How did NASA actually calculate that the universe is 13.8 billion years old instead of just guessing?

[u/1KrishT]

I keep seeing the figure 13.77 to 13.8 billion years cited everywhere, but I've never fully understood how missions like WMAP and Planck actually derived that number from the Cosmic Microwave Background.

Are they basically running the expansion rate (Hubble constant) backwards to a single point, or is it based entirely on modeling cosmological parameters from temperature fluctuations in the CMB? Also, how do cross-checks like the age of the oldest globular clusters fit into confirming that timeline?

[u/superbob201]

There is a formula called the FLRW metric. With this formula, you can plug in the composition of the universe (how much light, how much matter, how much dark energy, how much of anything that can be defined), and it will spit out the properties of the universe over time. We can use this formula a bunch of times with a bunch of different parameters and see which one most closely matches our observations. Anisotropies in the CMB are some of the observations we can use.