As The Universe Expands, Does Space Actually Stretch?

Travel the universe with Dr. Ethan Siegel as he answers the biggest questions of all

Or is ‘new space’ created in between the gaps of the ‘old’ space?

It’s been almost 100 years since humanity first reached a revolutionary conclusion about our Universe: space itself doesn’t remain static, but rather evolves with time. One of the most unsettling predictions of Einstein’s General Relativity is that any Universe — so long as it’s evenly filled with one or more type of energy — cannot remain unchanging over time. Instead, it must either expand or contract, something initially derived independently by three separate people: Alexander Friedmann (1922), Georges Lemaitre (1927), Howard Robertson (1929), and then generalized by Arthur Walker (1936).

Concurrently, observations began to show that the spirals and ellipticals in our sky were galaxies. With these new, more powerful measurements, we could determine that the farther away a galaxy was from us, the greater the amounts its light arrived at our eyes redshifted, or at longer wavelengths, compared to when that light was emitted.

But what, exactly, is happening to the fabric of space itself while this process occurs? Is the space itself stretching, as though it’s getting thinner and thinner? Is more space constantly being created, as though it were “filling in the gaps” that the expansion creates? This is one of the toughest things to understand in modern astrophysics, but if we think hard about it, we can wrap our heads around it. Let’s explore what’s going on.

An animated look at how spacetime responds as a mass moves through it helps showcase exactly how, qualitatively, it isn’t merely a sheet of fabric. Instead all of 3D space itself gets curved by the presence and properties of the matter and energy within the Universe. Multiple masses in orbit around one another will cause the emission of gravitational waves. (LUCASVB)

The first thing you have to understand is what General Relativity does, and doesn’t, tell us about the Universe. General Relativity, at its core, is a framework that relates two things that might not obviously be related:

the amount, distribution, and types of energy — including matter, antimatter, dark matter, radiation, neutrinos, and anything else you can imagine — that are present all throughout the Universe,
and the geometry of the underlying spacetime, including whether and how it’s curved and whether and how it will evolve.

If your Universe has nothing in it at all, no matter or energy of any form, you get the flat, unchanging, Newtonian space you’re intuitively used to: static, uncurved, and unchanging.

If instead you put down a point mass in the Universe, you get space that’s curved: Schwarzschild space. Any “test particle” you put into your Universe will be compelled to flow towards that mass along a particular trajectory.

And if you make it a little more complicated, by putting down a point mass that also rotates, you’ll get space that’s curved in a more complex way: according to the rules of the Kerr metric. It will have an event horizon, but instead of a point-like singularity, the singularity will get stretched out into a circular, one-dimensional ring. Again, any “test particle” you put down will follow the trajectory laid out by the underlying curvature of space.

In the vicinity of a black hole, space flows like either a moving walkway or a waterfall, depending on how you want to visualize it. At the event horizon, even if you ran (or swam) at the speed of light, there would be no overcoming the flow of spacetime, which drags you into the singularity at the center. Outside the event horizon, though, other forces (like electromagnetism) can frequently overcome the pull of gravity, causing even infalling matter to escape. (ANDREW HAMILTON / JILA / UNIVERSITY OF COLORADO)

These spacetimes, however, are static in the sense that any distance scales you might include — like the size of the event horizon — don’t change over time. If you stepped out of a Universe with this spacetime and came back later, whether a second, an hour, or a billion years later, its structure would be identical irrespective of time. In spacetimes like these, however, there’s no expansion. There’s no change in the distance or the light-travel-time between any points within this spacetime. With just one (or fewer) sources inside, and no other forms of energy, these “model Universes” really are static.

But it’s a very different game when you don’t put down isolated sources of mass or energy, but rather when your Universe is filled with “stuff” everywhere. In fact, the two criteria we normally assume, and which is strongly validated by large-scale observations, are called isotropy and homogeneity. Isotropy tells us that the Universe is the same in all directions: everywhere we look on cosmic scales, no “direction” looks particularly different or preferred from any other. Homogeneity, on the other hand, tells us that the Universe is the same in all locations: the same density, temperature, and expansion rate exist to better than 99.99% precision on the largest scales.

Our view of a small region of the Universe near the northern galactic cap, where each pixel in the image represents a mapped galaxy. On the largest scales, the Universe is the same in all directions and at all measurable locations, with the major difference being that distant galaxies appear smaller, younger, denser, and less evolved than the ones we find nearby: evidence for cosmic evolution with time, but no changes in isotropy or homogeneity. (SDSS III, DATA RELEASE 8)

In this case, where your Universe is uniformly filled with some sort of energy (or multiple different types of energy), the rules of General Relativity tell us how that Universe will evolve. In fact, the equations that govern it are known as the Friedmann equations: derived by Alexander Friedmann all the way back in 1922, a year before we discovered that those spirals in the sky are actually galaxies outside of and beyond the Milky Way!

Your Universe must expand or contract according to these equations, and that’s what the mathematics tells us must occur.

But what, exactly, does that mean?

You see, space itself is not something that’s directly measurable. It’s not like you can go out and take some space and just perform an experiment on it. Instead, what we can do is observe the effects of space on observable things — like matter, antimatter, and light — and then use that information to figure out what the underlying space itself is doing.

When a star passes close to a supermassive black hole, it enters a region where space is more severely curved, and hence the light emitted from it has a greater potential well to climb out of. The loss of energy results in a gravitational redshift, independent of and superimposed atop any doppler (velocity) redshifts we’d observe. (NICOLE R. FULLER / NSF)

For example, if we go back to the black hole example (although it applies to any mass), we can calculate how severely space is curved in the vicinity of a black hole. If the black hole is spinning, we can can calculate how significantly space is “dragged” along with the black hole due to the effects of angular momentum. If we then measure what happens to objects in the vicinity of those objects, we can compare what we see with the predictions of General Relativity. In other words, we can see if space curves the way Einstein’s theory tells us it ought to.

And oh, does it do so to an incredible level of precision. Light blueshifts when it enters an area of extreme curvature and redshifts when it leaves. This gravitational redshift has been measured for stars orbiting black holes, for light traveling vertically in Earth’s gravitational field, from the light coming from the Sun, and even for light passing through growing galaxy clusters.

Similarly, gravitational time dilation, the bending of light by large masses, and the precession of everything from planetary orbits to rotating spheres sent up to space has demonstrated spectacular agreement with Einstein’s predictions.

A photon source, like a radioactive atom, will have a chance of being absorbed by the same material if the wavelength of the photon doesn’t change from its source to its destination. If you cause the photon to travel up or down in a gravitational field, you have to change the relative speeds of the source and receiver (such as driving it with a speaker cone) in order to compensate. This was the setup of the Pound-Rebka experiment from 1959. (E. SIEGEL / BEYOND THE GALAXY)

But what about the Universe’s expansion? When you think about an expanding Universe, the question you should be asking is: “what, observably, changes about the measurable things in the Universe?” After all, that’s what we can predict, that’s what’s physically observable, and that’s what will inform us as to what’s going on.

Well, the simplest thing we can look at is density. If our Universe is filled with “stuff,” then as the Universe expands, its volume increases.

We normally think about matter as the “stuff” we’re thinking about. Matter is, at its simplest level, a fixed amount of massive “stuff” that lives within space. As the Universe expands, the total amount of stuff remains the same, but the total amount of space for the “stuff” to live within increases. For matter, density is just mass divided by volume, and so if your mass stays the same (or, for things like atoms, the number of particles stays the same) while your volume grows, your density should go down. When we do the General Relativity calculation, that’s exactly what we find for matter.

While matter and radiation become less dense as the Universe expands owing to its increasing volume, dark energy is a form of energy inherent to space itself. As new space gets created in the expanding Universe, the dark energy density remains constant. (E. SIEGEL / BEYOND THE GALAXY)

But even though we have multiple types of matter in the Universe — normal matter, black holes, dark matter, neutrinos, etc. — not everything in the Universe is matter.

For example, we also have radiation: quantized into individual particles, like matter, but massless, and with its energy defined by its wavelength. As the Universe expands, and as light travels through the expanding Universe, not only does the volume increase while the number of particles remains the same, but each quantum of radiation experiences a shift in its wavelength towards the redder end of the spectrum: longer wavelengths.

Meanwhile, our Universe also possesses dark energy, which is a form of energy that isn’t in the form of particles at all, but rather appears to be inherent to the fabric of space itself. While we cannot measure dark energy directly the same way we can measure the wavelength and/or energy of photons, there is a way to infer its value and properties: by looking at precisely how the light from distant objects redshifts. Remember that there’s a relationship between the different forms of energy in the Universe and the expansion rate. When we measure the distance and redshift of various objects throughout cosmic time, they can inform us as to how much dark energy there is, as well as what its properties are. What we find is that the Universe is about ⅔ dark energy today, and that the energy density of dark energy doesn’t change: as the Universe expands, the energy density remains constant.

When we plot out all the different objects we’ve measured at large distances versus their redshifts, we find that the Universe cannot be made of matter-and-radiation only, but must include a form of dark energy: consistent with a cosmological constant, or an energy inherent to the fabric of space itself. (NED WRIGHT’S COSMOLOGY TUTORIAL)

When we put the full picture together from all the different sources of data that we have, a single, consistent picture emerges. Our Universe today is expanding at somewhere around 70 km/s/Mpc, which means that for every megaparsec (about 3.26 million light-years) of distance an object is separated from another object, the expanding Universe contributes a redshift that’s equivalent to a recessional motion of 70 km/s.

That’s what it’s doing today, mind you. But by looking to greater and greater distances and measuring the redshifts there, we can learn how the expansion rate differed in the past, and hence, what the Universe is made of: not just today, but at any point in history. Today, our Universe is made of the following forms of energy:

about 0.008% radiation in the form of photons, or electromagnetic radiation,
about 0.1% neutrinos, which now behave like matter but behaved like radiation early on, when their mass was very small compared to the amount of (kinetic) energy they possessed,
about 4.9% normal matter, which includes atoms, plasmas, black holes, and everything that was once made of protons, neutrons, or electrons,
about 27% dark matter, whose nature is still unknown but which must be massive and clumps, clusters, and gravitates like matter,
and about 68% dark energy, which behaves as though it’s energy inherent to space itself.

If we extrapolate backwards, based on what we infer about today, we can learn what type of energy dominated the expanding Universe at various epochs in cosmic history.

The relative importance of dark matter, dark energy, normal matter, and neutrinos and radiation in the expanding Universe are illustrated here. While dark energy dominates today, it was negligible early on. Dark matter has been largely important for extremely long cosmic times, and we can see its signatures in even the Universe’s earliest signals. Meanwhile, radiation was dominant for the first ~10,000 years of the Universe after the Big Bang. (E. SIEGEL)

Notice, very importantly, that the Universe responds in a fundamentally different way to these differing forms of energy. When we ask, “what is space doing while it’s expanding?” we’re actually asking which description of space makes sense for the phenomenon we’re considering. If you consider a Universe filled with radiation, because the wavelength lengthens as the Universe expands, the “space stretches” analogy works very well. If the Universe were to contract instead, “space compresses” would explain how the wavelength shortens (and energy increases) equally well.

On the other hand, when something stretches, it thins out, just like when something compresses, it thickens up. This is a reasonable thought for radiation, but not for dark energy, or any form of energy intrinsic to the fabric of space itself. When we consider dark energy, the energy density always remains constant. As the Universe expands, its volume is increasing while the energy density doesn’t change, and therefore the total energy increases. It’s as though new space is getting created due to the Universe’s expansion.

Neither explanation works universally well: it’s that one works to explain what happens to radiation (and other energetic particles) and one works to explain what happens to dark energy (and anything else that’s an intrinsic property of space, or a quantum field coupled directly to space).

An illustration of how spacetime expands when it’s dominated by Matter, Radiation or energy inherent to space itself, such as dark energy. All three of these solutions are derivable from the Friedmann equations. Note that visualizing the expansion as either ‘stretching’ or ‘creating new space’ won’t suffice in all instances. (E. SIEGEL)

Space, contrary to what you might think, isn’t some physical substance that you can treat the same way you’d treat particles or some other form of energy. Instead, space is simply the backdrop — a stage, if you will — against or upon which the Universe itself unfolds. We can measure what the properties of space are, and under the rules of General Relativity, if we can know what’s present within that space, we can predict how space will curve and evolve. That curvature and that evolution will then determine the future trajectory of every quantum of energy that exists.

The radiation within our Universe behaves as though space is stretching, although space itself isn’t getting any thinner. The dark energy within our Universe behaves as though new space is getting created, although there’s nothing we can measure to detect this creation. In reality, General Relativity can only tell us how space behaves, evolves, and affects the energy within it; it cannot fundamentally tell us what space actually is. In our attempts to make sense of the Universe, we cannot justify adding extraneous structures atop what is measurable. Space neither stretches nor gets created, but simply is. At least, with General Relativity, we can accurately learn “how” it is, even if we can’t know precisely “what” it is.

Starts With A Bang is written by Ethan Siegel, Ph.D., author of Beyond The Galaxy, and Treknology: The Science of Star Trek from Tricorders to Warp Drive.

Travel the universe with Dr. Ethan Siegel as he answers the biggest questions of all