Cosmic Microwave Background Radiation.

An object which is equally efficient in absorbing and emitting radiation of all frequencies is referred to as a black body. Consider a cavity enclosed inside a black body at a temperature ${\rm T}$. The electromagnetic waves inside this cavity will be repeatedly absorbed and re-emitted by the walls of this cavity until the radiation is in thermal equilibrium with the black body. It is found that the radiation spectum inside this black body cavity is completely specified by ${\rm T}$ the temperature of the black body. This radiation is referred to as black body radiation. Writing the energy density $du_{\nu}$ of the black body radiation in a frequency interval as

the spectral energy density $u_{\nu}$ is found to be given by

$$u_\nu = \frac{8 \pi h \nu^3 }{c^3 } \frac{1}{\left[ \mbox{exp} \left( \frac{h \nu}{kT} \right)-1 \right]}$$ (9.2)

where $h=6.63\times 10^{-34}$ Joule-sec is the Planck constant and $k=R/N=8.314/(6.022\times 10^{23})= 1.38\times 10^{-23}$ Joules/Kelvin is the Boltzmann Constant. The spectral energy density can equivalently be defines in terms of the wavelength interval $d \lambda$ as $du_{\lambda}= \, u_{\lambda} \, d \lambda$.

Figure 9.4: (a) Black body spectrum and (b) CMBR spectrum

Figure 9.4 (a) shows the energy density of black body radiation for different values of the temperature $T$. The curves for different temperatures are unique and the curves corresponding to different values of $T$ do not intersect. The wavelength $\lambda_m$ at which the energy density peaks decreases with $T$, and the relation is given by the Wien's displacement law

$$\lambda_m T=2.898 \times 10^{-3} \,{\rm m \, K}$$ (9.3)

Radio observations carried out by poenting a radio receiver in different directions on the sky show that there is a radiation with a black body spectrum (Figure 9.4 (b)) at $T = 2.735 \pm 0.06 {\rm K}$ arriving from all directions in the sky. This radiation is not terrestrial in origin. It is believed that we are actually seeing a radiation which pervades the whole universe and is a relic of a hot past referred to as the hot Big Bang . This black body radiation is referred to as the Cosmic Microwave Background Radiation (CMBR) which peaks in the microwave region of the Spectrum.