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The cosmic microwave background radiation is simply electromagnetic radiation in the microwave region of the spectrum, left over from the Big Bang. It has been determined to be 2.7 degrees Kelvin. What does this mean? What is actually measured and how is that converted into a temperature? Fully describe the method, you do not need to actually do any calculations.

Solution

According to the Big Bang theory, during first 3 lakh years of the Universe, everything was in form of plasma. Atoms and molecules did not exist. The quanta of light i.e. photons were trapped inside this plasma “fog”. However, the universe cooled down and its density dropped to a point where ion and electrons in this “fog” were able to recombine. The recombination allowed atoms to form. At this time, the recombination process released photons. This time is referred to as the epoch of recombination. The photons released during this time were able to escape the “fog”. Thus, it is very evident that these photons are imprint of the Big Bang. These photons are now being detected and are called the “Cosmic Microwave Background Radiation”. So these radiations carry the information of what happened during the epoch of recombination.

It is important to note that the Universe has been expanding ever since.

The photons released during the epoch of recombination suffered multiple scattering by the plasma they were escaping. Because of the scattering, a Blackbody spectrum is expected and has been shown.

As already mentioned, these photons were produced at a time when Universe was in a form of plasma. The temperature of the Plasma (temperature of Universe) was about 3000 Kelvin. Thus the wavelength of the photons that were emitted at that time should have been of similar energy. But, it has been 13 billion years since the Universe started expanding. Thus, the wavelength of these radiations has red shifted. Because of the Doppler red shifting the wavelength of radiation has increased and the temperature has come down to 2.7 Kelvin. At the present age, the wavelength of these radiations fall in the microwave region of the electromagnetic spectrum.

Thus, these are the radiations that are actually detected. By detecting these radiations, we can find their wavelength, frequency, frequency range, energy density etc. The temperature is basically the equivalent energy.

To make temperature and Energy equivalent, we can do following.

Energy of a photon = (planck’s constant * speed of light)/ wavelength of radiation

Energy Unit in terms of temperature = KT where K is the Boltzmann constant and T is the temperature. Thus, KT = hc/ lambda. For example 1 eV corresponds to about 11000 Kelvin