Published by Patrick Mutisya · 8 days ago
The Cosmic Microwave Background Radiation is a faint glow of microwave‑frequency electromagnetic radiation that fills the entire Universe. It is observed at every point in space, regardless of direction, and is a relic of the early hot, dense state of the Universe.
\$\nu{\text{max}} = \frac{k{\text{B}}T}{h}\,x_{\text{max}} \approx 160.2\ \text{GHz}\$
where \$x_{\text{max}} \approx 2.82144\$ for a black‑body.
At a temperature of \$2.7\ \text{K}\$ the peak wavelength from Wien’s displacement law is
\$\lambda_{\text{max}} = \frac{b}{T} \approx \frac{2.898\times10^{-3}\ \text{m·K}}{2.7\ \text{K}} \approx 1.07\ \text{mm},\$
which lies in the microwave region of the electromagnetic spectrum (approximately \$1\ \text{mm}\$ to \$1\ \text{m}\$).
\$B(\nu,T)=\frac{2h\nu^{3}}{c^{2}}\frac{1}{e^{h\nu/k_{\text{B}}T}-1}\$
measured to high precision by the COBE, WMAP and Planck satellites.
| Property | Symbol / Value | Units | Notes |
|---|---|---|---|
| Average temperature | \$T\$ = 2.725 | K | Measured by COBE FIRAS |
| Peak frequency | \$\nu_{\text{max}}\$ ≈ 160.2 | GHz | From Wien’s law |
| Peak wavelength | \$\lambda_{\text{max}}\$ ≈ 1.07 | mm | Corresponds to microwave band |
| Energy density | \$u = aT^{4}\$ | J·m⁻³ | \$a = 7.5657\times10^{-16}\ \text{J·m}^{-3}\text{K}^{-4}\$ |
| Temperature anisotropy | \$\Delta T/T\$ ≈ \$10^{-5}\$ | – | Observed by WMAP & Planck |
Radio telescopes equipped with highly sensitive microwave receivers scan the sky. The signal is extremely weak, so observations are performed from high, dry sites or from space to minimise atmospheric absorption.