“I have long held an opinion… that the various forms under which the forces of matter are made manifest have one common origin; or, in other words, are so directly related and mutually dependent, that they are convertible, as it were, one into another, and possess equivalents of power in their action.” -

Michael Faraday

For centuries, the idea that you can’t get something for nothing was floating around *long* before we knew about the most important conservation law in all of the Universe: the Conservation of Energy.

For example, the ball rolling down this hill, picking up speed and gaining *kinetic energy* isn’t getting that energy *from nothing*! It’s actually turning a different form of energy — gravitational potential energy — *into* that kinetic energy. And, at *any* point along its journey, the total amount of energy — its **kinetic + potential energies** — is the same.

As long as you consider a *closed* system, or a system that cannot *gain/lose* energy from/to someplace outside itself, the law of conservation of energy is perfect.

The Earth, for example, is not a closed system *on its own*. It receives light and energy from all across the Universe, most notably from the Sun, and also radiates energy off into space. The Sun, too, is not closed, as it constantly radiates energy away into space, but its energy isn’t coming from *nowhere*; it’s being created by converting some of its rest mass energy into light and heat (and neutrinos) via nuclear fusion and E = mc^{2}. When all the input sources and output sources of energy are included, for *any* system in the Universe, the conservation law holds.

While there are some spooky quantum effects that may seem to violate our intuitions concerning this law, from the smallest subatomic scales to the largest cosmic ones, **once all the sources and sinks of energy are accounted for**, it still appears to hold.

How, then, do we answer the following question, posed by another astrophysicist:

What is the source of the energy for the accelerating universe?

This is an *amazingly* deep question, so let’s begin by talking about what it means to live in an accelerating Universe.

You can imagine the Early Universe — at least the portion of it observable to us — as a hot, dense, rapidly expanding sphere of matter and energy. But you also know that if your Universe is full of matter and energy, the force of gravity is going to do everything it can to try and pull this expanding Universe back together again. So — in the simplest terms you can imagine — that’s what you’ve got: an initially, rapidly expanding Universe, where gravity tries to slow, reverse, and recollapse it.

Looking at the image above, the leftmost diagram represents an expanding Universe where gravity eventually wins: the initial expansion is not enough for the amount of matter-and-energy present, and the Universe eventually reverses its expansion, recollapsing in a Big Crunch. The second image is one with a large initial expansion, but the amount of matter and energy is just *one subatomic particle short* of being able to recollapse the Universe! In this critical case, the Universe’s expansion rate continues to slow, asymptoting towards zero, but never reverses. And the third case — a *low density* Universe — continues to expand forever, as the gravitational attraction between all the Universe’s matter and radiation finds itself unable to counteract the initial expansion.

And then there’s the fourth case — the *actual* case — of an accelerating Universe. This is a Universe filled with dark energy, or a finite, positive amount of vacuum energy **intrinsic to space itself**. And in this case, the expansion of the Universe doesn’t just “fail to slow down enough” to give us recollapse, but rather distant galaxies moving away from us **move away from us faster and faster** as time goes on! This means that, if we take a finite sphere of matter and energy to start with, and let it expand over time, the radius of that sphere will increase like so:

Unlike the recollapsing (orange) case, our Universe will never recollapse. Unlike even the critical (green) or low-density (blue) curves, the “size” of our Universe is increasing *at an exponential rate* as shown by the red curve. What our best measurements tell us is that the energy density of space itself (i.e., the **dark energy density**) is neither increasing nor decreasing, but remaining the same.

But this might bother you: if the energy *density* is staying the same, but *space is expanding*, doesn’t that violate the conservation of energy? In other words, aren’t we making *more and more* energy in our Universe over time, and didn’t we learn that energy **needs to be conserved**?

*Technically*, we can weasel our way out of this by noting that the big picture I gave you, above, isn’t *entirely* how it works. Our large-scale Universe is ruled by General Relativity as our theory of gravity. And strictly speaking, energy is not *defined* in General Relativity, so why worry about conserving it? But there is a very smart way of looking at “energy” that allows us to show, in fact, that energy *is* conserved even in this seemingly paradoxical situation.

I want you to remember that, in addition to chemical, electrical, thermal, kinetic, and potential energies, among others, there’s also work.

Work, in physics, is when you apply a **force** to an object **in the same direction as the distance it moves**. What this means is that if you apply a force *upwards* to this upwards moving weight, you do *positive* work. (I.e., you *add* energy to the system.) But if you apply a force *upwards* to a *downwards* moving object, you do *negative* work. (I.e., you *remove* energy from the system.)

This is perhaps clearer if you think about putting your hand underneath a book, and raising and then lowering it.

When you push in the *same* direction the book is moving, you do *positive* work, adding energy to the system, and when you push in *the opposite* direction, you do *negative* work.

So now, let’s think of the Universe. You’ve got this sphere-like object expanding, and there you are, this **constant energy density** (i.e., dark energy) filling the sphere. You’re *positive* energy. You’re gravitationally *pulling* this sphere in on itself. But what’s the sphere doing?

It’s **expanding**. In other words, you’re pulling in the *opposite direction* as the expansion, and so you’re doing **negative work**! (**Update**: So why, then, does the expansion *speed up*? Sure, dark energy’s **positive energy density** means that it’s gravitationally attractive to any matter in the Universe, but the magnitude of its **negative pressure** is what determines the overall rate of expansion!) And so if you’re asking where the energy for this “dark energy” comes from, it comes from the negative work done on the expansion of the Universe!

A little more technically, as Carroll, Press, and Turner stated in 1992,

…the patch does negative work on its surroundings, because it has negative pressure. Assuming the patch expands adiabatically, one may equate this negative work to the increase of mass/energy of the patch. One thereby recovers the correct equation of state for dark energy: P = – ρ c

^{2}. So the mathematics is consistent.

Or a little less technically,

“Suck it, monkeys!” -

Liz Lemon

And that’s why energy *can be* conserved, even in a Universe with dark energy!