Did LIGO Detect Dark Matter?

It has often been said, including by me, that one of the most intriguing aspects of dark matter is that provides us with the best current evidence for physics beyond the Core Theory (general relativity plus the Standard Model of particle physics). The basis of that claim is that we have good evidence from at least two fronts — Big Bang nucleosynthesis, and perturbations in the cosmic microwave background — that the total density of matter in the universe is much greater than the density of “ordinary” matter like we find in the Standard Model.

There is one important loophole to this idea. The Core Theory includes not only the Standard Model, but also gravity. Gravitons themselves can’t be the dark matter — they’re massless particles, moving at the speed of light, while we know from its effects on galaxies that dark matter is “cold” (moving slowly compared to light). But there are massive, slowly-moving objects that are made of “pure gravity,” namely black holes. Could black holes be the dark matter?

It depends. The constraints from nucleosynthesis, for example, imply that the dark matter was not made of ordinary particles by the time the universe was a minute old. So you can’t have a universe with just regular matter and then form black-hole-dark-matter in the conventional ways (like collapsing stars) at late times. What you can do is imagine that the black holes were there from almost the start — that they’re primordial. Having primordial black holes isn’t the most natural thing in the world, but there are ways to make it happen, such as having very strong density perturbations at relatively small length scales (as opposed to the very weak density perturbations we see at universe-sized scales).

Recently, of course, black holes were in the news, when LIGO detected gravitational waves from the inspiral of  two black holes of approximately 30 solar masses each. This raises an interesting question, at least if you’re clever enough to put the pieces together: could the dark matter be made of primordial black holes of around 30 solar masses, and could two of them have come together to produce the LIGO signal? (So the question is not, “Are the black holes made of dark matter?”, it’s “Is the dark matter made of black holes?”)

LIGO black hole (artist's conception)

This idea has just been examined in a new paper by Bird et al.:

Did LIGO detect dark matter?

Simeon Bird, Ilias Cholis, Julian B. Muñoz, Yacine Ali-Haïmoud, Marc Kamionkowski, Ely D. Kovetz, Alvise Raccanelli, Adam G. Riess

We consider the possibility that the black-hole (BH) binary detected by LIGO may be a signature of dark matter. Interestingly enough, there remains a window for masses 10M≲Mbh≲100M where primordial black holes (PBHs) may constitute the dark matter. If two BHs in a galactic halo pass sufficiently close, they can radiate enough energy in gravitational waves to become gravitationally bound. The bound BHs will then rapidly spiral inward due to emission of gravitational radiation and ultimately merge. Uncertainties in the rate for such events arise from our imprecise knowledge of the phase-space structure of galactic halos on the smallest scales. Still, reasonable estimates span a range that overlaps the 2−53 Gpc−3 yr−1 rate estimated from GW150914, thus raising the possibility that LIGO has detected PBH dark matter. PBH mergers are likely to be distributed spatially more like dark matter than luminous matter and have no optical nor neutrino counterparts. They may be distinguished from mergers of BHs from more traditional astrophysical sources through the observed mass spectrum, their high ellipticities, or their stochastic gravitational wave background. Next generation experiments will be invaluable in performing these tests.

Given this intriguing idea, there are a couple of things you can do. First, of course, you’d like to check that it’s not ruled out by some other data. This turns out to be a very interesting question, as there are good limits on what masses are allowed for primordial-black-hole dark matter, from things like gravitational microlensing and the fact that sufficiently massive objects would disrupt the orbits of wide binary stars. The authors claim (and quote papers to the effect) that 30 solar masses fits snugly inside the range of values that are not ruled out by the data.

The other thing you’d like to do is figure out how many mergers like the one LIGO saw should be expected under such a scenario. Remember, LIGO seemed to get lucky by seeing such a big beautiful event right out of the gate — the thought was that most detectable signals would be from relatively puny neutron-star/neutron-star mergers, not ones from such gloriously massive black holes.

The expected rate of such mergers, under the assumption that the dark matter is made of such big black holes, isn’t easy to estimate, but the authors do their best and come up with a figure of about 5 mergers per cubic gigaparsec per year. You can then ask what the rate should be if LIGO didn’t actually get lucky, but simply observed something that is happening all the time; the answer, remarkably, is between about 2 and 50 per cubic gigaparsec per year. The numbers kind of make sense!

The scenario would be quite remarkable and significant, if it turns out to be right. Good news: we’ve found that dark matter! Bad news: hopes would dim considerably for finding new particles at energies accessible to particle accelerators. The Core Theory would turn out to be even more triumphant than we had believed.

Happily, there are ways to test the idea. If events like the ones LIGO saw came from dark-matter black holes, there would be no reason for them to be closely associated with stars. They would be distributed through space like dark matter is rather than like ordinary matter is, and we wouldn’t expect to see many visible electromagnetic counterpart events (as we might if the black holes were surrounded by gas and dust).

We shall see. It’s a popular truism, especially among gravitational-wave enthusiasts, that every time we look at the universe in a new kind of way we end up seeing something we hadn’t anticipated. If the LIGO black holes are the dark matter of the universe, that would be an understatement indeed.

Gravitational Waves at Last

ONCE upon a time, there lived a man who was fascinated by the phenomenon of gravity. In his mind he imagined experiments in rocket ships and elevators, eventually concluding that gravity isn’t a conventional “force” at all — it’s a manifestation of the curvature of spacetime. He threw himself into the study of differential geometry, the abstruse mathematics of arbitrarily curved manifolds. At the end of his investigations he had a new way of thinking about space and time, culminating in a marvelous equation that quantified how gravity responds to matter and energy in the universe.

Not being one to rest on his laurels, this man worked out a number of consequences of his new theory. One was that changes in gravity didn’t spread instantly throughout the universe; they traveled at the speed of light, in the form of gravitational waves. In later years he would change his mind about this prediction, only to later change it back. Eventually more and more scientists became convinced that this prediction was valid, and worth testing. They launched a spectacularly ambitious program to build a technological marvel of an observatory that would be sensitive to the faint traces left by a passing gravitational wave. Eventually, a century after the prediction was made — a press conference was called.

Chances are that everyone reading this blog post has heard that LIGO, the Laser Interferometric Gravitational-Wave Observatory, officially announced the first direct detection of gravitational waves. Two black holes, caught in a close orbit, gradually lost energy and spiraled toward each other as they emitted gravitational waves, which zipped through space at the speed of light before eventually being detected by our observatories here on Earth. Plenty of other places will give you details on this specific discovery, or tutorials on the nature of gravitational waves, including in user-friendly comic/video form.

What I want to do here is to make sure, in case there was any danger, that nobody loses sight of the extraordinary magnitude of what has been accomplished here. We’ve become a bit blasé about such things: physics makes a prediction, it comes true, yay. But we shouldn’t take it for granted; successes like this reveal something profound about the core nature of reality.

Some guy scribbles down some symbols in an esoteric mixture of Latin, Greek, and mathematical notation. Scribbles originating in his tiny, squishy human brain. (Here are what some of those those scribbles look like, in my own incredibly sloppy handwriting.) Other people (notably Rainer Weiss, Ronald Drever, and Kip Thorne), on the basis of taking those scribbles extremely seriously, launch a plan to spend hundreds of millions of dollars over the course of decades. They concoct an audacious scheme to shoot laser beams at mirrors to look for modulated displacements of less than a millionth of a billionth of a centimeter — smaller than the diameter of an atomic nucleus. Meanwhile other people looked at the sky and tried to figure out what kind of signals they might be able to see, for example from the death spiral of black holes a billion light-years away. You know, black holes: universal regions of death where, again according to elaborate theoretical calculations, the curvature of spacetime has become so pronounced that anything entering can never possibly escape. And still other people built the lasers and the mirrors and the kilometers-long evacuated tubes and the interferometers and the electronics and the hydraulic actuators and so much more, all because they believed in those equations. And then they ran LIGO (and other related observatories) for several years, then took it apart and upgraded to Advanced LIGO, finally reaching a sensitivity where you would expect to see real gravitational waves if all that fancy theorizing was on the right track.  Continue reading

Guest Post: Grant Remmen on Entropic Gravity

Grant Remmen“Understanding quantum gravity” is on every physicist’s short list of Big Issues we would all like to know more about. If there’s been any lesson from last half-century of serious work on this problem, it’s that the answer is likely to be something more subtle than just “take classical general relativity and quantize it.” Quantum gravity doesn’t seem to be an ordinary quantum field theory.

In that context, it makes sense to take many different approaches and see what shakes out. Alongside old stand-bys such as string theory and loop quantum gravity, there are less head-on approaches that try to understand how quantum gravity can really be so weird, without proposing a specific and complete model of what it might be.

Grant Remmen, a graduate student here at Caltech, has been working with me recently on one such approach, dubbed entropic gravity. We just submitted a paper entitled “What Is the Entropy in Entropic Gravity?” Grant was kind enough to write up this guest blog post to explain what we’re talking about.

Meanwhile, if you’re near Pasadena, Grant and his brother Cole have written a musical, Boldly Go!, which will be performed at Caltech in a few weeks. You won’t want to miss it!


One of the most exciting developments in theoretical physics in the past few years is the growing understanding of the connections between gravity, thermodynamics, and quantum entanglement. Famously, a complete quantum mechanical theory of gravitation is difficult to construct. However, one of the aspects that we are now coming to understand about quantum gravity is that in the final theory, gravitation and even spacetime itself will be closely related to, and maybe even emergent from, the mysterious quantum mechanical property known as entanglement.

This all started several decades ago, when Hawking and others realized that black holes behave with many of the same aspects as garden-variety thermodynamic systems, including temperature, entropy, etc. Most importantly, the black hole’s entropy is equal to its area [divided by (4 times Newton’s constant)]. Attempts to understand the origin of black hole entropy, along with key developments in string theory, led to the formulation of the holographic principle – see, for example, the celebrated AdS/CFT correspondence – in which quantum gravitational physics in some spacetime is found to be completely described by some special non-gravitational physics on the boundary of the spacetime. In a nutshell, one gets a gravitational universe as a “hologram” of a non-gravitational universe.

If gravity can emerge from, or be equivalent to, a set of physical laws without gravity, then something special about that non-gravitational physics has to make it happen. Physicists have now found that that special something is quantum entanglement: the special correlations among quantum mechanical particles that defies classical description. As a result, physicists are very interested in how to get the dynamics describing how spacetime is shaped and moves – Einstein’s equation of general relativity – from various properties of entanglement. In particular, it’s been suggested that the equations of gravity can be shown to come from some notion of entropy. As our universe is quantum mechanical, we should think about the entanglement entropy, a measure of the degree of correlation of quantum subsystems, which for thermal states matches the familiar thermodynamic notion of entropy.

The general idea is as follows: Inspired by black hole thermodynamics, suppose that there’s some more general notion, in which you choose some region of spacetime, compute its area, and find that when its area changes this is associated with a change in entropy. (I’ve been vague here as to what is meant by a “change” in the area and what system we’re computing the area of – this will be clarified soon!) Next, you somehow relate the entropy to an energy (e.g., using thermodynamic relations). Finally, you write the change in area in terms of a change in the spacetime curvature, using differential geometry. Putting all the pieces together, you get a relation between an energy and the curvature of spacetime, which if everything goes well, gives you nothing more or less than Einstein’s equation! This program can be broadly described as entropic gravity and the idea has appeared in numerous forms. With the plethora of entropic gravity theories out there, we realized that there was a need to investigate what categories they fall into and whether their assumptions are justified – this is what we’ve done in our recent work.

In particular, there are two types of theories in which gravity is related to (entanglement) entropy, which we’ve called holographic gravity and thermodynamic gravity in our paper. The difference between the two is in what system you’re considering, how you define the area, and what you mean by a change in that area.

In holographic gravity, you consider a region and define the area as that of its boundary, then consider various alternate configurations and histories of the matter in that region to see how the area would be different. Recent work in AdS/CFT, in which Einstein’s equation at linear order is equivalent to something called the “entanglement first law”, falls into the holographic gravity category. This idea has been extended to apply outside of AdS/CFT by Jacobson (2015). Crucially, Jacobson’s idea is to apply holographic mathematical technology to arbitrary quantum field theories in the bulk of spacetime (rather than specializing to conformal field theories – special physical models – on the boundary as in AdS/CFT) and thereby derive Einstein’s equation. However, in this work, Jacobson needed to make various assumptions about the entanglement structure of quantum field theories. In our paper, we showed how to justify many of those assumptions, applying recent results derived in quantum field theory (for experts, the form of the modular Hamiltonian and vacuum-subtracted entanglement entropy on null surfaces for general quantum field theories). Thus, we are able to show that the holographic gravity approach actually seems to work!

On the other hand, thermodynamic gravity is of a different character. Though it appears in various forms in the literature, we focus on the famous work of Jacobson (1995). In thermodynamic gravity, you don’t consider changing the entire spacetime configuration. Instead, you imagine a bundle of light rays – a lightsheet – in a particular dynamical spacetime background. As the light rays travel along – as you move down the lightsheet – the rays can be focused by curvature of the spacetime. Now, if the bundle of light rays started with a particular cross-sectional area, you’ll find a different area later on. In thermodynamic gravity, this is the change in area that goes into the derivation of Einstein’s equation. Next, one assumes that this change in area is equivalent to an entropy – in the usual black hole way with a factor of 1/(4 times Newton’s constant) – and that this entropy can be interpreted thermodynamically in terms of an energy flow through the lightsheet. The entropy vanishes from the derivation and the Einstein equation almost immediately appears as a thermodynamic equation of state. What we realized, however, is that what the entropy is actually the entropy of was ambiguous in thermodynamic gravity. Surprisingly, we found that there doesn’t seem to be a consistent definition of the entropy in thermodynamic gravity – applying quantum field theory results for the energy and entanglement entropy, we found that thermodynamic gravity could not simultaneously reproduce the correct constant in the Einstein equation and in the entropy/area relation for black holes.

So when all is said and done, we’ve found that holographic gravity, but not thermodynamic gravity, is on the right track. To answer our own question in the title of the paper, we found – in admittedly somewhat technical language – that the vacuum-subtracted von Neumann entropy evaluated on the null boundary of small causal diamonds gives a consistent formulation of holographic gravity. The future looks exciting for finding the connections between gravity and entanglement!

The Big Picture: Table of Contents

Greetings, surface-dwellers! I have finally emerged from the secret underground laboratory where I have been polishing the manuscript for The Big Picture: On the Origins of Life, Meaning, and the Universe Itself. We pushed up the publication date to May 10, so you’ll get it in plenty of time for your summer beach reading. Evidence that it exists, all 145,000 glorious words:

TBP-pages

As will happen in the writing process, the organization of the book has changed since I first mentioned it. Here is the final table of contents. As you might gather, I went with an organization of many short chapters. Hopefully that will help give the book the feeling of a light and enjoyable read.

THE BIG PICTURE: ON THE ORIGINS OF LIFE, MEANING, AND THE UNIVERSE ITSELF

    0. Prologue

* Part One: Cosmos

  • 1. The Fundamental Nature of Reality
  • 2. Poetic Naturalism
  • 3. The World Moves By Itself
  • 4. What Determines What Will Happen Next?
  • 5. Reasons Why
  • 6. Our Universe
  • 7. Time’s Arrow
  • 8. Memories and Causes

* Part Two: Understanding

  • 9. Learning About the World
  • 10. Updating Our Knowledge
  • 11. Is It Okay to Doubt Everything?
  • 12. Reality Emerges
  • 13. What Exists, and What Is Illusion?
  • 14. Planets of Belief
  • 15. Accepting Uncertainty
  • 16. What Can We Know About the Universe Without Looking at It?
  • 17. Who Am I?
  • 18. Abducting God

* Part Three: Essence

  • 19. How Much We Know
  • 20. The Quantum Realm
  • 21. Interpreting Quantum Mechanics
  • 22. The Core Theory
  • 23. The Stuff of Which We Are Made
  • 24. The Effective Theory of the Everyday World
  • 25. Why Does the Universe Exist?
  • 26. Body and Soul
  • 27. Death Is the End

* Part Four: Complexity

  • 28. The Universe in a Cup of Coffee
  • 29. Light and Life
  • 30. Funneling Energy
  • 31. Spontaneous Organization
  • 32. The Origin and Purpose of Life
  • 33. Evolution’s Bootstraps
  • 34. Searching Through the Landscape
  • 35. Emergent Purpose
  • 36. Are We the Point?

* Part Five: Thinking

  • 37. Crawling Into Consciousness
  • 38. The Babbling Brain
  • 39. What Thinks?
  • 40. The Hard Problem
  • 41. Zombies and Stories
  • 42. Are Photons Conscious?
  • 43. What Acts on What?
  • 44. Freedom to Choose

* Part Six: Caring

  • 45. Three Billion Heartbeats
  • 46. What Is and What Ought to Be
  • 47. Rules and Consequences
  • 48. Constructing Goodness
  • 49. Listening to the World
  • 50. Existential Therapy
  • Appendix: The Equation Underlying You and Me
  • Acknowledgments
  • Further Reading
  • References
  • Index

A lot of ground gets covered. In Part One we set the stage, seeing how discoveries in science have revealed a universe that runs under unbreakable, impersonal laws of nature. In Part Two we think about how to conceptualize such a universe: how to learn about it (Bayesian inference, abduction) and how to talk about it (emergence and overlapping theoretical vocabularies). In Part Three we get down and dirty with quantum mechanics, the Core Theory, and effective field theories. In Part Four we start down the road of connecting to our macroscopic world, seeing how complexity and life can arise due to the arrow of time. In Part Five we think about the leading challenge to a physicalist worldview: the existence of consciousness. And in Part Six we recognize that the universe isn’t going to tell us how to behave, and acknowledge that the creation of meaning and purpose is ultimately our job.

Now back to being a scientist with me. I have drafts of four different papers on my computer that need to be kicked out and onto the arxiv!