---
title: "How the universe became transparent"
description: "Follow hydrogen recombination and the last scattering of light, then read what tiny departures from a blackbody can record."
canonical_url: "https://sandboxphysics.com/stories/cosmic-transparency/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/cosmic-transparency/"
last_modified: "2026-11-14"
---

# How the universe became transparent

Sandbox Physics · 2026-11-12

Begin with the near-perfect blackbody of the microwave background. Work out when hydrogen atoms formed, where the light last scattered, and which shapes extra energy would leave in the spectrum. Then rerun the model and read a published limit.

1. L1 · Concept

   ## [What can tiny departures from a perfect blackbody record?](https://sandboxphysics.com/stories/cosmic-transparency/a-nearly-perfect-blackbody/)

   The microwave background is almost a perfect blackbody. Tiny departures would record energy released from two months to 370,000 years after the start.

2. L1 · Chapter

   ## [Saha balance and the recombination bottleneck](https://sandboxphysics.com/stories/cosmic-transparency/saha-and-the-recombination-bottleneck/)

   Saha equilibrium puts half of hydrogen in atoms by redshift 1370. A slow last step leaves 30 times more free electrons at redshift 1100.

3. L2 · Chapter

   ## [Optical depth and the visibility function](https://sandboxphysics.com/stories/cosmic-transparency/optical-depth-and-the-visibility-function/)

   Adding up scatterings off free electrons gives where background light last scattered: a shell near redshift 1081, about 200 wide in this model.

4. L3 · Chapter

   ## [Thermalization, chemical-potential and Compton distortions](https://sandboxphysics.com/stories/cosmic-transparency/thermalization-mu-and-y/)

   Derive the temperature, chemical-potential and Compton shapes, the energy each carries, and when an energy release leaves each one.

5. L3 · Method

   ## [Comparing Saha, a three-level atom and a frozen CLASS reference](https://sandboxphysics.com/stories/cosmic-transparency/compare-recombination-codes/)

   Rerun a standard-library Python model against HyRec-2 output and Green's functions frozen in CLASS v3.3.4, with inputs, errors and failure cases.

6. L4 · Paper guide

   ## [How to read the decaying dark matter limits of Lucca and colleagues](https://sandboxphysics.com/stories/cosmic-transparency/reading-energy-injection-limits/)

   A guided reading of Figure 8 in arXiv:1910.04619v3: which decays FIRAS and Planck exclude, and what proposed spectrometers assume.