--- title: "The Scale Factor, the Friedmann Equation and the Age of the Universe" description: "Expansion is written as one function of time multiplying every distance, and the equation governing it comes from applying general relativity to a uniform universe. What the universe contains fixes ho" canonical: https://lightmysky.com/learn/science/the-scale-factor-the-friedmann-equation-and-the-age-of-the-universe-mt_v3VEzinvJe source: https://lightmysky.com/learn/science/the-scale-factor-the-friedmann-equation-and-the-age-of-the-universe-mt_v3VEzinvJe.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # The Scale Factor, the Friedmann Equation and the Age of the Universe Expansion is written as one function of time multiplying every distance, and the equation governing it comes from applying general relativity to a uniform universe. What the universe contains fixes how that function behaves, so the measured contents predict an age and a fate. Subject: Science · Area: Astronomy & Astrophysics · Ages 21 to 22 Page: https://lightmysky.com/learn/science/the-scale-factor-the-friedmann-equation-and-the-age-of-the-universe-mt_v3VEzinvJe ## Ready when they can - Writes redshift as a ratio of scale factors and explains why that is not a Doppler shift through space - States how matter, radiation and a cosmological constant each dilute as the universe expands, and which dominates when - Estimates an age from an expansion rate and says why the simplest estimate is not the measured answer ## Lesson: One number stretches the whole universe Cosmic expansion is written as one function of time, the scale factor, multiplying every distance. Light stretched while it travelled records this growth as redshift: one plus z equals the scale factor now divided by the scale factor back then. Nothing moves through space. Space itself stretches the waves, and the expansion has no centre. **Example.** Suppose light left a galaxy when the scale factor was half its present value. One plus z equals one divided by one half, which is two, so z equals one. The same rule runs the contents: if the scale factor doubles, matter thins eightfold with the volume, radiation thins sixteenfold because each photon also reddens, and dark energy stays constant. The Friedmann equation governs the scale factor by tying the expansion rate to what the universe contains. More density means stronger braking on the expansion, while dark energy pushes outward. Because each component dilutes differently, each era has its own ruler: radiation ruled the hot start, matter built the galaxies, and dark energy drives today. **Tip.** To estimate the age, run the expansion backwards. The naive guess of one over the Hubble rate lands near fourteen billion years. The measured answer differs because early matter slowed the expansion and late dark energy speeds it. Dating the oldest stars cross checks the result, and the microwave background plus the light elements confirm the hot dense start. **Recap.** The scale factor stretches all distances, its contents set its pace, and the naive age needs their correction. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Galaxies, Redshift and the Expanding Universe](https://lightmysky.com/learn/science/galaxies-redshift-and-the-expanding-universe-mt_-POhqrng-Q) - [General Relativity: Curved Spacetime and Its Tests](https://lightmysky.com/learn/science/general-relativity-curved-spacetime-and-its-tests-mt_-rZZxZwU2L) - [The Cosmic Microwave Background and the Light Elements](https://lightmysky.com/learn/science/the-cosmic-microwave-background-and-the-light-elements-mt_oz0MJXiuVt)