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The spectrum of the CMB

Since the CMB is the remnant from the epoch when the universe was very hot and dense, it should have a so-called ``black body'' spectrum. This a (somewhat unfortunate) term scientists use to describe the radiation which was in the equilibrium with the gas it was emitted by.

For example, solar radiation has a black body spectrum, even if the Sun is not black at all.

When the universe was dense and hot, everything was in the equilibrium then. Such an equilibrium is called ``thermal equilibrium''. Thus, the CMB should also have an equilibrium, black body spectrum.

COBE was able to verify that to the accuracy of 1 part to 100,000! No other number in Astronomy is known to such a precision!

COBE also measured the temperature of the CMB:

\begin{displaymath}T_{\mbox{CMB}} = 2.728\pm0.002 \mbox{~degree~Kelvin}. \end{displaymath}

Anisotropies of the CMB

The Big Bang theory also predicts that even if the CMB is highly homogeneous and isotropic, it is not 100% so, only 99.999%.

There should be anisotropies in the CMB at a level of about 1 part in 100,000, COBE managed to detect these anisotropies and measure them very precisely.

Anisotropies in the CMB are indeed sound waves passing through the cosmic gas when it was dense and hot. (Those sound waves are very very quiet, much quieter than any whisper you can hear).

However, COBE's ``vision'' was not very sharp, it was able to see only details with the size larger than 10 degrees on the sky. A human eye is 500 times better than that.

Thus, COBE found the anisotropies (inhomogeneities), but did not tell much about them.

The anisotropies are usually studied by measuring their spectrum.

The spectrum of anisotropies tells us how the power in a given sound wave changes with the wavelength. On the sky, wavelengths are measured in multipoles l: l=0 is the whole sky, l=1 is half the sky, l=2 is quarter of the sky, l=3 is one-sixth of the sky etc.


Currently, there exist many ground- and balloon-based experiments that measure the CMB anisotropies on small angular scales (less than 1 degree rather than 10 degrees, as COBE). The two best ones are called BOOMERANG and MAXIMA-1. They provide a reasonably accurate measurement of the first peak in the power spectrum.
The first peak is very important - it gives us a direct mesurement of the curvature of the universe.

BOOMERANG and MAXIMA-1 find that the universe is flat to a very high precision!

The future lies with two space missions:

They both will measure the anisotropies to sub-degree scales: MAP to about 20 minutes of arc (2/3 the Moon size) and Planck to 10 minutes (1/3 the Moon size, only 5 times worse than a human eye). They both will measure the spectrum to about 1% accuracy.

Homepages:

Why should we study the CMB?

The CMB is not only of interest by itself, hidden in it is the information about the universe we live in.

In other words, the spectrum of the CMB contains in the encoded form the values of all the cosmological parameters: H0, $\Omega_0$, $\Omega_\Lambda$ and some others.

The spectrum changes dramatically when those parameters are changed. Thus, by measuring the spectrum accurately, we can decode the parameters of the universe we are living in.

CMB anisotropies and galaxies

So, there are tiny ripples on the CMB. Surprisingly, there ripples have the direct connection to the galaxies that surround us today.

Since the CMB was emitted long time ago, small inhomogeneities in the universe on small enough scales had a long time to grow. By our time they grew so much as to become galaxies, clusters of galaxies, and large-scale structure (super-clusters).

Thus, the ripples in the CMB are the direct ancestors of galaxies!

Evolution of the CMB

As the universe cools and expands, so does the CMB. Thus, in the past the CMB was hotter. Quantitatively, the temperature of the CMB decreases in proportion to the scale factor:

\begin{displaymath}T_{\mbox{CMB}} = {2.73\over R} \mbox{~degree~Kelvin}, \end{displaymath}

or, in terms in cosmological redshift z:

\begin{displaymath}T_{\mbox{CMB}} = 2.73(1+z) \mbox{~degree~Kelvin}. \end{displaymath}

\framebox{\Huge\bf ?}At z=3 the CMB temperature was
A
2.73 degree Kelvin
B
3*2.71=8.19 degree Kelvin
C
4*2.73=10.84 degree Kelvin
D
-440 degree Fahrenheit

Cosmography

Another way to study these ripples is to study the distribution of galaxies around us. In other words, to study local cosmography.

We can see millions of galaxies on the sky, but in order to reconstruct the full three-dimensional picture of galaxies around us, we need to measure the redshifts to those galaxies. This is a formidable task, and at the moment we know redshifts of about 50,000 galaxies.

In cosmography, we are now living in the age of the first explorers: we roughly know contours of continents, but have no idea about all the islands and peninsulas there.

But here again, in the next decade or so we will greatly advance our knowledge.

There are currently two large-scale projects under way:

2dF will be completed by 2001, and Sloan by 2004, but Sloan will study a much larger area on the sky.

Homepages: 2dF and Sloan