Could the Universe End by Tearing Apart Every Atom? (Script) (Patreon)

Of all the unlikely ends of the universe, the Big Rip has to be the most spectacular. Galaxies ripped to shreds, dogs and cat first living together, then tragically separated by the infinitely accelerating expansion of space on subatom scales. Good thing it's not going to happen. Or is it?

The universe is expanding, and that expansion is accelerating. We don’t know what’s causing that acceleration, but that hasn’t stopped us from giving it a name. We call this unknown influence dark energy. The observed acceleration is, for the most part, nicely described with a constant density of dark energy – the same amount of this stuff in every block of space. Which means if you increase the volume you increase the overall amount of dark energy – hence accelerating expansion. Mathematically we describe a constant energy density with the cosmological constant in the equations of Einstein’s general theory of relativity. But what if dark energy is NOT constant? What if the energy density in each patch of space increases over time? In that case, the acceleration itself could be … accelerating.  That would be bad.

As long as the rate of acceleration doesn’t increase, the accelerating expansion of the universe isn’t a big deal. At least for those of us safe and sound in nice galaxies like the Milky Way. Here, the Galaxy’s gravitational field is plenty strong enough to resist in miniscule effect of dark energy. It’s in the vast tracts of space between the galaxy clusters – over countless trillions of  cubic light years of emptiness -  that dark energy adds up. The sum of its outward push ultimately overcomes the inward gravitational pull between the galaxies. Galaxies will eventually be so far apart that they can’t see each other, let along feel each other’s gravity. But as long as dark energy doesn’t increase, there’ll be no expansion inside those lonely galaxies. They’ll be safe to fade to heat-death, as we cheerily discuss in this episode.

And, in fact, that’s probably what will happen. But it’s fun to think about even-worst-case-scenarios. Also, there’s a tiny bit of very circumstantial evidence that we might not be so safe from dark energy after all. But before we get to the potential disaster of an increasing dark energy, and the Big Rip that follows, let’s do a quick refresher on how dark energy works in the language of Einstein’s general relativity. I say refresher because we spend a whole playlist delving into the mysteries of dark energy. We actually used math – the Friedmann equations. We’re not going to go so deep here, but be we are going to take a quick mathy detour. Feel free to review that playlist before or after if you’re into that sort of thing. Or, you know, take a nap and wake up when the pretty pictures come back.

This beautiful thing is the second Friedmann equation. It’s basically the equivalent to Newton’s law of gravity for the whole universe, describing the acceleration or deceleration of the expansion rate, which depends on how much stuff there is in the universe.  Because this is Einstein’s gravity, not Newton’s, gravity is influenced by mass and energy density, and also by pressure. Both mass-energy density and any positive pressure act to DEceleration the universe – to cause it to recollapse. In fact, for regular matter the effect of density is much higher than the effect of pressure. The ratio pressure over density is basically zero. By the way, in cosmology we call this ratio – pressure over density – the equation of state. 

It’s a simplification of the good ol’ equation PV=nkT, relating pressure, volume, temperature, and the amount of stuff. Anyway, the upshot is that positive density and no real pressure leaves the right side of the equation negative – so negative acceleration. Matter on its own can only  cause DEceleration. What goes up must come down.

OK, let’s add dark energy in the form of a cosmological constant. It usually hangs out outside the brackets because it’s emo, but we can make it join the party. We can express our lambda as a sort of equivalent mass and pressure. 

In fact let’s just make it an emo party and get rid of regular mass and pressure. After all, in the future dark energy will completely dominate the expansion. So we have the energy density of the vacuum and the pressure that it exerts. But now the pressure term is important. The equation of state of dark energy is pressure-divided-by-density=-1.  That just means that as volume increases density does not go down – the basic definition of the cosmological constant. So now this pressure term is a) negative, and b) because of this factor of 3 it’s a bigger influence than the density. So this whole party in the brackets becomes negative – SO emo. That cancels this negative sign and makes the right side of the equation positive – the acceleration is positive, which means dark energy is pushing outwards to increase the expansion. 

In fact any equation of state parameter less than -1/3 would cause that effect. It would mean that stuff diluted away a little less quickly than the universe expands. In fact if the parameter is below -⅓ but larger than -1, that’s still accelerating expansion but in that case dark energy is decreasing over time. The popular idea for that scenario is called quintessence, and it’s something for a future episode.

For today, let’s push things to the limit. What if we make the equation of state parameter smaller than -1? How about -1.5, -3, -a million? That’s the case where the density doesn’t just stay constant as the universe expands, it increases. The result would be that the acceleration increases over time. Off hand that doesn’t sound so much crazier than regular old dark energy, except it is. Much crazier.

As the rate of expansion increases, and with no gravitational bodies left to resist the expansion, all points in space will be eventually racing apart from each other at faster than the speed of light. That faster-than-light recession of space is already happening - but for patches of space VERY far away. Like, … billion light years. If two patches are moving away from each other faster than light then can never ever communicate with each other. The distance from us to that inaccessible region of space is called the cosmic event horizon. Now if the expansion is accelerating then over time the distance between patches of light-speed space gets smaller. And that’s also happening: your cosmic event horizon gets closer and closer. Eventually we won’t even be able to see the nearest galaxies because they’ll be moving away too quickly.

But as long as we have a nice, gravitationally bound galaxy to live in the cosmic event horizon can never shrink to a size smaller than that galaxy. That’s not the case if dark energy increases. After our galaxy is disrupted by the increasing dark energy there’s no protection from the encroaching cosmic event horizon. The final result is that no particles will be close enough to interact with each other ever, so even protons and neutrons will be separated into their component quarks. That is the big rip scenario. It happens when the cosmic event horizon is smaller than the smallest possible structure.

What could cause something like this? No idea. No one does. That doesn’t stop us giving it a name – we call any dark energy that increases in strength – so any with an equation of state less than -1 - phantom energy. The name seems to have been coined by Dartmouth physicist Robert Caldwell in a seminal 2002 paper “The Phantom Menace”. It was three years after the theatrical release and we still thought it was a sign of the end of the universe. Actually, Caldwell explains the choice – a phantom is something that is apparent to the senses but has no corporeal reality. In this case, phantom energy is apparent to our mathematical senses – we can “see” that we can put any number we like as the equation of state parameter. But that doesn’t mean it has anything to do with reality.

So let’s see what this made up math has to say about when the Big Rip would happen. Any equation of state parameter smaller than -1 means a Big Rip. The smaller the parameter the sooner that happens. Caldwell does this calculation in the case of w=-1.5. In this scenario the Big Rip happens in 22 billion years. Things don’t get messy until near the end. Around a billion years before the Big Rip galaxy clusters are ripped apart. At 60 million years the Milky Way is shredded. Now this doesn’t mean that the cosmic event horizon is quite inside the Milky Way yet – just that the effect of phantom energy is stronger than the gravity binding it together.

In fact at this point the cosmic event horizon is at about 200 million light years, and so there should be a handful of galaxies still visible to us. There are some millions of years of fun as we watch the those galaxies disassemble and the constellations of stars in the Milky Way also fly apart. The final deadly stage only happens in the last month or so, when the solar system is pulled apart. In the last 30 minutes phantom energy is strong enough to overcome the Earth’s own gravitational binding and the planet is disrupted. Moments later, at 10^-19th of a second before absolute disruption it will overcome all chemical bonds, then the force binding atoms together, then nucleons, and then presumably anything smaller. In its final state, a Big Rip universe will be nothing but hopelessly isolated elementary particles separated by infinitely expanding space. 

That’s a hell of a story. How sure can we be that it won’t happen? Somewhat. Mostly. Our efforts to understand the nature of dark energy are focused on measuring the value of this equation of state parameter thing. We can do that by combining all the clues to dark energy’s behavior – for example the patterns in the cosmic microwave background, baryon acoustic oscillations, supernovae. We’ve talked about all of these things before. Combined with a few other measures, these tell us that the equation of state of dark energy is very, very close to -1. The Planck science team calculate -1.028 +/- 0.032. Phantom energy is still a faint possibility, but at its most extreme from the Planck estimate has the Big Rip at around 75 billion years away. Time to get our affairs in order.

But more likely is that w is exactly -1, meaning dark energy is constant. For three reasons: first, it seems too much of a coincidence that it should be so close to -1 without being -1. Second, there’s a plausible physical explanation for a constant dark energy: that the vacuum has a set amount of energy per volume. There are at least some physical ideas for that. As far as I know there aren’t serious ideas for an increasing dark energy. And the final reason to hate on phantom energy: it violates energy conservation way far worse than regular dark energy. It violates the same energy conditions of general relativity that prohibit negative mass and time travel.

OK, so after all that hate, let’s finally get to the one significant result that suggests that dark energy may be increasing after all. In fact we already covered it in a journal club episode: the acceleration rate measured using distant quasars hints at an equation of state parameter slightly less than -1, although not yet with enough significance to overturn all the other results. Probably – PROBABLY – the universe will still end in a long, cold heat death in which the stars of our galaxy wink out, become black holes, and then evaporate over an unthinkably long future. But maybe, if you believe in phantoms, it’ll all be over much sooner when the universe is ripped to shreds by the infinitely accelerating subatomic space time.