
pieces
of evidence that indicate that our universe began with a Bang are the
linearity of the Hubble
expansion law and the universal cosmic abundances of the light element
isotopes, such as helium, deuterium, and lithium.)
At some point about 400,000 years after the Bang, the universe had
cooled
to the point where the matter became neutral, at which point the
universe's
matter also became transparent to the radiation. (Completely
ionized
matter can absorb any wavelength radiation; neutral matter can only
absorb
the relatively few wavelengths that carry the exact energy that match
energy
differences between electron energy levels.) The temperature at
which
this transition from ionized to neutral (called the "moment of
decoupling")
occurred was roughly 3000 K.
The spectrum as measured by the COBE satellite looks like
It indeed had the blackbody spectral shape predicted, but the peak in
the
microwave spectrum indicated a temperature of 2.726 K. Although
this
temperature is clearly insufficient to ionize hydrogen, the entire
spectrum
has been redshifted from that at the moment of decoupling (when the
temperature
was
3000 K) by the expansion of the universe. As space expands, the
wavelengths of the CMB expand by the same factor. Wien's
blackbody
law says that the wavelength peak of the CMB spectrum is inversely
proportional
to the temperature of the CMB. Therefore, the drop in the CMB
temperature
by a factor of 1100 (= 3000 K/2.73 K) indicates an expansion of the
universe
by a factor of 1100 from the moment of decoupling until now.
what it can tell us
In addition to measuring the temperature
of
the overall CMB, anisotropies in the CMB are capable of telling us the
Earth's motion with respect to the CMB, the geometry (or curvature) of
the universe, the baryon content of the universe, the dark matter and
dark energy content
of the universe, the value of the Hubble constant, whether inflation
incurred
in the early universe, and more.
What various groups are measuring is usually presented in a format such
as
BOOMERandG in April
2001
WMAP February 2003
what it means
The above diagrams plot the CMB power as a
function
of harmonic number. These diagrams are very much like that for a
complex musical instrument note, which is also the sum of the
amplitudes
(or "power") of various frequencies or harmonics. For example, in
the diagram below, 6 harmonics (top picture: each is a sinusoidal wave
with an integral multiple of the fundamental frequency) are added
together
to produce the complex-shape wave shown in the middle picture.
The
bottom picture shows the relative amplitude contribution of each of the
harmonics.
The CMB power spectra similarly plot the
relative
contribution of each spatial frequency (instead of temporal
frequency).
the math and physics of anisotropies
If
the CMB
had precisely the same temperature in every direction
in the sky, the sky would have the same brightness in every
direction.
Astronomers often use a false coloring scheme to represent brightness
(different
brightnesses are represented by different colors) especially when the
radiation
is being emitted in a part of the spectrum that is not visible to the
human
eye. A uniformly bright CMB would therefore be represented by a
single
color. This power is called the "l = 1" contribution to the power
spectrum. If we could see the CMB with our eyes, the sky would
look uniformly the same, as in the figure at the left.
(In this and subsequent diagrams, the
entire sky is represented by a
Mercator projection, the same technique often employed to portray the
entire earth. The equator (latitude 0 for earth) is a horizontal
line in the middle of the oval, with northern latitudes above and
southern latitudes below. The Greenwich meridian (longitude 0 on
Earth) is a vertical line through the middle, with western longitudes
to the left and eastern longitudes to the right. In a similar
manner, the galactic equator or plane (latitude 0) is a line running
through the middle of the sky pictures. The galactic center
(galactic longitude 0) is at the center of the diagram.
In
reality,
however, not all directions in the sky appear to have the same CMB
brightness. The earth is moving with respect to the matter that
last
emitted the CMB, and therefore the CMB spectrum looks bluest (and, by
Wien's
law, therefore hottest) in that direction and reddest (and coolest)
opposite to that direction.
This effect would contribute to the CMB power spectrum at a spatial
frequency
of l = 2. The "l = 2" contribution is often called a dipole
contribution, because the brightness distribution over the sky has 2
poles (one hot, one cool) in it. If we were somehow able to see
ONLY this dipole contribution [the brightness amplitude of which is far
less than the that of the dominant "l=1" contribution] by removing the
average brightness (or temperature) from
the preceding diagram and amplify the contrast by approximately a
thousand,
the sky now looks like the figure at the right.
By measuring the amount of the dipole anisotropy (the bluest part
of the sky is
.0033 K hotter than average), we can determine the magnitude of the
earth's motion with respect to the CMB: the earth is moving at a speed
of 370 km/s in the direction of the constellation Virgo.
If the dipole contribution due to Earth's motion is now subtracted
out,
the sky looks like the figure at the left.
The temperature differences that remain are a composite of two
things:
a contribution from our galaxy and the true anisotropies in the CMB
that
were present at the moment of decoupling, hundreds of thousands of
years
after the Big Bang.
The galaxy is bright at microwave wavelengths due to emission by
molecules
(particularly CO), dust,
The anisotropies present at the moment of decoupling represent random
noise
present in the very early universe that was amplified by inflation to
cosmic-sized
scales. The anisotropies present at the moment of decoupling are
of the appropriate magnitude to account for how the large-scale
structures
that we see today (from galaxies to superclusters of galaxies) formed
under
the influence of gravity.
It is possible to remove the contribution of the galaxy's emission by
measuring
Once the galactic contribution is removed, COBE saw this:
This diagram is the sum of the amplitude (or power) contributions
of all spatial frequency harmonics (but with those of l = 1 and l = 2
removed). It is the equivalent of the complex wave musical
instrument wave shape above, which was formed by the sum of the
amplitude (or audio power) contributions of several temporal (or
harmonic) frequencies. The difference is that
the CMB diagram shows the power as a function of position in the sky
(i.e.,
as a function of galactic latitude and longitude), whereas the musical
instrument wave shape shows the power as a function of the single
dimension of time.
The goal for the CMB researchers is to decompose the CMB diagram into
its
harmonic components. And fortunately the relative amounts of the
harmonic components are determined by intrinsic properties of the
universe
(such as the Hubble constant, the amount of dark matter, and the value
of the cosmological constant, the age of the universe, and the amount
of dark eenergy).
who is measuring this
COBE
(Cosmic Background Explorer, launched in 1989) was the first satellite
launched to measure the CMB properties outside Earth's
atmosphere.
COBE established the precise blackbody character of the radiation and
measured
the temperature as 2.726 K, measured the earth's velocity relative to
the
matter that last emiited the radiation, and eventually detected
anisotropies
in the background at the level of 1 part in 105.
BOOMERanG
measures
CMB properties by launching balloon-borne instruments at the South
Pole.
Here is their latest version of the anisotropy of a piece of the
sky
MAXIMA does the
same
NASA/WMAP Science Team
MAP (launched
6/30/01) will measure the individual properties of the universe (e.g.,
the Hubble constant, the baryon density, the cosmological constant
value)
to within 5%. The first MAP pictures (feb 2003) is on the left
with the COBE result from 5 years earlier for comparison. Note
that the MAP resolution is significantly better than the COBE
resolution.
MAP
found the following values (2003) for cosmological
parameters:
present age: 13.7 (+
0.1) Gyr
geometry of the universe: consistent with flat: omega total = 1.02 + 0.02
omega (dark energy) = 0.73
omega (dark matter) = 0.23
omega (baryons) = 0.044 +
0.004
omega (neutrinos) <
0.0005
omega (radiation) = 0.0001
the content of the universe:
epoch of first star formation (end of the dark ages): 200 Myr after
the Bang
moment of decoupling: 379,000 yr after the Bang
Hubble's constant = 71 (+
3) km/s/Mpc
how YOU can calculate the spectrum anisotropies
go to Max's
cosmic cinema, where you plug in your own parameters for the
universe
and see the resulting anisotropy plot interactively... you can then see
how well it fits the observations