Explain that the CMBR was produced shortly after the Universe was formed and that this radiation has been expanded into the microwave region of the electromagnetic spectrum as the Universe expanded

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – Topic 6.2.3 The Universe

6.2.3 The Universe

Learning Objective

Explain that the Cosmic Microwave Background Radiation (CMBR) was produced shortly after the Universe was formed and that this radiation has been stretched into the microwave region of the electromagnetic spectrum as the Universe expanded.

Key Concepts

  • The early Universe was extremely hot and dense.

  • When the temperature fell to about \$3000\ \text{K}\$, electrons and protons combined to form neutral hydrogen – the epoch of recombination.

  • At recombination photons decoupled from matter and began to travel freely through space.

  • These photons constitute the Cosmic Microwave Background Radiation (CMBR).

  • As the Universe expands, the wavelength of the CMBR photons is stretched (red‑shifted) into the microwave region.

Timeline of the Early Universe

Time after the Big BangTemperature (K)Key Event
\$10^{-43}\ \text{s}\$\$>10^{32}\$Planck epoch – quantum gravity dominates
\$10^{-12}\ \text{s}\$\$10^{15}\$Electroweak symmetry breaking
\$1\ \text{s}\$\$10^{10}\$Neutrino decoupling; nucleosynthesis begins
\$3\ \text{min}\$\$10^{9}\$Formation of light nuclei (H, He, Li)
\$380\,000\ \text{yr}\$\$3000\$Recombination – photons decouple → CMBR released
\$13.8\ \text{Gyr}\$ (today)\$2.73\$CMBR observed as microwave radiation

Why the CMBR Is Now in the Microwave Region

The expansion of space stretches the wavelength \$\lambda\$ of every photon. The relationship between the observed wavelength \$\lambda{\text{obs}}\$ and the emitted wavelength \$\lambda{\text{emit}}\$ is given by the cosmological redshift \$z\$:

\$1 + z = \frac{\lambda{\text{obs}}}{\lambda{\text{emit}}} = \frac{a0}{a{\text{emit}}}\$

where \$a\$ is the scale factor of the Universe. At recombination the scale factor was roughly \$a{\text{emit}} \approx 1/1100\$ of its present value \$a0\$. Consequently, photons that were originally in the visible/infrared range (\$\lambda{\text{emit}} \sim 1\ \mu\text{m}\$) have been stretched by a factor of about 1100, giving an observed wavelength of \$\lambda{\text{obs}} \sim 1\ \text{mm}\$, which lies in the microwave region.

Properties of the CMBR

  • Almost perfectly isotropic – the same intensity in every direction.

  • Black‑body spectrum with a temperature of \$2.73\ \text{K}\$.

  • Small anisotropies (temperature variations of \$\sim 10^{-5}\$) provide clues about the early density fluctuations that grew into galaxies.

Implications for Cosmology

  1. Evidence that the Universe had a hot, dense beginning (the Big Bang).

  2. Provides a “snapshot” of the Universe at the moment of recombination.

  3. Allows measurement of the Universe’s geometry, composition, and rate of expansion.

Suggested diagram: A timeline showing the expansion of the Universe with the CMBR photon wavelength stretching from visible/infrared at recombination to microwave today.

Summary

Shortly after the Big Bang, the Universe cooled enough for electrons and protons to combine, releasing a flood of photons. These photons have travelled unhindered for billions of years. As space itself expanded, the photons’ wavelengths were stretched, shifting the original visible/infrared radiation into the microwave region we detect today as the Cosmic Microwave Background Radiation. The CMBR is a cornerstone of modern cosmology, confirming the hot‑big‑bang model and providing a wealth of information about the early Universe.