Swiss Cheese, Statistics and the Early Universe

How could a fermented milk product riddled with holes relate to the cold space filled with hydrogen gas and stars, and to a branch of  mathematics that no one understands? The answer depends on how you look at the Universe. Regular readers may know that our colleagues in the Low-frequency Cosmology (LoCo) group here at ASU are building instruments to observe 21 cm spectrum of hydrogen from the early Universe. In a non-scientific description, we are trying to look at “rainbows” emitted by hydrogen gas using radio telescopes. The “rainbows” from different periods of time in the Universe also happen to fall into different frequencies of radio signal. Observing them at various radio frequencies will let us construct a cube showing the distribution of hydrogen in the early universe as a function of time. Now, emission from stars and galaxies breaks up hydrogen atoms surrounding them into nuclei and electrons, creating “bubbles” in which hydrogen gas is ionized, and there will be no 21 cm spectrum from within the “bubbles.” As a result you will see holes in the cube, like a block of Swiss cheese! I should also point out that the size of these “bubbles” can tell you what the stars that produce them look like!

Unfortunately, our current generation of instruments is not good enough to construct a clean data cube that will let us directly look at the “bubbles” and measure them, and we will have to learn from statistics. Think about it this way: You count all the holes with a particular size or volume in your block of Swiss cheese. Then you chop up the cheese into pieces to “contaminate” them (be careful not to cut through the holes too much), then mix in small pieces of another type of cheese with tiny holes, like Tilsit, and randomly put all the pieces back into a block. If you then count the holes and measure their sizes again, the number should be relatively the same. (Remember that holes in Swiss cheese are big!)  This analogy does not exactly describe what  we will be seeing in our data, but it roughly explains what I meant by statistics. The bottom line is that you can still learn something about the Universe from bad data by using statistics.

Figuring our what type of statistics to use and the best way to use them on the 21 cm data will be my Ph.D. thesis.  Please cheer and support me!

Piyanat Kittiwisit, or Boom (as he likes to be called), is a graduate student in the Low-frequency Cosmology group in the School of Earth and Space Exploration at ASU.