Can dark energy and dark matter emerge together with gravity?

A macaroni pie? Elephants blowing ballons? 
No, it’s Verlinde’s entangled universe.

In a recent paper, the Dutch physicist Erik Verlinde explains how dark energy and dark matter arise in emergent gravity as deviations from general relativity.

It’s taken me some while to get through the paper. Vaguely titled “Emergent Gravity and the Dark Universe,” it’s a 51-pages catalog of ideas patched together from general relativity, quantum information, quantum gravity, condensed matter physics, and astrophysics. It is clearly still research in progress and not anywhere close to completion.

The new paper substantially expands on Verlinde’s earlier idea that the gravitational force is some type of entropic force. If that was so, it would mean gravity is not due to the curvature of space-time – as Einstein taught us – but instead caused by the interaction of the fundamental elements which make up space-time. Gravity, hence, would be emergent.

I find it an appealing idea because it allows one to derive consequences without having to specify exactly what the fundamental constituents of space-time are. Like you can work out the behavior of gases under pressure without having a model for atoms, you can work out the emergence of gravity without having a model for whatever builds up space-time. The details would become relevant only at very high energies.

As I noted in a comment on the first paper, Verlinde’s original idea was merely a reinterpretation of gravity in thermodynamic quantities. What one really wants from emergent gravity, however, is not merely to get back general relativity. One wants to know which deviations from general relativity come with it, deviations that are specific predictions of the model and which can be tested.

Importantly, in emergent gravity such deviations from general relativity could make themselves noticeable at long distances. The reason is that the criterion for what it means for two points to be close by each other emerges with space-time itself. Hence, in emergent gravity there isn’t a priori any reason why new physics must be at very short distances.

In the new paper, Verlinde argues that his variant of emergent gravity gives rise to deviations from general relativity on long distances, and these deviations correspond to dark energy and dark matter. He doesn’t explain dark energy itself. Instead, he starts with a universe that by assumption contains dark energy like we observe, ie one that has a positive cosmological constant. Such a universe is described approximately by what theoretical physicists call a de-Sitter space.

Verlinde then argues that when one interprets this cosmological constant as the effect of long-distance entanglement between the conjectured fundamental elements, then one gets a modification of the gravitational law which mimics dark matter.

The reason is works is that to get normal gravity one assigns an entropy to a volume of space which scales with the surface of the area that encloses the volume. This is known as the “holographic scaling” of entropy, and is at the core of Verlinde’s first paper (and earlier work by Jacobson and Padmanabhan and others). To get deviations from normal gravity, one has to do something else. For this, Verlinde argues that de Sitter space is permeated by long-distance entanglement which gives rise to an entropy which scales, not with the surface area of a volume, but with the volume itself. It consequently leads to a different force-law. And this force-law, so he argues, has an effect very similar to dark matter.

Not only does this modified force-law from the volume-scaling of the entropy mimic dark matter, it more specifically reproduces some of the achievements of modified gravity.

In his paper, Verlinde derives the observed relation between the luminosity of spiral galaxies and the angular velocity of their outermost stars, known as the Tully-Fisher relation. The Tully-Fisher relation can also be found in certain modifications of gravity, such as Moffat Gravity (MOG), but more generally every modification that approximates Milgrom’s modified Newtonian Dynamics (MOND). Verlinde, however, does more than that. He also derives the parameter which quantifies the acceleration at which the modification of general relativity becomes important, and gets a value that fits well with observations.

It was known before that this parameter is related to the cosmological constant. There have been various attempts to exploit this relation, most recently by Lee Smolin. In Verlinde’s approach the relation between the acceleration scale and the cosmological constant comes out naturally, because dark matter has the same origin of dark energy. Verlinde further offers expressions for the apparent density of dark matter in galaxies and clusters, something that, with some more work, can probably be checked observationally.

I find this is an intriguing link which suggests that Verlinde is onto something. However, I also find the model sketchy and unsatisfactory in many regards. General Relativity is a rigorously tested theory with many achievements. To do any better than general relativity is hard, and thus for any new theory of gravity the most important thing is to have a controlled limit in which General Relativity is reproduced to good precision. How this might work in Verlinde’s approach isn’t clear to me because he doesn’t even attempt to deal with the general case. He starts right away with cosmology.

Now in cosmology we have a preferred frame which is given by the distribution of matter (or by the restframe of the CMB if you wish). In general relativity this preferred frame does not originate in the structure of space-time itself but is generated by the stuff in it. In emergent gravity models, in contrast, the fundamental structure of space-time tends to have an imprint of the preferred frame. This fundamental frame can lead to violations of the symmetries of general relativity and the effects aren’t necessarily small. Indeed, there are many experiments that have looked for such effects and haven’t found anything. It is hence a challenge for any emergent gravity approach to demonstrate just how to avoid such violations of symmetries.

Another potential problem with the idea is the long-distance entanglement which is sprinkled over the universe. The physics which we know so far works “locally,” meaning stuff can’t interact over long distances without a messenger that travels through space and time from one to the other point. It’s the reason my brain can’t make spontaneous visits to the Andromeda nebula, and most days I think that benefits both of us. But like that or not, the laws of nature we presently have are local, and any theory of emergent gravity has to reproduce that.

I have worked for some years on non-local space-time defects, and based on what I learned from that I don’t think the non-locality of Verlinde’s model is going to be a problem. My non-local defects aren’t the same as Verlinde’s entanglement, but guessing that the observational consequences scale similarly, the amount of entanglement that you need to get something like a cosmological constant is too small to leave any other noticeable effects on particle physics. I am therefore more worried about the recovery of local Lorentz-invariance. I went to great pain in my models to make sure I wouldn’t get these, and I can’t see how Verlinde addresses the issue.

The more general problem I have with Verlinde’s paper is the same I had with his 2010 paper, which is that it’s fuzzy. It remained unclear to me exactly what are the necessary assumptions. I hence don’t know whether it’s really necessary to have this interpretation with the entanglement and the volume-scaling of the entropy and with assigning elasticity to the dark energy component that pushes in on galaxies. Maybe it would be sufficient already to add a non-local modification to the sources of general relativity. Having toyed with that idea for a while, I doubt it. But I think Verlinde’s approach would benefit from a more axiomatic treatment.

In summary, Verlinde’s recent paper offers the most convincing argument I have seen so far that dark matter and dark energy are related. However, it is presently unclear if not this approach would also have unwanted side-effects that are in conflict with observation already.