# How Fast is the Universe Expanding?

In the last post I commented on the fact that the Universe is expanding. That raises the question, how fast is it expanding? At first sight, who cares? If all the other galaxies will be out of sight in so many tens of billions of years, we won’t be around to worry about it. However, it is instructive in another way. Scientists make measurements with very special instruments and what you get are a series of meter readings, or a printout of numbers, and those numbers have implied dimensions. Thus the number you see on your speedometer in your car represents miles per hour or kilometers per hour, depending on where you live. That is understandable, but that is not what is measured. What is usually measured is actually something like the frequency of wheel revolutions. So the revolutions are counted, the change of time is recorded, and the speedometer has some built-in mathematics that gives you what you want to know. Within that calculation is some built-in theory, in this case geometry and an assumption about tyre pressure.

Measuring the rate of expansion of the universe is a bit trickier. What you are trying to measure is the rate of change of distance between galaxies at various distances from you, average them because they have random motion superimposed, and in some cases regular motion if they are in clusters. The velocity at which they are moving apart is simply change of distance divided by change of time. Measuring time is fine but measuring distance is a little more difficult.  You cannot use a ruler.  So some theory has to be imposed.

There are some “simple” techniques, using the red shift as a Doppler shift to obtain velocity, and brightness to measure distance. Thus using different techniques to estimate cosmic distances such as the average brightness of stars in giant elliptical galaxies, type 1a supernovae and one or two other techniques it can be asserted the Universe is expanding at 73.5 + 1.4 kilometers per second for every megaparsec. A megaparsec is about 3.3 million light years, or three billion trillion kilometers.

However, there are alternative means of determining this expansion, such as measured fluctuations in the cosmic microwave background and fluctuations in matter density of the early Universe. If you know what the matter density was then, and know what it is now, it is simple to calculate the rate of expansion, and the answer is, 67.4 +0.5 km/sec/Mpc. Oops. Two routes, both giving highly accurate answers, but well outside any overlap and hence we have two disjoint sets of answers.

So what is the answer? The simplest approach is to use an entirely different method again, and hope this resolves the matter, and the next big hope is the surface brightness of large elliptical galaxies. The idea here is that most of the stars in a galaxy are red dwarfs, and hence the most “light” from a galaxy will be in the infrared. The new James Webb space telescope will be ideal for making these measurements, and in the meantime standards have been obtained from nearby elliptical galaxies at known distances. Do you see a possible problem? All such results also depend on the assumptions inherent in the calculations. First, we have to be sure we actually know the distance accurately to the nearby elliptical galaxies, but much more problematical is the assumption that the luminosity of the ancient galaxies is the same as the local ones. Thus in earlier times, since the metals in stars came from supernovae, the very earliest stars will have much less so their “colour” from their outer envelopes may be different. Also, because the very earliest stars formed from denser gas, maybe the ratio of sizes of the red dwarfs will be different. There are many traps. Accordingly, the main reason for the discrepancy is that the theory used is slightly wrong somewhere along the chain of reasoning. Another possibility is the estimates of the possible errors are overly optimistic. Who knows, and to some extent you may say it does not matter. However, the message from this is that we have to be careful with scientific claims. Always try to unravel the reasoning. The more the explanation relies on mathematics and the less is explained conceptually, the greater the risk that whoever is presenting the story does not understands it either.