Superclusters: My Senior Thesis

Today marks one year since my official graduation from Carleton College. Which is bonkers, because it feels like it’s been about 3 months. Anyway, in honor of the anniversary of my graduation, I though I’d share my senior thesis with you. It’s titled “Superclusters and the Large-Scale Structure of the Universe” and it was my final collegiate assignment. Prior warning, though, it’s not written for the layperson, but rather for an audience with an undergraduate education in physics. There is math in it. It’s pretty long. It was quite an endeavor to write. I’m proud of it.

Without further ado:

Leah’s COMPS Paper

A Beginner’s Guide to Gravitational Waves and LIGO

For months, rumors have been circulating the scientific community about the discovery of gravitational waves. LIGO (the Laser Interferometer Gravitational-Wave Observatory), an enormous inter-institutional effort to find these theorized waves, has scheduled a press conference for this Thursday (2/11/2016).

So, what exactly are gravitational waves?

In order to start answering that question, we must first go over some basic concepts from Einstein’s theory of general relativity, starting with the so-called “fabric of spacetime.” In this metaphor (it’s a mathematical model really, but in this case it does the same thing as a metaphor), space and time form a fabric upon which physical items (stars, planets, and the like) sit.


Two orbiting objects distending the fabric of spacetime. Source: BBC Horizon

Just like a marble on a mattress, matter within spacetime creates a dip, a curve in spacetime. Other objects follow that curve, as shown in the animation above: when a star creates a dip in the fabric of spacetime, planets and other items in space are drawn toward that dip (like that marble rolling toward the lowest point on the mattress). This is gravity. If the planets/asteroids/dust are moving with just the right momentum in just the right direction, they can orbit the star instead of crashing into it. The universe, in this representation, is essentially an enormous (extra-quadruple-California-king-sized) mattress covered in billions and billions of rolling marbles of assorted sizes, each creating its own dip in the mattress that is proportional to its mass.

Now, gravity cannot be detected directly: we can tell an object’s gravitational “dent” by how it affects the items around it, but we can’t see it with a telescope. However, Einstein’s theory of general relativity predicts that when massive objects move, they create ripples in spacetime which propagate outward at the speed of light.


A model of the theoretical gravitational waves from a binary system. Source: NASA JPL

Gravitational waves would behave similarly to those created when you drop a pebble in a lake: anything floating on the lake would be moved very slightly – just a tiny bob. But, for particularly huge objects and events like supernovae, colliding stars, and binary systems of neutron stars or black holes, those ripples may be detectable.

LIGO is one of several detectors looking for gravitational waves. It consists of two major observatories, the LIGO Livingston Observatory in Louisiana, and the LIGO Hanford Observatory in Washington.


The LIGO Livingston Observatory in Louisiana. Source: Caltech/MIT/LIGO Lab

Each of these observatories consists of two giant concrete tubes which are kept pumped to a vacuum. Inside those tubes is a scientific instrument called a Michelson interferometer. As shown in the animation below, a laser beam is shot through a beam splitter, causing part of the beam to go down each arm of the observatory’s concrete L. Those beams each hit a carefully calibrated mirror at the end of the tube and bounce back to the middle, where they are compared. (Note that this, like the earlier explanation of gravitational waves, is a simplistic view – the arms actually contain special cavities to increase their effective lengths, and everything is carefully stabilized and measured and calibrated.)


A basic Michelson interferometer. Source: Jaime E. Villate,

When a gravitational wave washes over the interferometer, it causes spacetime in the area to stretch or compress extremely slightly, moving the mirrors and changing the length of the tubes by a miniscule amount, thousands of times smaller than an atom. These tiny changes affect the laser beams: when the two beams return to the “screen” where they’re measured, they are compared. If the changes in the beams match up to the theoretical effects of a gravitational wave passing through the interferometer, gravitational waves will have been detected. If a gravitational wave is detected at both LIGO interferometers, scientists may even be able to point out a general area in the sky where the event creating the gravitational waves occurred, up to 260 million light-years away (with a range set to extend to 650 million light-years in the next two years).

According to LIGO’s media advisory, their press conference this Thursday is because:

This year marks the 100th anniversary of the first publication of Albert Einstein’s prediction of the existence of gravitational waves. With interest in this topic piqued by the centennial, the group will discuss their ongoing efforts to observe gravitational waves.

However, rumors have been circulating through the scientific community that the press conference will, in fact, contain an announcement that gravitational waves have been detected.

If they have, it could lead to a whole new field in astronomy, similar to how the discovery of observation in radio or infrared frequencies did. Gravitational wave astronomy would allow us to indirectly observe the movements of mass: we’d be able to see how things are moving, even if we couldn’t actually see those things (say, because they’re inside a supernova). The possibilities for new discovery through gravitational waves would be endless!

…If LIGO has observed them. To find out, we’ll just have to wait until Thursday!

Further Information:

LIGO’s website:

People who will probably be tweeting about LIGO:

A more in-depth article for laypeople by Matthew R. Francis:

An article on this particular round of LIGO hype by Joshua Sokol:



Here is video of the press conference:

Here is a Storify of some tweets about it with lots of information about what they found and why it’s important:

Here is Matthew R. Francis’ post-presser article:

Here are two links to the paper itself, in Physical Review Letters: