We deduce the age of the Universe from observations we make now, coupled with an assumption that the fundamental physical laws of today also operated in the past.
This is pretty much the way historians work out human history – make observations of things like buildings, artefacts or written records, and make deductions based on an understanding human behaviour. Cosmologists have a bit of an advantage because particles, stars and galaxies are more predictable than people.
There are two or three key observations that determine the age of the Universe.
The first is that the galaxies we observe around us are all receding. This means the Universe is expanding. So in the past it was smaller. If the rate of expansion were constant, that would immediately give us a point in time when it was zero size, which we could label the beginning: the Big Bang.
It is a bit more complicated than that – for example, the rate of expansion actually seems to be increasing. Still, the expansion tells us the Universe hasn’t been here, looking just the same, forever. It is dynamic.
A second important piece of the puzzle is called the cosmic microwave background. This is background noise (actually photons – electromagnetic radiation) left over from the Big Bang.
When all of matter was crammed into a tiny space, the energy density would have been very high. This means atoms would not hold together, as the electrons would keep getting knocked away by energetic photons. However, as the Universe expanded and cooled, the energy of the photons decreased.
At some point it became too low to stop electrically-neutral atoms forming. Since that happened (about 380,000 years after the Big Bang), the photons have hung around getting lower and lower in energy. They are still there, at a temperature 2.7°C above absolute zero, and we have measured them very precisely.
Not only are they further evidence for the Big Bang, but because we know very well how electrons and photons behave, studying the spectrum and distribution of the cosmic microwave background constrains the age of the Universe very tightly.
Finally, knowing that there was a Big Bang, we can look how long it must have taken to make various objects in the Universe. Light elements (hydrogen, helium and a bit of lithium) would be made as a result of the Big Bang itself, but heavier elements require nuclear reactors – that is, stars.
These take time to form, as matter comes together under gravity, and time to burn, explode and distribute carbon, silicon, iron and the rest around the Universe to make new stars, planets, and of course physicists.
Some of the objects we see around us are very old – not least because they are so far away that the light we see them by was emitted billions of years ago. All of this says the Universe is definitely very old, and gives estimates consistent with the more precise values deduced from the cosmic microwave background.