Dark energy may be the information of the vacuum
The Holographic Principle with a Quantum Information Twist.
Since 1998, when the accelerating expansion of the universe was announced, Dark Energy has been one of the foremost mysteries of the cosmos along with dark matter.
Dark Energy is a strange substance, not matter, but a type of energy that resembles tension in space itself. It is as if the fabric of reality is being pulled taut and that has real gravitational consequences for the universe. One of them is causing the expansion that we have known about for nearly a century to accelerate.
The best model of Dark Energy right now is the Lambda-Cold Dark Matter model which assumes that Dark Energy is just a constant in Einstein’s equations. That constant, called the cosmological constant, is a major conundrum for physicists and dozens of explanations with hundreds of published papers have attempted to solve it either in the vein of Lambda-CDM, as a constant, or with a more dynamical approach.
The Lambda-CDM model suffers from two major problems: (a) why is the density of Dark Energy so small, the so-called fine tuning problem, and (b) why is its density on the order of the density of matter, the so-called, coincidence problem. Both of these issues, of course, deal with density as an order of magnitude. Dark Energy takes up about 70% of the matter/energy density in the universe, but why not 99.999999%? 70% is an odd number from a physics standpoint.
One of the most intriguing suggestions is that Dark Energy is the effect that information has on gravity. In other words, it is not a substance but bits, ones and zeros, that creates Dark Energy and that, in turn, has gravitational effect.
You wouldn’t think that the data stored on your computer, not the medium in which it is stored but the data itself, has weight, but in a quantum universe information is not weightless, not exactly at least. It has energy.
That energy, however, does not interact with light; therefore, it is dark.
The information approach to DE arises from one of the most intriguing ideas ever proposed in physics: the holographic principle. This principle states that all the information in a volume of space can be explained by what is going on on its boundary. When you combine the holographic principle with some physics constants like the universal gravitational constant and the quantum Planck’s constant as well as something called the IR cut-off, given by the inverse of the Hubble parameter governing the expansion rate of the universe, you get a constant that is very close to the cosmological constant we observe.
You can think of the holographic principle in general as the idea that there is no such thing as an infinite expanse of space. Rather, all regions of space (in our universe at least) are bounded by an event horizon. This horizon is not a black hole event horizon; rather, it is a boundary of causality. For a black hole, the event horizon is absolute, dividing all points inside from all points outside. In other cases, causal boundaries depend on where you place your observer. Here on Earth we can see about 46 billion light years away. That is our current causal boundary. There might be more universe further away than that, but we can’t see it and it can’t see us.
The holographic principle says that for any event horizon (causally connected region) all the information inside it can be described by information about or on its boundary. Thus, anything here on Earth can be explained by the information on the 6.65 sextillion square lightyear causal boundary.
Another principle is that no event horizon should contain more matter, energy, or information than a black hole with an event horizon of the same size. Black holes and their horizons are, in a sense, a measuring rod for information content.
There are some issues with using the Hubble parameter in this back of the envelope computation of the cosmological constant. For one, it predicts that dark energy should behave like matter, not like tension in space that causes accelerating expansion.
Others have gotten around this by throwing out the Hubble constant and replacing it with something else, but without a lot of justification.
If you accept the holographic principle which seems reasonable, then it becomes necessary to find the right estimate of the constant.
A very intriguing solution to this problem, however, comes from estimating the constant as arising from the energy of the entanglement entropy of the universe.
Entanglement entropy, of course, are correlations between quantum particles that exist across time and space that violate ordinary “classical” laws of probability.
Two entangled particles, A and B, have a correlation that violates the rule of locality. In other words, the measurement of one somehow transmits information about that measurement to the other one. A common example are two photons that are produced from pion decay.
Photons have spin, which means the particles have angular momentum that is intrinsic to them. Pions do not have spin. Therefore, by conservation of angular momentum, when a pion decays into photons, those two photons have to have opposite spin that cancels out. If I measure the spin of one photon, A, at one location and the spin of the other photon, B, at another, they will be exactly opposite.
The real weirdness here is that in quantum mechanics I can only measure one of the two components of the spin of a photon not the other. If I measure the y axis spin of A in some coordinate system and the x axis spin of B, they will be uncorrelated, but I will automatically know the x-axis spin of A and the y-axis spin of B because I know them to be exactly opposite. If, however, I measure them at some angle, part x and part y, they will be correlated according to the cosine of the angle between my two measurements. That is impossible unless locality is violated somehow and the results of one measurement are transmitted to the other instantaneously.
This classic result called Bell’s theorem shows that quantum entanglement is not just ordinary correlation but an almost physical connection between the particles.
(Other explanations exist of course that don’t require instantaneous transmission but the point is that they are entangled in a way that classical physics cannot explain.)
In the universe, any particles that have interacted at any time will be entangled to some extent and entanglement, of course, carries some measure of entropy, which is a measure not of any matter or energy but of a quantity related to information. It is related to the degree to which those particles are correlated in the quantum realm.
The entanglement dark energy theory proposes that the entanglement of the vacuum with itself carries energy and that this energy creates the cosmological constant through the holographic principle.
Thus, from a point of view, information in the vacuum, the mere entanglement of it is causing the accelerating expansion of the universe.
Since we are using the holographic principle, we still need to have some kind of a boundary. The boundary selected in this theory is called the future event horizon. This is the boundary of all points in the universe that are causally reachable from a person at the present moment for infinite time into the future. Or all points in the universe that a person at a fixed position will ever observe.
You might think that this boundary should be infinite. After all, in an infinite amount of time light should be able to travel an infinite distance. This is not so, however, in an expanding universe. As light travels away from us, the universe continues to expand. Certain points far enough away in the universe will be expanding just a bit too fast for that light ever to reach. Therefore, the future event horizon is actually finite. There is a finite amount of the universe that we can ever see from a fixed vantage point.
The entanglement entropy is given by a quantity called the Von Neumann entropy which is analogous to ordinary entropy but for quantum theory. When an event horizon such as the future horizon is present, the entanglement entropy is split into two (since entanglement occurs because of interaction in the past) entanglement within the horizon and entanglement outside the horizon.
This means that the Von Neumann entropy of the vacuum within the future horizon is related to the size of that horizon.
From the Von Neumann entropy of this huge causally connected region derives the entanglement energy of the vacuum, related to the entropy by the Gibbons-Hawking temperature of the future event horizon. (The Gibbons-Hawking temperature is a temperature related to any causally connected region and is inversely proportional to its radius. Smaller radius, higher temperature.)
From these and quantum information theory, we get a density for DE that fits with those given by all holographic principle theories of DE and incorporates the amount of entanglement information within the future event horizon.
So what we have done is basically computed the quantum entropy of the future event horizon, defined Dark Energy in terms of it and the Gibbons-Hawking temperature for that region, and discovered the density of DE in terms of quantum information of the vacuum. Neat.
But what does that get us?
Well, the computed value corresponds well to measured values of the Dark Energy density based on WMAP’s survey of the Cosmic Microwave Background, studies of Baryon Acoustic Oscillations, and Type Ia supernovae (the three main ways to study dark energy). So far so good.
Besides fitting well with observation, holographic principle theories of dark energy solve the fine-tuning problem and provide some indication of how to solve the coincidence problem as well.
The fine-tuning problem is also called the old cosmological constant problem. It is the idea that vacuum energy should be the source of the cosmological constant. We know from quantum theory that the vacuum has energy and all energy gravitates; therefore, it seems logical. The problem is that a naive way of computing the vacuum energy makes it 120 orders of magnitude too large.
This estimate of the density of dark energy is not compatible with the holographic principle. A key argument is to note that if you accept the estimate of vacuum energy density from quantum field theory, the density within an event horizon of a black hole is less than a region of empty space the same volume. The holographic principle suggests that a black hole should have more since it represents a minimal boundary for maximal information density. That suggests that there must be some cutoff (called a UV-cutoff) to the vacuum energy at the scale of a black hole that eliminates the naive estimate.
This leaves us to assume that the vacuum energy density within a causally contained region must be on the order of the mass of a black hole with the same size event horizon. I.e., if a black hole event horizon contained our universe, the total vacuum energy should be no more than the mass of that black hole. This turns out to be in the right neighborhood of the measured density of dark energy.
There have been many papers using the holographic principle to explain the coincidence problem as well. This is not so straightforward as the fine tuning problem. Some look at understanding how DE interacts with Dark Matter over time. Others are interested in how the inflationary epoch, when the universe underwent massive inflation, diluted DE density. Both ideas have made progress in understanding that problem without relying on things like the Anthropic principle or other such non-scientific explanations. The basic idea is that the density of matter, Dark Matter, and Dark Energy are related and undergoing an evolution that show DE dominating the future universe, a likely case if DE is vacuum dependent while matter continues to thin out.
Without a verified theory of quantum gravity, it is hard to say if this idea is true or not as it relies, in part, on ideas about quantum gravity that are piecemeal at best. Nevertheless, the idea that dark energy may come from vacuum information is compelling.
Lee, Jae-Weon, Jungjai Lee, and Hyeong-Chan Kim. “Dark energy from vacuum entanglement.” Journal of Cosmology and Astroparticle Physics 2007.08 (2007): 005.
Wang, Shuang, Yi Wang, and Miao Li. “Holographic dark energy.” Physics reports 696 (2017): 1–57.