Cosmic Static: The Stochastic Gravitational Wave Background

What would you hear if you could listen back to the very moment the universe burst into existence? Using the Cosmic Microwave Background (explained in Beatrice’s blog post), we have a picture of what the Universe looked like at ~380,000 years old, but we can’t use light to look any farther back in time because before the moment captured by the CMB, the universe consisted of an opaque plasma. Instead of using light, however, we can use gravity to probe our Universe’s earliest days. As explained in Sydney’s blog post, violent acceleration of extremely massive objects emits gravitational waves, and turbulent early universe processes like inflation (see Anne-Sylvie’s post) created the perfect environment for gravitational waves. The stochastic gravitational wave background is analogous to the CMB; it comes from the superposition of many gravitational wave signals that are individually indistinguishable, so it appears as a persistent background signal. The stochastic background can be dominated by cosmological sources like inflation, phase transitions, and cosmic strings, in which case it would provide a soundbite of the early days of our cosmic history. It can also be dominated by astrophysical sources- many overlapping individual signals coming from compact objects like black holes and neutron stars smashing into each other that are too weak or too distant to be detected individually- in which case it would provide a soundbite of our present astrophysical environment.

 

Why do we see the CMB but listen to gravitational waves? As a gravitational wave passes over Earth, it stretches space in one direction and contracts it in the perpendicular direction, so using extremely sensitive detectors, we can measure the frequency of these expansions and contractions, or measure their pitch. In order to explain some of the properties of the stochastic background, we will use the analogy of a crowded rock concert. Before the show, all the spectators are packed into the venue, each having a separate conversation. You can’t hear individual conversations, but you can hear the buzz of chatter. Each conversation represents an individual gravitational wave signal, too weak to be detected on its own, but combined with all the other conversations which are conducted at around the same volume, the room is filled with background noise. This background noise is the stochastic gravitational wave background.

 

If the concert is sold out, there is an equal conversation density in all directions. No matter which way you turn to listen, the background sounds the same in all directions, which means it’s “isotropic” in physics lingo. Cosmological backgrounds, a relic of an earlier time in the universe when matter was distributed nearly evenly across space, are expected to be isotropic. Now imagine several really loud groups of people come and sit down a few rows in front of you. You still can’t really hear their individual conversations, but you can definitely tell that the background is louder in their direction. If there was a dense population of coalescing stars or black holes in one specific region of the universe, the stochastic background would be louder in that direction, so it would be “anisotropic”.
 

If you’ve been waiting for the concert to start for a while already, the background chatter sounds the same now as it did 5, 10, or 15 minutes ago; it’s a stationary background that doesn’t depend on the time when you started listening. Similarly, if the background consists of independent conversations that last longer than the time between them, it is called a Gaussian background due to the Central Limit Theorem. However, if you’re one of the first people to arrive, you may be able to pick out bits and pieces of individual conversations starting up around you. The time between conversations is longer than the conversations themselves; this is a popcorn background. The same would be said of a stochastic background caused by overlapping gravitational wave signals whose duration is shorter than the period of time between individual events. This results in a background that sounds like popcorn in a microwave.

 

When Einstein predicted the existence of gravitational waves 100 years ago, his Theory of General Relativity (GR) predicted that gravitational waves could only move or stretch space in two ways, the plus and the cross tensor polarizations modes. Since we are interested in using gravitational waves to test GR, we can compare the polarization of the stochastic background predicted by GR to that predicted by alternative gravity theories, which allow gravitational waves to move in up to six directions, adding two vector and two scalar polarization modes to the two tensor modes already predicted by GR. The image below shows how a gravitational wave of each polarization would stretch and squeeze a test mass ring. Just like the ring responds differently to each polarization, so does the gravitational wave detector, so we can measure the polarization content of the stochastic background by analyzing the detector’s response and allowing for the possibility of all six modes. If we were to detect any polarization mode besides the two tensor modes predicted by GR, this would prove that GR is incorrect and force us to reconsider everything we thought we knew about gravity. For this reason, the stochastic background is a powerful tool not only for learning about our cosmic history and our astrophysical environment, it can also be used to learn about gravity itself.

 

For more information about stochastic backgrounds and testing general relativity, check out this arXiv preprint!

Author: Andrea Sylvia

Sylvia recently graduated from Penn State with a BS in Physics and a BA in Spanish, conducting research with Prof. Mostafa on ultra high energy cosmic rays and on gravitational waves with Prof. Hanna's group. Her honors thesis focused on using data from the Pierre Auger Observatory to determine the mass composition of the highest energy particles in the universe. She has also conducted research with LIGO, using the search for a stochastic gravitational wave background to test General Relativity. She will continue her studies of gravitational waves through a Fulbright Postgraduate Scholarship at Monash University in Australia and will then return to the US to complete her PhD in Physics at the Massachusetts Institute of Technology.