# Cosmology - Cosmic Microwave Background

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The CMB (Cosmic Microwave Background) essentially is constituted by the photons of the time when matter and radiation was in equilibrium. By the 1920s, the idea of an expanding universe was accepted and could answer several questions. But questions about the abundance of heavier elements and the abundance were left unanswered. Moreover, the expanding universe implied that the density of matter should decrease down to 0.

In 1948, George Gammow and Ralph Alpher explained the Origin of heavier elements and the abundance using “Big Bang”. They along with Robert Herman predicted the existence of “Relict Radiation” or radiation remaining from the “Big Bang”. The predicted temperature for this remnant radiation was between 50-6 K. In 1965, Robert Dicke, Jim Peebles and David Wilkinson along with the Amo Perizias’ Research Group experimentally detected the CMB.

The early universe was very hot and the energy was too high for the matter to remain neutral. Hence, matter was in the ionized form - Plasma. The Radiation (photons) and Matter (plasma) interacted mainly through the following three processes.

• Compton Scattering − (Major Interaction Process) Inelastic scattering between high energy photon and low energy charged particle.

• Thomson Scattering − Elastic scattering of photon by a free charged particle.

• Inverse Compton Scattering − High energy charged particle and low energy photon. These interactions finally resulted in matter and radiation being in Thermal equilibrium.

## Thermal Equilibrium

In Thermal equilibrium, the radiation obeys the Planck Distribution of Energy,

$$B_v(T) = \frac{2hv^3}{c(e^{hv/k_BT}-1)}$$

During this time, due to the highly frequent interactions, the mean free path of photons was very small. The universe was Opaque to radiation. The early universe was radiation dominated. The universe evolved in such a way that matter and radiation reached Thermal Equilibrium and their energy density became equal. This can be seen from the graph showing evolution of density with the scale factor. Let us find out the scale factor (time) (a(t)) at which the matter and the radiation reached equilibrium.

$$\rho_m \propto \frac{1}{a^3}, \: \rho_r \propto \frac{1}{a^4}$$

$$\frac{\rho_{m,t}}{\rho_{r,t}} = \frac{\Omega_{m,t}}{\Omega_{r,t}} = \frac{\Omega_{m,0}}{\Omega_{r,0}}a(t)$$

At equilibrium,

$$\frac{\rho_{m,t}}{\rho_{r,t}} = \frac{\Omega_{m,t}}{\Omega_{r,t}} = 1$$

$$\Rightarrow \frac{\Omega_{m,0}}{\Omega_{r,0}}a(t) = 1 \: \Rightarrow a(t) = 2.96 \times 10^{-4}$$

using $\Omega_{m,0} = 0.27$ and $\Omega_{r,0} = 8 \times 10^{−5}$. The red shift corresponding to this scale factor is given by −

$$z = 1/a(t)-1 \approx 3375$$

The energy density of the radiation went down due to the expansion of the universe. Thus the universe started to cool down. As the energy of the photons started to decrease, neutral atoms started to form. Thus, around a redshift of 1300, neutral Hydrogen started to form. This era had a temperature close to 3000K.

The interaction between matter and radiation became very infrequent and thus the universe started becoming transparent to radiation. This time-period is called “Surface of last scattering” as the mean free path of the photons became very large due to which hardly any scattering took place after this period. It is also called as “Cosmic Photosphere”.

## Points to Remember

• CMB is constituted by the photons of the time when matter and radiation was in equilibrium.

• The early universe was very hot and the energy was too high for matter to remain neutral, so it existed as ionized matter-Plasma.

• Compton Scattering, Thomson Scattering, Inverse Compton Scattering were the 3 matter-radiation interaction processes then.

• Universe evolved such that matter and radiation reached Thermal equilibrium.

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