# Lecture 4

```Applications of Physics to Astronomical Systems
Lecture 4
5) The Cosmic Microwave Background
The most direct evidence that the Universe really did go through a very dense phase in the past
an aerial, to collect the electromagnetic waves and convert them into currents in a wire, an
amplifier, to bring the signals up to a measurable level, a filter to separate out the band of
frequencies that we wish to measure, and a square-law detector, which converts the AC wave into a
DC voltage proportional to the power in the original signal.
Aerial
Amplifier
Filter
Detector
In most receivers the filtering process is actually done in two stages. There is an initial filtering at
the original radio frequency (RF) and then the signal is “mixed” with a cw (continuous wave – i.e.
sinusoidal waveform) from a local oscillator (LO) in a non-linear device – e.g. a semi-conductor
diode. The beat frequency from this is at an intermediate frequency (IF) equal to the difference
between the RF frequency and the LO frequency. More filtering and amplification can be applied
at the IF frequency.
Any such receiver system inevitably suffers from noise and this limits its performance for
communications purposes. Noise arises from many sources, including thermal emission from the
surroundings of the aerial, thermal fluctuations in the resistive components in the receiver “Johnson
noise”, and the quantum noise due to the fact that electrical currents are made up of a flow of
electrons which have a fixed change and arrive at random times (“shot noise”). The total amount of
noise can be described by the “noise temperature” which is the temperature which a resistor
connected to the input of the system would need to have in order to produce that same amount of
power at the output as the noise does. For a modern transistor amplifier, such as is used on a
satellite TV receiver operating at ~ 12 GHz, this might be about 30K.
The discovery of the cosmic microwave background was in fact a result of an attempt to measure
the noise of a microwave system very carefully. Penzias and Wilson used resistive “loads” at
different cryogenic temperatures to characterise their receiver very well. They then measured the
noise when they attached their large horn antenna. They found noise from the sky, some of which
could be ascribed to the emission from the Milky Way and some to the Earth’s atmosphere. Even
when these were subtracted off however, there remained an additional source of noise which
amounted to about 3K. Later measurements showed that this has exactly the spectrum as expected
from a “black body”, i.e. the Planck function, and that the precise temperature is 2.725 +/– 0.002K .
Although many measurements of the CMB spectrum were made from the ground and later from
rockets, the definitive result was produced by the COBE satellite in the early 1990’s. This used a
polarising Michelson interferometer to measure the spectrum. The signals are split in two, one is
delayed by a variable amount and then they are recombined. The interference pattern that this
produces is the Fourier transform of the spectrum coming in. The polarizing version of the
Michelson is particularly good for this application because it can be arranged that the signal
measured is the difference between the input and a reference black-body at a known temperature.
The fact that the background has the form of a back body (to an accuracy of at least 1 in 10 4) can
only realistically be explained if the Universe once consisted of a hot uniform gas which was in
thermal equilibrium and opaque to radiation. The standard picture of cosmology is that this was the
situation from very early times up until about 300,000 years after the Big Bang. Up until then the
gas would have been fully ionised, but when it had cooled a temperature of about 4000K it
recombined to form atoms of hydrogen, helium, etc. This corresponds to a redshift, z, of about
1400. (Remember that we have frequency emitted equals (1 + z) times frequency observed today,
and that the temperature is proportional to frequency, since they appear in the Planck formula in the
combination h  / kB T.)
This recombination makes the gas become transparent to the radiation, which would then have had
the peak of its spectrum at optical wavelengths where hydrogen and helium have very few
absorption lines. The microwave radiation we observe today has therefore travelled direct to us
from this very early time. We can think of what we see as being the inside of a spherical surface
which is located where the photons were scattered by the matter for the last time.
Given that there is so much structure on all scales in the Universe today, one would expect to see
the early signs of this structure forming imprinted on the microwave background in the form of
temperature variations. It is indeed there but it is extremely faint: the fluctuations are only about 1
part in 10.5. To measure these has required a great deal of effort and in particular the use of
instruments designed specifically to look for temperature differences.
The “Differential Microwave Radiometer” (DMR) on COBE did this by switching the input to the
receiver between two horns 60 degrees apart on the sky. The satellite was then rotated so that the
horns swept out a cone on the sky and the axis of rotation was allowed to precess around until
essentially the whole sky had been covered.
From these differential measurements it was then
possible to reconstruct a map of the brightness variations
around the entire sky. This showed that there variations
in the apparent temperature at the level of a few tens of
micro-Kelvins.
Map of sky in “galactic” coordinates
Block diagram of DMR
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