Does the Universe expand by stretching or creating space?

It’s been almost 100 years since humanity first reached a revolutionary conclusion about the nature of our Universe: space itself cannot and does not remain static, but rather evolves with the passage of time. One of the most unsettling predictions of Einstein’s general relativity is that any Universe?—?so long as it’s uniformly (or almost uniformly) filled with one or more species of matter, radiation, or energy?—?cannot remain the same over time. Instead, it must either expand or contract, something initially derived independently by three separate people: Alexander Friedmann (1922), Georges Lemaitre (1927), and Howard Robertson (1929), and was later generalized by Arthur Walker (1936).

Right at around the same time, starting in 1923, observations began to show that the spirals and ellipticals in our sky were actually galaxies: “island universes” that were well outside of our own Milky Way. With new, more powerful measurements, we could determine that the farther away a galaxy was from us, the greater the arriving light in our instruments was redshifted, or observed at longer wavelengths, compared to the light that was initially emitted. It was as though the very act of journeying through space altered the wavelength of that traveling light.

But what, exactly, happens to the fabric of space itself while this process occurs? Is the space itself stretching, as though it’s getting thinner and stretched out? 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 conceive of in modern astrophysics. If we think hard about it, however, we’re capable of wrapping 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, while any light passing through a region that contains this distorted spacetime will be bent, distorted, and possibly magnified by the effects of curved space.

The starting point of our conversation has to be general relativity: our modern theory of gravity first put forth by Einstein. 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 spacetime itself will evolve.

If we inhabited a completely empty Universe, or a Universe that contains nothing within it at all — no matter, radiation, or energy of any form — you’d get the flat, Newtonian-like space you’re intuitively used to: something that’s static, uncurved, and unchanging.

But what if we then considered the absolute simplest case of a non-empty Universe? If, instead, we were to put down a point mass in the Universe, we’d find out that space was curved in a particular way: Schwarzschild space. Any “test particle” that we’d put down onto our Universe would be compelled to flow toward that mass, following a particular trajectory.

And if we were to then make our physical situation just a little bit more complicated, by putting down a point mass that also rotates, we’d 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. Unlike in the non-rotating case, the event horizon splits into two, while the central singularity gets stretched out into a one-dimensional ring. Nobody knows what occurs at the central singularity, or even whether the singularity is physically real, or merely a mathematical artifact.

These spacetimes are clearly much more complicated than a spacetime that’s simply flat. However, they are still “static” in the sense that any distance scales you might include or measure — like the size of the event horizon or the distance between two arbitrary points within this spacetime — don’t change over time. If we could somehow “exit” a Universe with this spacetime and return to it later, whether a second, an hour, or a billion years later, the structure of this spacetime would be identical, irrespective of when we returned to it. In spacetimes like these, there’s no cosmic expansion that’s present. There’s no change in the distance or the light-travel-time between any points within this spacetime. With just one (or fewer) sources of matter inside, and no other forms of energy, these “model Universes” really can be static.

But it’s a very different game when you choose not to put down isolated sources of mass or energy, but instead to fill your Universe, uniformly, with “stuff” everywhere. In fact, the two criteria we normally assume about our Universe, and which are 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.

As far as we can tell, our Universe, on large cosmic scales, is indeed both isotropic and homogeneous.

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.

In this case, having a Universe that’s uniformly filled with some sort of energy (or multiple different types of energy), the rules of general relativity not only mandate that the Universe must evolve, they tell us how. The equations that govern the evolution of the Universe are known as the Friedmann equations: derived by Alexander Friedmann all the way back in 1922, a year before we even discovered that the largest, most prominent spiral in the sky — the great nebula in Andromeda — was actually a galaxy outside of and beyond the Milky Way. (In short order, we extended that knowledge to practically all the spiral and elliptical nebulae known.)

The spacetime fabric of the Universe, if it’s uniformly filled with one or more types of matter and/or energy, must expand or contract according to these equations. The mathematics tells us, with no ambiguity, that this must occur.

But what, exactly, does “expansion” or “contraction” actually mean when it comes to space itself?

You see, space itself is not something that’s directly measurable. It’s not like we can go out and take some space and just perform an experiment on it. Instead, all 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 must be doing to cause those effects.

When a star approaches and then reaches the periapsis of its orbit around a supermassive black hole, its gravitational redshift and its speed both increase. In addition, the purely relativistic effects of orbital precession should affect the motion of this star around the galactic center. Close orbits around large masses deviate from Newton’s predictions; general relativity is required to match observations.

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 that black hole’s vicinity. If the black hole is spinning, we can calculate how significantly space is “dragged” along with the black hole due to the presence of the black hole’s 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 actually perform experiments to determine whether space curves in the way Einstein’s theory tells us it ought to in a wide variety of ways. As soon as the first conflict arises — as soon as a single observation is inconsistent with Einstein’s predictions — we will have a compelling case for extending the theory of gravity beyond Einstein’s general relativity.

But that day, a full 109 years after general relativity was first put forth, has not yet arrived. To an incredible level of precision, every observation matches and agrees with general relativity’s predictions. 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. It’s also been measured right here on Earth, as light redshifts when it travels upward in Earth’s gravitational field, and blueshifts when it travels downward, closer to Earth’s center.

Similarly, other predictions such as:

• 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,

have all spectacularly agreed with Einstein’s predictions.

Physicist Glen Rebka, at the lower end of the Jefferson Towers, Harvard University, calling Professor Pound on the phone during setup of the famed Pound-Rebka experiment. A photon emitted from the bottom of the tower would not be absorbed by the same material at the top without further modifications: evidence of gravitational redshift. When a speaker “kicked” the emitting photon with additional energy, the atoms at the top of the tower could suddenly absorb those emitted photons, strengthening the case for our understanding of gravitational redshift as predicted by general relativity.

But what about the Universe’s expansion? When we think about the expanding Universe scientifically, the question we should be asking ourselves is: “What, observably, is changing about the things we’re capable of measuring in the Universe?” After all, that’s what we can physically predict, that’s what’s physically observable, and that’s what will inform us as to what’s actually physically occurring. Anything else is us placing a veneer — a mask reflecting the limits of our own intuition — atop what we actually understand about reality.

The simplest evolving quantity we can consider in an expanding Universe is density. If our Universe is filled with “stuff,” then as the Universe expands, the volume of the space that this ”stuff” occupies will increase.

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, if 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 consistent with what we find for matter.

Matter (both normal and dark) and radiation become less dense as the Universe expands, where radiation also gets stretched to longer wavelengths as the Universe expands. If the number of particles remains fixed while volume increases, the density goes down. For dark energy, however, it’s a form of energy inherent to space itself. As new space gets created in the expanding Universe, the dark energy density still remains constant.

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 entities, 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 toward the redder end of the spectrum: longer wavelengths. This redshifting effect is how the expanding Universe was first detected, and shows up in every galaxy and quasar we measure beyond our own Local Group.

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 redshifting light from distant objects evolves as a function of distance. 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 ? dark energy today, and that the energy density of dark energy doesn’t change: as the Universe expands, the energy density remains constant.

A plot of the apparent expansion rate (y-axis) vs. distance (x-axis) is consistent with a Universe that expanded faster in the past, but where distant galaxies are accelerating in their recession today. This is a modern version of, extending thousands of times farther than, Hubble’s original work. Note the fact that the points do not form a straight line, indicating the expansion rate’s change over time. The fact that the Universe follows the curve it does is indicative of the presence, and late-time dominance, of dark energy.

When we put the full picture together from all the different sources of data that we have, a single, mostly 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 backward, 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 different energy components in the Universe at various times in the past.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. Note that in the future, when dark energy reaches a number near 100%, the energy density of the Universe (and, therefore, the expansion rate) will remain constant arbitrarily far ahead in time.

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.)

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On the other hand, when something stretches in a conventional fashion, it thins out, just as when something compresses, it thickens up. This is a reasonable line of thought for describing the behavior of light and other forms of 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. From the perspective of dark energy, it’s as though new space is getting created due to the Universe’s expansion.

Neither explanation works well universally: it’s that one explanation succeeds at explaining what happens to radiation (and other energetic particles) while the other 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) as the Universe either expands or contracts.

This diagram shows, to scale, how spacetime evolves/expands in equal time increments if your Universe is dominated by matter, radiation, or the energy inherent to space itself (i.e., during inflation or dark energy dominance). The bottom-most scenario corresponds to exponential expansion via both dark energy (today) and inflation (at early times). Note that visualizing the expansion as either ‘the existing space stretching’ or ‘the creation of new space’ won’t suffice in all instances.

Space, contrary to what you might think, isn’t some measurable, physical substance that you can treat the same way you’d treat particles or some other form of energy that would appear inside a detector. Instead, space is simply the backdrop?—?a stage, if you will?—?against or upon which the “play” of the Universe unfolds. We can use the measurements of particles and quanta we can detect from all over the Universe to infer the properties of space, 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, including all the quanta we’re capable of detecting.

All of the radiation within our Universe, including every gravitational wave, 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 a philosophical sense.

In our attempts to make sense of the Universe, we must recognize that there is no justification to adding extraneous structures atop what is measurable. Space neither stretches nor gets created, but simply is as Einstein’s theory describes it. At least, within the context of general relativity, we can accurately learn “how” it is, even if the information of precisely “what” it is lies beyond the realm of science at present.

 09.05.2024