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Starts With A Bang

Ask Ethan: If The Universe Ends In A Big Crunch, Will All Of Space Recollapse?

Our future fate is likely already determined. If we end in a Big Crunch, what does that mean?

The ultimate fate of the Universe is one of the biggest existential questions we can ask. Given that our Universe has been around for billions of years since the Big Bang, is filled with stars and galaxies strewn across the vast recesses of space, and appears to be expanding and cooling in all directions, there appear to be fascinating possibilities for what might arise in the future. Perhaps we’ll expand forever; perhaps we’ll cease expanding and recollapse; perhaps the expansion will speed up, tearing us apart. One possible fate is the Big Crunch, and that interests our Patreon supporter Jim Nance, who asks:

When you describe the Big Crunch, you talk about a race between gravity and the expansion of space. It’s not clear to me that if gravity wins that race, whether space stops expanding, or simply that the matter in space stops expanding. I’d love to hear your explanation of this.

This is a complex question, but the physics we know today allows us to rise to the challenge and give a definitive answer.

The different possible fates of the Universe, with our actual, accelerating fate shown at the right. As time goes on, unbound galaxies get exponentially farther away from each other. (NASA & ESA)

When we look out at the distant galaxies beyond our own local group, we find that the light from them is redshifted. Normally, the most important property of light is its wavelength: the distance between successive peaks or troughs in the oscillating electromagnetic fields that define a light wave. Wavelength determines light’s frequency, color, energy, and momentum.

Whenever we have an atomic transition — where electrons jump from one energy level to another — it’s accompanied by either the absorption or emission of a photon. Because those energy levels have specific values, that means the photons that are absorbed or emitted will have particular wavelengths associated with them. When you see a series of absorption or emission lines, that allows you to identify which elements are present, and in what abundance.

The visible light spectrum of the Sun, which helps us understand not only its temperature and ionization, but the abundances of the elements present. The long, thick lines are hydrogen and helium, but every other line is from a heavy element that must have been created in a previous-generation star, rather than the hot Big Bang. These elements all have specific signatures corresponding to explicit wavelengths. (NIGEL SHARP, NOAO / NATIONAL SOLAR OBSERVATORY AT KITT PEAK / AURA / NSF)

Measuring the various wavelengths of light is part of the astronomical science of spectroscopy. For any star or galaxy that we look at, we can detect the presence — if our equipment and observations are good enough — of the various spectral lines that correspond to the presence or absence of specific atoms, ions, and molecules.

But when we look at galaxies that are beyond our own, we find that those spectral signatures of absorption and emission lines are systematically shifted. For each individual galaxy we measure, there’s a unique shift that affects all of the lines equally. A very small number of the galaxies we look at appear to be blueshifted: where the light shifts towards higher energies and shorter wavelengths. But almost all of them are redshifted, and are more severely redshifted the farther away they are.

First noted by Vesto Slipher, the more distant a galaxy is, on average, the faster it’s observed to recede away from us. For years, this defied explanation, until Hubble’s observations allowed us to put the pieces together: the Universe was expanding. (VESTO SLIPHER, (1917): PROC. AMER. PHIL. SOC., 56, 403)

The phenomenon of galactic redshifts is an observational fact that dates back more than a century: to the work of Vesto Slipher. In the 1920s, Edwin Hubble’s work allowed us to add in the galactic distances as well, with the redshift-distance relation discovered shortly thereafter by both Hubble and Georges Lemaître. However, the cause of this wasn’t immediately clear, as there were two possible explanations.

  1. Redshifts and blueshifts could be caused by individual galactic motions, as galaxies moving towards us would appear blueshifted and galaxies moving away from us would be redshifted.
  2. Redshifts could be caused by the expansion of the fabric of space itself, with the wavelengths of light from more distant galaxies getting stretched by the fabric of the expanding Universe.
A two-dimensional slice of the overdense (red) and underdense (blue/black) regions of the Universe nearby us. The lines and arrows illustrate the direction of peculiar velocity flows, which are the gravitational pushes and pulls on the galaxies around us. However, all of these motions are embedded in the fabric of expanding space. (COSMOGRAPHY OF THE LOCAL UNIVERSE — COURTOIS, HELENE M. ET AL. ASTRON.J. 146 (2013) 69)

Both of these explanations could, at least in the early stages, be considered consistent with the data.

In reality, both effects exist. Galaxies do move relative to one another, as the gravitational forces from the matter in the Universe push and pull everything around. But the fabric of spacetime itself cannot remain constant, either.

It isn’t simply that galaxies are moving away from us that causes a redshift, but rather that the space between ourselves and each galaxy redshifts the light on its journey from that distant point to our eyes. This affects all forms of radiation, including the leftover glow from the Big Bang. (LARRY MCNISH / RASC CALGARY CENTER)

In General Relativity, spacetime is a dynamic entity. When you have a Universe like ours — where matter and energy are relatively evenly distributed on the largest scales — any relativistic solution that results in a static Universe is fundamentally unstable. The Universe must be expanding or contracting, as it cannot remain in an unchanging state. We cannot necessarily know which one it’s doing from first principles alone; we require measurements to teach us what’s going on.

Thankfully, we’ve made those measurements, and the conclusion is inescapable.

The redshift-distance relationship for distant galaxies. The points that don’t fall exactly on the line owe the slight mismatch to the differences in peculiar velocities, which offer only slight deviations from the overall observed expansion. The original data from Edwin Hubble, first used to show the Universe was expanding, all fit in the small red box at the lower-left. (ROBERT KIRSHNER, PNAS, 101, 1, 8–13 (2004))

Expansion it is. The fabric of our Universe, at present, is expanding. This doesn’t mean it will always expand, though, and it also doesn’t mean that there aren’t galactic motions superimposed atop the expanding fabric of space. You’ll notice, above, that very few of the galaxies we observe actually fall exactly on the best-fit line for a redshift-distance relationship.

That line corresponds to the overall expansion of space, but the actual data points can fall on either side of the line. This is due to the fact that galaxies do move relative to one another in the expanding Universe, including our own Milky Way, which moves at about 370 km/s relative to the Hubble expansion of the Universe.

Special relativity (dotted) and general relativity (solid) predictions for distances in the expanding Universe. Definitively, only the expanding Universe’s predictions for general gelativity match what we observe.(WIKIMEDIA COMMONS USER REDSHIFTIMPROVE)

As we look to greater and greater distances (and redshifts), however, we can absolutely rule out the case where individual motions are responsible for 100% of the observed redshifts. Relativity offers different predictions at large distances for an expanding Universe as compared to a rapid motion away from us, and the data agrees with expansion, not with large-magnitude motions.

So that settles any doubts you may have had about whether the fabric of space itself is expanding: it is. The reason galaxies appear to recede from us — and from one another — is because the Universe is expanding. However, expansion isn’t the only possible solution. If we look at the equations governing the expansion of the Universe, we find something interesting: they don’t give us a value for the expansion rate. Rather, they give us a value for the expansion rate squared.

A photo of me at the American Astronomical Society’s hyperwall in 2017, along with the first Friedmann equation at right. The first term in the Friedmann equation details the Hubble expansion rate squared, which governs the evolution of spacetime. The remaining terms include all the different forms of matter and energy, along with spatial curvature, which determines how the Universe evolves in the future. This has been called the most important equation in all of cosmology, and was derived by Friedmann in essentially its modern form back in 1922. (PERIMETER INSTITUTE / HARLEY THRONSON)

You might not see a big difference initially. If I told you the expansion rate squared was equal to 4, you’d just take the square root and tell me the expansion rate was 2.

And then I’d ask you if you were sure.

“Is he trying to trick me?” Maybe, but the point isn’t to trick you. The square root of 4 could be 2, but it could also be -2. When we solve our equations for the expansion rate, we could wind up with an expanding Universe. But we could also wind up with a negatively expanding Universe, which corresponds to a contracting Universe. Even though we know it’s expanding today, because we measure it, there’s nothing that prevents the Universe from reaching a maximum size, ceasing in its expansion, and turning around to contract.

The expected fates of the Universe (top three illustrations) all correspond to a Universe where the matter and energy fights against the initial expansion rate. In our observed Universe, a cosmic acceleration is caused by some type of dark energy, which is hitherto unexplained. All of these Universes are governed by the Friedmann equations, which relate the expansion of the Universe to the various types of matter and energy present within it. (E. SIEGEL / BEYOND THE GALAXY)

Yes, as we look out at the distant Universe, we presently see that things are continuing to expand. If the Universe will end in a Big Crunch, it hasn’t yet reached its turnaround point.

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It doesn’t look likely that a Big Crunch is in store for us, either. When we measure the way the expansion rate has changed over our cosmic history, it gives every indication that the expansion rate isn’t going to drop to zero and reverse itself. The way the expansion rate changes over time is determined by the total amount and types of matter and energy present within it. Because our Universe has too little matter, too little radiation, and too much dark energy, it looks like we’ll keep on expanding forever.

Unless, of course, dark energy is dynamical, and capable of changing over time.

The far distant fates of the Universe offer a number of possibilities, but if dark energy is truly a constant, as the data indicates, it will continue to follow the red curve. If it’s not, however, a Big Crunch could still be in play. (NASA / GSFC)

If dark energy’s energy density changes over time in any number of particular fashions, it can cause our Universe to end in a Big Crunch. We often take it as a given that our Universe will end in a Big Freeze, owing to the apparent acceleration of distant galaxies away from us, but there are still five viable, possible fates for our Universe. As I’ve written previously, dark energy could weaken and decay as the Universe further expands:

If it decays away to zero, it could lead to one of the original possibilities expressed above: the Big Freeze. The Universe would still expand, but without enough matter and other forms of energy to recollapse.

If it decays away to become negative, however, it could lead to another of the possibilities: a Big Crunch. The Universe could be filled with energy intrinsic to space that suddenly switched signs and caused space to recollapse. While the timescale for these changes is constrained to be far longer than the time since the Big Bang, it could still occur.

When astronomers first realized the Universe was accelerating, the conventional wisdom was that it would expand forever. However, until we better understand the nature of dark energy other scenarios for the fate of the Universe are possible. This diagram outlines these possible fates. (NASA/ESA AND A. RIESS (STSCI))

But the link between all the matter and energy in the Universe, on one hand, and the expansion of the fabric of space itself, on the other, cannot be denied. We live in a Universe that, on the largest scales, is isotropic, homogeneous, and governed by General Relativity. In a very general sense, that means there’s a connection between how the Universe expands and what’s present within it.

If all the matter in the Universe stops expanding away, reverses itself, and begins to recollapse towards us, then that necessitates that the fabric of space is going to recollapse, too. There truly is a cosmic race occurring: between the expansion of the Universe and the force of gravity. Right now, it looks like the expansion’s going to win, but if dark energy is dynamical, that throws the outcome into doubt. If gravity does wind up winning, and the Big Crunch is our ultimate fate, someone, a long time from now, might live to see the entire shebang recollapse into a singular state. We can only imagine what that might lead to.

Send in your Ask Ethan questions to startswithabang at gmail dot com!

Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.