On Feburary 11 2016, the collaboration of LIGO-Virgo, the gravitational wave interferometery facility, announced the first ever direct detection of gravitational waves in human history. The signal is from an event of two black holes merging into each other that happened about a billion years ago (1.3 billion light years away, to be precise,) with signal captured on Earth on September 14, 2015. It is a truly amazing progress of physics, especially after noting the tremendous amount of effort put into building the experiment. Michael Peskin’s description of the effort that led to the discovery of Higgs boson seems to apply here as well: “Those of us who scribble equations for a living are humbled by the enormous effort it takes to find out whether those equations are relevant to the real world.”

To the world, the gravitational waves verify what Einstein predicted nearly a century ago, put considerable constraints on theories describing gravity different from General Relativity, and gives us a good handle on violent environment that is both far away and deep into the past. For us phenomenologists and theorists, it is extra exciting because it provides us a new type of tool – a new machinery, a new sensor, the third eye, whatever you call it – to probe theories beyond the Standard Model of particle physics. As we all know that physics relies heavily on new experiment data and observations, without which theorists have no choice but turn to the help of self-consistency of the theory, as well as simple guidance such as naturalness and occam’s razor. However, no matter how beautiful a theory looks under the criteria of all the guiding device, it is not guaranteed to be “relevant to the real world.” In a nutshell, this is part of the reason for the excitement regarding the gravitational wave, among the theory crowd in the last a couple of years.

There are many ways of generating gravitational waves, such as from inflationary process, from phase transition, and from binary mergers of compact objects (say black holes or neutron stars,) all of which require some sort of violent disturbance of the space-time that goes beyond dipole expansion – for example a rotating ball will not radiate gravitational wave.

Let us look at the gravitational waves from binary mergers in particular. There are three phases of the merging process: the inspiral phase, the merger phase, and the ring down phase. The amplitude of the amplitude of the signal is inversely proportional to distance squared, the compactness of each of the pair, and the merger’s mass. All of these are macroscopic observables. Keep in mind that most of the beyond of Standard Model theories deal with microscopic scale process (sub-atomic physics.) Bridging the two is the first challenge we have to face, in order to turn gravitational wave into a real probe of New Physics.

One good candidate to bridge this gap is the Bose-Einstein Condensate of ultra-light bosons. It is known that when temperature is below the critical temperature, bosons tend to occupy the lowest quantum state, a phenomena also proposed by Einstein (and Bose) and observed in the lab. When we take the ultralight bosons to be our dark matter candidate, the smaller is the scalar mass, the higher is their critical temperature – therefore easier to form Bose-Einstein Condensate. More importantly, the mass of the Condensate depends on the scalar’s mass. A rough correspondence is that \(10^{-10}\) electronvolt scalar gives about 1 solar mass. To summarize, the fundamental scalar’s properties (mass) is imprinted on the macroscopic Condensate, which is in turn read out through the gravitational wave signal measured at LIGO-Virgo.

To add a final twist, the compactness-mass profile of the Bose-Einstein Condensate also has dependence on the scalar’s potential. Intuitively, this is because the self-gravity supplies us with a super dense environment, so dense that the field’s value gets large. The large field value ultimately probes a bigger range of the scalar potential instead of just around the local minimum.

In my recent work with my wonderful colleagues Djuna Croon and JiJi Fan, we demonstrate this idea on a concrete level. We show that a simple approximation of the axion’s potential with the first few terms (truncated at the quartic, to be precise) is not precise enough for very dense Condensates. The higher order non-renormalizable terms will affect the mass profile when included. This shows the possibility to test different forms of axion potentials, even though they could share the same mass and similar quartic interactions.

This is an exciting time to come up with creative ideas of making use of the newly discovered gravitational waves. My good friend Zhong-Zhi Xianyu said the other day that the whole world was thinking about it, and I don’t think that’s an exaggeration. As Lisa Randall once said during a discussion, you are all welcome to think about how to use gravitational wave to probe New Physics.

(Cover image credit: NASA)