How do we determine the age of the universe?
You explained how 1/H is an inaccurate way of determining the age of the universe. Is there any other quantitative and observational way of more accurately representing the age of the universe?
As we discussed, defining the age of the universe as 1/H is not really correct because it assumes H has been the rate of expansion throughout the universe's history (and thus that the expansion rate has been constant, not accelerating or decelerating).
There are a couple of ways to get good estimates on the age of the universe, but no way to know exactly for sure. For an idea of how hard this is, let's pretend I show you a person and ask you to guess how old she is. It would be somewhat difficult to guess the exact right age, but how would you do it? You would think about how old that person looks compared to other people you know of different ages. Well, we only have one universe, so we can't compare it with other universes so determining the age is very hard! Here are three of the more accurate ways:
1) I mentioned just using 1/H was not a very accurate way of finding the age if we use the current measurement of H only. Remember H measures the rate of expansion so assuming H is constant in time says the universe has always been expanding at the same rate. We know this is not true (we believe the universe is actually accelerating) so to be more accurate we have to come up with a model for what we think the expansion rate has been like. In other words, we have to find H as a function of time, integrate over the history of the universe, and then take the inverse of that to get a more accurate age estimate. We're still doing some guesswork here, because we don't know exactly what H was at every moment in the past (it was hard enough for us to figure out what it is now!) Each model will give a different value for the age, but one of the most popular models gives about 13.7 billion years.
2) Another method is looking at clusters of stars (groups of stars all born at the same time that are at the same distance from us). When stars are in the longest stage of their lives (burning hydrogen) we can put them on a plot of temperature versus luminosity (how bright they are) and we find they all fall in a straight line (we call it the "main sequence"). Based on our knowledge of stars, we know how long each type of star stays on the main sequence. When we observe a cluster of stars, we can see all types of stars filling out the line we call the main sequence. Thus we can see what types of stars have already left the main sequence in old clusters to find an upper limit for the age of the cluster and thus the universe. This method gives ages of 11-13 billion years.
3) There is a special kind of event in some stars' lives called a supernova. A certain kind of supernova occurs when the core of a star becomes a white dwarf (a really compact star near the end of its life) and the star's outer layers bounce off this core and fly into space in a huge explosion. The white dwarf left behind glows at first and then cools as it ages. If we find white dwarves that are really cool, we can estimate how much time must have passed in order for them to get that cool and get a value for the age of the universe. This method gives ages of around 12.7 billion years.
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