4.2 Dark Energy

summary

Repulsive gravity is a feature of Einstein's general theory of relativity.

We tend to think of gravity as being an attractive force, but in certain cases, gravity can be repulsive, for instance with Dark Energy.
Newton described the strength of gravity as depending only upon an object’s mass. In Einstein’s version of gravity, the strength depends on pressure too:$$\rho+3p=E(1+3w)$$where $w$ is pressure over energy density.
For ordinary matter, $w\approx 0$. If $w<-\frac{1}{3}$, gravity is repulsive.
What sources gravity is not just matter or energy, but it also depends on what the stuff is made of. From the Friedmann equations, derived from Einstein’s field equations, the source of gravity in general relativity is given by the term $\rho +3p$, where $\rho$ is the mass (or energy) density and $p$ is the pressure.
In this equation, pressure is allowed to be negative. Negative pressure describes something elastic, like a rubber band.
We get black holes when $p\gtrsim \frac{\rho}{3}$ and very elastic stuff with repulsive gravity when $p<-\frac{\rho}{3}$.
For massive objects like the Sun, their pressure is millions of times smaller than their energy density. Something whose pressure is comparable to its energy density is very unusual. The simplest example of this would be $\Lambda$, the cosmological constant, or vacuum energy ($p=-\rho$).
The accelerated expansion of the universe is caused by the repulsive gravity of Dark Energy.

The gravity of 'nothing' is repulsive.

According to quantum mechanics, “nothing” is filled with particles living on borrowed energy & time—virtual particles of the quantum vacuum.
The existence of virtual particles is observable in many physical phenomena, such as:
- The Lamb shift—virtual particles bumping into an electron orbiting the hydrogen atom alter its orbit slightly. This was one of the first direct experimental signs of virtual particles’ existence, winning Willis Lamb the 1955 Nobel Prize in Physics.
- The Coulomb force—caused by exchange of virtual photons, resulting in the inverse square law for electric force.
- The Casimir effect—attraction between a pair of neutrally-charged metal plates, caused by the quantized electromagnetic field.
- The strong and weak nuclear forces—caused by the exchange of virtual gluons and virtual W and Z bosons, respectively.
The vacuum energy is mathematically equivalent to $\Lambda$, the cosmological constant. In a sense, calculating how much “nothing” weighs could demonstrate that Dark Energy is made up of these virtual particles.
Theorists have attempted to calculate the weight of the virtual particles, and they almost have the right answer—only off by a factor of 10⁵⁵.
The vacuum energy is a good candidate for Dark Energy, but cosmologists aren’t quite satisfied. We still don’t have a good theoretical understanding of what Dark Energy is.

Solving the cosmic acceleration riddle will require a profound new idea.

We now have two puzzles: “Why does nothing weigh so little?” and “What is Dark Energy?” These questions could be related or completely unrelated.
If the world were supersymmetric, we could show that the quantum vacuum energy is zero. But perhaps the world isn’t exactly supersymmetric—the supersymmetric partners don’t weigh the same as their counterparts. At first, this sounds like it could explain the small vacuum energy. However, the mathematics yield a vacuum energy on the order of 10⁵⁵.
In superstring theory, there are many solutions, all with different energies, differing by an enormous amount. This results in many different energy states for the universe—10⁵⁰⁰ vacua. One of them could have the right value for vacuum energy.
Or perhaps there is no Dark Energy, and it’s simply a new aspect of gravity we’ve discovered. An “empty” universe undergoes accelerated expansion—and our universe today is considerably more “empty” than it was many billions of years ago, about 100 orders of magnitude less dense than at the end of inflation.

How do we describe Dark Energy?

A defining feature of Dark Energy is that it has a large negative pressure, smoothly distributed, which leads to repulsive gravity.
Dark Energy is described by the equation-of-state parameter $w$, the pressure/energy density. It tells us how the Dark Energy changes with time.$$\rho_{DE}\sim(1+z)^{3(1+w)}$$
If the pressure is equal to the (negative) energy density, that is, if $w=-1$, Dark Energy doesn’t change at all with time. If $w$ differs from −1 at all, then the Dark Energy can slowly increase or slowly decrease. Measurements indicate that $w=-1.02\pm 0.06$, remarkably close to −1.
We know that Dark Energy is smooth, not particulate, is very relativistic ($\frac{\left|p\right|}{\rho}\sim 1$), has repulsive gravity, is the energy of “nothing,” and is similar to the cosmological constant $\Lambda$.
Two big questions that still remain:
- “Does Dark Energy change with time?” — No, at the 10% level
- “Does cosmic acceleration require going beyond general relativity?” — Not well tested

Until we know what Dark Energy is, we don't know the fate of our universe.

If Dark Energy stays constant, then the universe’s expansion will continue to accelerate, and we are destined for a cosmic “dark-out.”
If Dark Energy is increasing, then the universe will get ripped apart in the “Big Rip.” The acceleration of the universe will rip apart galaxies, stars, and even atoms.
If Dark Energy is decreasing, the universe will eventually recollapse in the “Big Crunch.”
It’s an exciting time in cosmology. We know a lot about our universe. We’ve identified many of its features, and now we’re trying to figure out what it all means.