Forget acceleration, the jerk of the universe could change everything
Jerk and snap may lead us into a Big Rip or a Crunch.
Jerk is not commonly known as a physics term but all nonlinear systems have it. The rate of change of acceleration, jerk is the third derivative of position.
Most intro physics courses don’t go into jerk much because it instantly complicates relatively simple second order equations, but, when it comes to how the universe changes, jerk could be a much bigger factor than acceleration.
We all know that the universe is expanding. That is a first order change in scale. Everything is moving apart. Edwin Hubble discovered this fact back in 1929 and Einstein very nearly predicted it. Yet no Nobel prize was ever given for the discovery.
Fast forward to the 21st century and we have found that the universe is not only expanding but its expansion is not constant but accelerating. That is the second order effect of changing rate of expansion.
A Nobel prize was given for that discovery.
Now we know the universe is accelerating, and we think it must be some kind of Dark Energy. We know this energy takes the form of vacuum energy in that it has negative pressure. But we don’t know what it is or where it comes from.
Future observations of the universe will give us more confidence in how the rate of acceleration is changing: the cosmic jerk. We may even be able to determine constraints on the fourth order of the scale, the cosmic snap.
All of these rates of change provide not only amusing names but constraints on and potential violations of Einstein’s theory of gravity.
Up until now the primary theory of cosmology, the Lambda Cold Dark Matter theory, has assumed a constant density of dark energy. The Lambda is the cosmological constant. This makes sense because as the universe expands there is more vacuum, hence more dark energy, but the density remains the same.
Meanwhile, the density of ordinary matter decreases as it moves apart, meaning in the distant future almost all the energy in the universe will be dark.
This is consistent with a vacuum energy theory, but just because dark energy has characteristics of vacuum energy does not mean that’s what it is.
In fact numerous papers propose alternatives to vacuum energy that nevertheless exhibit equivalent characteristics. These theories tend to fall in a few groups: those that propose dark energy is a property of matter (e.g., it is the gravity of entropy or information) and those that propose it is a form of as yet unknown matter (e.g., a scalar field that permeates space). A third suggests that dark energy is an illusion.
Any of these theories might suggest a different equation of state than the leading theory. And that could have very big consequences for the ultimate fate of the universe.
An equation of state shows how quantities vary with respect to one another for a gas or fluid. You might have been taught PV=nRT for ideal gases. This equation of state shows how pressure, volume, and temperature all relate. These are called state variables because they relate to the overall macroscopic state of the gas. Another version of this same equation of state is p =ρRT which simply divides both sides by V for some small volume so that n/V becomes the density ρ. You can then divide both sides by the density to get a ratio RT =p/ρ. The quantity RT is the square of the average velocity of the molecules.
All the matter in the universe from stars to galaxies to superclusters behave, at the scale of billions of lightyears, like a fluid or gas. So the same equations that apply to molecules in a container also apply to galaxies in the universe.
Dark energy is one component of this fluid and so participates in the overall equation of state. A more accurate measurement of the equation of state for dark energy would tell us how the quantities we measure such as density and pressure that relate to dark energy as a whole relate to one another and to time and point to the best model for what dark energy is. Right now that relationship is very simple: the pressure is just the negative of the density in each spatial direction and this never changes. That means our RT which is given the symbol w is just -1. If the equation of state were to change, that would be a big deal.
Right now we have measured w to be -1.028+/-0.032, so it is right around -1.
The jerk of the universe is related to the rate of change in the equation of state.
So what is the jerk the universe?
The jerk of the universe is predicted to be one.
All factors related to the expansion of the universe from the Hubble constant, which relates to the rate of expansion to the acceleration to jerk and snap can be, in principle, measured from cosmic redshift. They arise from the terms of the dynamics of the redshift with time and so, with more and more precise measurements, can be teased out.
It turns out that none of this need depend on the Einstein equations. Redshift is simply an observation and the Hubble constant, acceleration, jerk, and snap are part of the dynamics of that redshift. That these depend only on time and are the same everywhere in the universe are assumptions, but have nothing to do with relativity. Yet, relativity predicts that they will have certain values.
If you do assume the Einstein equations, then these measurements tell you something about the nature of the universe. For example, a jerk of one tells us that the universe is spatially flat.
If the jerk is less than 1 or changes with time that could imply any number of things from needing a new theory of gravity to exotic matter.
If it is exotic matter, it could have the power to create a “Big Rip” singularity and destroy the universe.
The best measurements for jerk right now are that it is positive. And there are no bounds on snap. Whoever measures these precisely could determine that Einstein was wrong or that some new kind of matter is out there that isn’t vacuum energy. Or they could, ho hum, confirm everything we now believe to be true and that jerk is one.
On the other hand, there might be another Nobel waiting for the one who discovers that the fate of the universe is not what we think it is. And that may depend on measuring the jerk and finding it is not one.
Visser, Matt. “Jerk, snap and the cosmological equation of state.” Classical and Quantum Gravity 21.11 (2004): 2603.
Dunajski, Maciej, and Gary Gibbons. “Cosmic jerk, snap and beyond.” Classical and Quantum Gravity 25.23 (2008): 235012.