You know, it's really hard to start the story of our universe at the place it should—the start of the universe—because strictly speaking, the universe doesn't have a beginning. Or maybe it does.
It's complicated.
Here's the problem. We live in an expanding universe. Every second of every day, galaxies are generally getting farther away from each other. Run the clock backward, and you quickly realize that in the past, galaxies were closer together. This is pretty straightforward logic, I suppose.
Run the clock back further, and there aren't galaxies anymore—all the matter is too smooshed together. There's just a bunch of junk filling up the universe. Keep going, and eventually the entire universe, as big as it appears today, shrinks and shrinks to an infinitely small point. That is precisely what general relativity, our mathematical tool for understanding the evolution of the universe over these almost incomprehensible timescales, tells us: that at a finite time in the past (spoiler alert for later chapters: around 13.8 billion years ago), the universe was compressed into a singularity, a point of infinite density.
Of course, that's wrong. Nature doesn't like infinities. But we have to separate what nature actually does from how we model it. Physics is a mathematical description of the world around us. And that mathematics provides a wonderful tool. For one, math compacts vague natural-language sentences into precise, meaning-filled equations. You could go on and on about how a wave of electromagnetic radiation propagates (and in fact I'm probably going to do that later) without getting all the details right, simply because English isn't really equipped to describe it. But a couple of neat equations can do all the work for us, summarizing and describing in one elegant go.1
Math also forces logical consistency, which is handy when a physicist wants to make predictions. “If we assume this is true based on the evidence, then that must happen” is a soothing statement that calms us during bouts of midnight existential dread.
But it does have its shortcomings. We can only provide approximate descriptions of nature, because we are fundamentally limited by uncertainties in measurement. Sometimes those approximations are really really (really) good, so we don't care about the discrepancy anymore. But sometimes the math is so broken, so dysfunctional, that we can't use it to piece together what Mother Nature is whispering to us at all.
And that's the case with singularities. When a singularity appears in a description, it's the mathematics itself telling you that you've gone too far—your fancy equations are no good here. It means you're doing something wrong, and the math wants no part of your shenanigans.
Singularities are actually pretty common, at least in mathematics. If I model the force provided by a simple spring, I can use Hooke's law: The more I compress the spring, the harder it will push back on me. But if I were to compress it all the way, so that the spring was a single point, the force pushing back on me would be infinite. That seems like a dumb thing to say, but that's what Hooke's mathematics tells us.
But duh, you can only compress a spring just so far until some other force takes over—like, say, the electric repulsion of the atoms in the metal, preventing them from squeezing down to infinity. The singularity appears in the math, but nature knows better.
Now take this example and replace Hooke's law with general relativity, and the spring with the entire universe. Welcome to the cosmologist's nightmare.
Einstein's theory of general relativity is fantastically easy to state: we all live embedded in space-time. The presence of mass or energy distorts space-time “underneath” it (in a three-dimensional sense, but there aren't any good English words for it), and that distortion tells other matter how to move. Put two kids on a trampoline: they can affect the motion of each other without touching. Now imagine that in four dimensions, and you have gravity.
It's almost funny how a somewhat benign statement like the one above masks such a horrible snake pit of mathematics. General relativity itself is a set of ten complicated, interwoven equations describing the detailed relationship between space-time and matter and energy, plus some more equations governing how objects move. Heavy stuff.
General relativity is the story of gravity, and at the very largest scales (i.e., bigger than galaxies), gravity is the only force with enough oomph. It's incredibly weak but affects all matter and energy across infinite range, and it's that staying power that provides its dominance at large scales. On balance the universe is neutral, so the electromagnetic force cancels out. The strong nuclear force peters out past an atomic nucleus, and the weak nuclear force is, well, weak. When it comes to cosmology, only gravity matters.
Except when it doesn't, like in the earliest fraction of a fraction of second into the existence of the universe as we know it.
Cosmology is the story of gravity at large scales, and general relativity is just fine and dandy for describing that gravity—giving us the very history of our cosmos. But there are singularities lurking within Einstein's greatest hit. We use general relativity to understand the evolution of our universe, and those mathematics say—and logic tells us—if we live in an expanding universe (and we do!), then at one time in the past, everything was crammed into an infinitely dense point.
Unless something got in the way. Unless something prevented or replaced the inevitable collapse, stopping the universe from becoming infinitely dense—just significantly or even stupendously dense. Anything but infinite and we can handle it. And in fact, something must prevent it. We know that singularities don't actually appear in nature; they are flaws in our model of reality.
So general relativity draws a line in the sand: we could mine the entire universe for information, extract every single bit of useful data from our observations, but we will never, ever understand the earliest moments of the universe unless we try some other tool in our mathematical toolbox. When it comes to the first 10−43 seconds, we simply have no idea what's going.
It's here where speculation reigns. We have a relatively firm grasp of the history of the universe, but not its origins. Or even if origins is the right word. We haven't (yet) developed the mathematical language to describe these initial moments. Or even if initial is the right word.
Maybe there's more “universe” happening before what we call the big bang (as you can see, this term is meant to describe not the birth of our universe but its very early history). Maybe the very concepts of space and time break down. Maybe there's no such thing as “before” the universe. There are a lot of speculative ideas beyond our known physical laws floating around in the minds of physicists and their arcane academic journals. Maybe string theory has an answer here, or was it loop quantum gravity? Who knows?2
The singularity draws the eye of the theoretical physicist because it's an unambiguous signpost that there's more to be learned here. For all other times and scales in the universe, we have at least some guidance on how to proceed. But in this moment, when the universe has a temperature of more than 1032 Kelvin and is no bigger than 10−35 meters across, we don't have much to guide us.
To give you a sense of the extremity of the tininess of this epoch—called the Planck era, by the way—hold out your hands as far as they can reach. Go ahead, you could use the stretch. The scale difference between the width of the observable universe today (about ninety-three billion light-years) and your outstretched hands is about the same as the scale difference between your outstretched hands and the size of the universe at this newborn state—if the universe were about a billion times wider back then.
In other words, imagine how long it would take to stretch out your arms so wide that you could hug the present-day universe. The Planck-era universe would have to do that a billion times over to give you a friendly squeeze.
I'm sorry—there just aren't a lot of useful analogies for these sorts of situations. The temperatures, densities, and length scales in operation at the early stages of our universe aren't something we normally come in contact with, so we don't have handy metaphors or explanatory tools at the ready. Usually in these situations we can instead appeal to the mathematics to guide us, like a distant lighthouse in a storm of nonsense, but even here the light is gone out.
We don't understand the Planck era because we don't understand physics at those scales, but it is at least reassuring to know where our laws break down. And that Planck era, with its characteristic energy and length scales, isn't just pulled out of the Random Number Jar to sound impressive—there's a reason our understanding goes so haywire at numbers so small.
Let's say you have to pick your top five most important physical constants that appear in our descriptions of the universe. Actually, skip that; I'll just tell you what they are. You have the familiar speed of light, which appears in electromagnetism and special relativity, and you need to include Newton's classic gravitational constant. You might not recognize the Coulomb constant, which is like the gravitational constant but for electricity, but it's important too. Plus you need to toss in the Boltzmann constant, which for gases connects things we can easily measure (like temperature) to things we can't (like energy of the gas particles).
Last but certainly not least is the Planck constant itself, warily introduced by Max Planck in the early 1900s.3 Originally shoehorned into his math to help him understand the behavior of light (and one of its uses is to define the relationship between the wavelength of light and the amount of energy it carries), it quickly grew to become the numerical ambassador for quantum mechanics itself. I'll get into that story more later.
All these constants help us relate one thing to another. If I have this much charge, how strong will its electric force be? Coulomb can tell us. If I start waving around some electric and magnetic fields, how fast will they move? Speed of light. How much mass do I need to hold down my coffee? Newton's got your back.
These constants are like little governors for their respective domains of physics. What's really fun is when we start combining physics, and the relationships between these constants tell us when and where multiple areas of physics get together and start partying. To find out, we combine the governing constants in interesting ways, known as the Planck units.
Take the Planck length, which combines Newton's constant, the speed of light, and the original Planck constant (sorry that his name keeps popping up in confusing ways; he was kind of smart and kind of important). That number comes out to about 1.6 × 10−35 meters…hey, wait a minute, that's the size of the universe where our physical theories break down!
Now we can see why: the Planck constant tells us about where we need to care about quantum mechanics, and Newton's constant tells us the same for gravity. The Planck length is a scale where both gravity and quantum mechanics matter. It's not like the universe magically transforms into something weird and wonderful at those scales, but since the Planck length is constructed from other useful numbers, when you're trying to play the gravity-quantum matchmaking game, those same numbers are going to crop up. So think of the Planck length as a warning sign: here be dragons.
And those are quantum gravity dragons. We do not, at the time of the writing of this book and most likely also at the time of your reading, have a quantum description of gravity. Why not? That's a long story, and probably a tale for another book.4 For our purposes, we simply don't have a single mathematical language that incorporates gravity into our quantum worldview. And it's that lack of language that prevents us from fully understanding those first moments in the universe, and especially what might come “before.”
I'm purposely not spending a lot of time discussing what some speculative ideas might be for combining gravity with quantum mechanics and for the origins of the universe. Things like colliding branes and collapsing universal wave functions sound super awesome, but at this point they're one step away from pure fantasy. Not that such hypotheticals shouldn't be explored—far from it. We need creative ideas to move forward. But we're so far out on the ledge that it's hard to tell a good idea from a bad one. I would hate to waste your precious time describing in detail a concept that a year from now will be ruled out by experiment (or, more likely, go out of fashion), especially when there's so much more cool stuff to talk about.
It's the ultimate irony that the work of Kepler would set us down a path of completely reimagining the universe and our place in it. He believed that the motions of heavenly objects contained divine truths that could be expressed in pure mathematics, and now we're starting our cosmological story—the very birth of the universe, if that's even the right turn of phrase—in murky haze that even our most sophisticated mathematics is only beginning to penetrate. Not only does the universe barely care for us, we don't even have the right language to begin caring about the early universe.
Once things get going, so to speak, the veil begins to lift. We're still not at the stage where we can directly observe anything (that won't come for another 380,000 years, an incomprehensibly distant future compared to the timescales of physics in the early cosmos), but we do begin to have hints of the mathematics involved.
Now I get to say one of my favorite phrases, a sentence that captures my own imagination, that summarizes our current state of existence as viewed through the lens of modern physics: we live in a broken universe. That trite statement is motivated by a simple question. Why are there four forces of nature? Electromagnetism, gravity, and the twin nuclear forces describe the complete variety of physical interactions in the world around us. Why not three? Why not seventeen?
Here's another amazing statement: there weren't always four forces of nature. Or rather, there aren't always four forces of nature.
When we crank up the energies in our particle colliders above 246 GeV (short for giga-electron volt, or a billion electron volts5), the four forces of nature disappear.
Gravity and strong nuclear are preserved, but the electromagnetic and weak merge into something else, handily called the electroweak force. The photon, carrier of the electromagnetic force, disappears. As do the W+, W-, and Z bosons, the inscrutable names we give to the carriers of the weak nuclear force. Their identities and everything we associate with them simply melt away. In their place, a quartet of new particles does the work of ferrying the electroweak force from place to place.
To make this splitting happen, Peter Higgs in the 1960s realized that there needs to be a new ingredient in the recipe of the universe: a Higgs field (so named later; he was not so vain as to name it after himself).6 This field simply exists, permeating all of space-time, hanging out, minding its own business. But through *insert complicated mathematics here* it does the work of splitting the electromagnetic force from the weak nuclear. No Higgs, no symmetry breaking, no separation of forces. Hence all the buzz in 2012 when the Large Hadron Collider found evidence for the Higgs field.
The Higgs field is that one guy on the floor who finds a couple waltzing together perfectly, like they belong together for the rest of their lives, and asks for a dance.
That merging of the fundamental forces is an expression of a deep and fundamental symmetry in our universe. A single mathematical expression describes both the electromagnetic and weak nuclear interactions in one fell swoop—but only at high energies. At low energies (and our everyday experiences qualify as “low energies” in this context), that symmetry breaks, revealing two separate forces.
A pencil balanced on its tip is very symmetrical, but also unstable. It can only exist under a very narrow set of circumstances. As soon as it falls, it's much more stable, but asymmetric. Meditate on that the next time you flick the light switch.
It gets better, and where it gets better is relevant to the early universe. At even higher energies, somewhere north of 1016 GeV, the strong nuclear force joins the unification party, leaving only two forces at play in the fresh universe: gravity and what's called the electronuclear force, a Grand Unification of three forces in the universe. Obviously that unification is a bit harder to study because (a) the math gets hard, quick, and (b) that energy scale is a trillion times higher than what we can achieve with the world's most super of supercolliders.
Apparently that unification happened only once, for a brief moment, when the universe was less than 10−36 seconds old and smaller than a single electron. The words “brief” and “small” in the preceding sentence seem hopelessly inadequate, but here we are.
At the end of that Grand Unification epoch (also known as the GUT epoch, for this is the age when a supposed Grand Unified Theory prevails—but don't mistake a GUT for a TOE, a theory of everything that would hold in the Planck era) (no, I'm not making any of this up), the strong nuclear force splits off and we're back in (kind of) familiar territory with gravity, strong nuclear, and electroweak forces bouncing around. But in terms of narrative of the universe, that's still practically a lifetime away.
I don't want you to get the impression that we actually know what happens in this era. It's not as smoke-and-mirrors as times in the Planck scale, but it's very, very hazy stuff indeed. We do not yet have a single Grand Unified Theory that presents three of the four forces of nature in a coherent fashion. We have hints, we have clues, we have some scrappy-looking backwoods trails, but that's it.
At our best guess, as the universe expanded and cooled, at some point the energies lowered enough for the strong force to split away, delivering a solid GUT punch to the universe.
You'll see why that's more than just an amazing pun in a little bit.
If you've ever made ice cubes, you've witnessed one of nature's minor miracles: a phase transition. There's nothing different about the water molecules themselves in liquid versus solid, yet at different temperatures those molecules exhibit wildly different properties. The phase transition marks the boundary between ice and not-ice, between free-flowing liquid and rigid crystal structures. It's abrupt, too, which is what makes phase transitions so fascinating. It's not like the water slowly and gradually transforms into ice, taking its sweet time. As soon as a critical threshold is reached, bam, now you're looking at a block of ice.
Go ahead and reach into your freezer for an ice cube. You may notice internal cracks and fissures. Hmmm. Usually we associate cracks with trauma; something made that defect. But how could something cause such a crack deep within the ice, where before there was only pure water?
The reason is that ice does take a little bit of time to form, after all, and it doesn't form as soon as the temperature hits its special point. You can hold (not with your hands!) liquid water below its freezing point for as long as you want. It takes a nucleation point, a trigger, to start the ice-forming party. Once a couple of molecules decide to line up in nice, neat regimented order, they convince their nearby relatives to join in, followed by their surrounding close friends, then coworkers, then acquaintances, then fellow standers in line, and so on, until the entire liquid is transformed.
But what if more than one spot gets the same idea at the same time? There's nothing stopping a bowl of water from having multiple nucleation points. And each nucleation point will choose a particular random orientation for its ice arrangement. The water will crystallize moving outward from each independent point, with each realm having a different configuration.
You'll still get ice, but it will be multiple arrangements of ice smashed together. One region, seeded by a particular nucleation point, might be of the up-down variety, while a neighboring region, seeded by an independent-minded point, might be of the more left-right persuasion.
And where those domains meet, you get a defect. A flaw in the ice that marks the boundary between two hostile neighbors. There's nothing you can do about that flaw, either; it's literally frozen into place.
Now, enough about cold water—let's talk about the hot universe. As the early universe expanded and cooled, it underwent dramatic phase transitions. One transition occurred when gravity (hypothetically) split off from the (speculative) unified force. We know hardly anything about that process and how it might affect the later universe, so I'm just going to skip it.
The next phase transition occurred when the strong force splintered from the (still pretty hypothetical) electronuclear force. And just as in a phase transition with liquid water cooling into ice, defects appeared.
These defects are strange beasts indeed and come in a suitable menagerie of horrors: The magnetic monopole. The cosmic string. The domain wall. Monsters of crippled space-time and exotic forces; relics of the ancient universe.
By far the most common is the monopole. You may have noticed in your daily life a strange dichotomy between electric and magnetic forces: an electric charge can be either positive or negative, and the two can happily live quite separately, but magnets always come in pairs. Slice a north-south bar magnet in half, and you get two little baby north-south magnets in its place. This is due to the way that magnetic fields are produced in our normal everyday experience: not as isolated charges, but through the motions of charges.7
But the early universe is not within our normal everyday experience. It's thought, based on our current understanding of Grand Unified Theories, that when the strong force broke off, that phase transition led to defects, and one of those defects acted like a massive single pole of magnetism. A lonely north or a solitary south. A freak of nature.
Our simplest theories of what went down around the 10−36-second mark in the age of the cosmos predict an absolute flooding of space with these creatures. Creatures that should be easy to spot even billions of years later. I mean, come on—they'd be pretty dang obvious, right? And yet we don't see a single one. No evidence of even one monopole floating around our vast cosmos.
So where did they go?
Our best answer, as first cooked up by physicist Alan Guth in the early 1980s, was that they were just—are you ready for this?—inflated away.8 Blasted off to the four corners of the cosmos. Spread so far apart that they simply don't matter. I know, I know—hang in there with me.
Just as the end of the GUT era generated its own problems, it also provided the seeds of their resolution. Guth's hypothesis went like this: suppose, for instance, that for a fleeting moment the universe got really, really big, really, really fast.
Voilà: inflation.
This proposed solution to the monopole problem is brutal in its efficiency. Yes, many monopoles were produced, but the entire universe is simply much, much larger than our local observable patch. It's so much larger, in fact, that despite the monopolar infestation in the early cosmos, our universe is now so darn big that you only expect to find one monopole—tops—in the volume that we can actually see. No monopole, no problem.
This reasoning sounds kind of fishy, and it kind of is. But inflation theory has stuck around for the past few decades because (a) it's not as crazy as it sounds, and (b) it also solves a bunch of other problems in cosmology. Oh, and (c) we have evidence for it, but that comes later in our story. I promise.
The explanation for inflation lies in the very heart of the GUT transition itself. Just as later on the electroweak force will split apart with the handy help of the Higgs field, there ought to be another field around to do the work of prying the nuclear force away from the warm embrace of everybody else. While we certainly don't know the nature of that field, it could have certain beneficial properties. Like, say, being staggeringly repulsive.
That repulsiveness is physical, driving the expansion of the universe to rates never seen before and never to be seen again, taking a mere 10−32 seconds to inflate from the size of an electron to the size of a golf ball. That may not sound impressive, but when was the last time you saw something—anything—grow by a factor of a billion billion billion billion in a billionth of a billionth of a billionth of a billionth of a second?
That's what I thought.
Inflation is attractive because it solves (more like sweeps under the cosmic rug) the monopole problem, but that's not enough. After all, the monopole “problem” may not exist at all! It's an artifact of high-energy physics, a regime that we don't know too much about and honestly can't speak to with any level-headed confidence. So at first blush, inflation is using one speculation to cancel out another. The sum: we still have no idea what's going on.
That's a legitimate gripe, so I'll let it stand. But in defense of inflation, let me offer exhibit B: the horizon problem. And if you actually flipped to the back of the book to read the previous citation, you already knew this was coming. Look in any one direction of the universe. I mean way look, as deep as you can see. Measure the properties of the stuff you find there. Say, the average temperature of that patch of space, or the average distance between galaxies. Just, whatever.
Now pick a completely different direction and go as deep as you can there. Repeat the above exercise. You'll find, much to your delight and amusement, that the universe is very boring. At large enough scales, our cosmos is pretty much the same from place to place.
That by itself is not that big of a deal until you do a little math: the universe is about 13.8 billion years old and has a diameter of around 90 billion light-years. Yes, that means the universe expands faster than light (90 being a larger number than 13.8, after all), but no, that's not a problem, and yes, I'll talk about that later.
Right now we have a deeper problem. The only way for one patch of the universe to know what everybody else is up to is by interacting via some force—gravity and electromagnetism at these scales, specifically. And those forces take time to propagate, because, you know, the speed of light. So is it a totally random coincidence that at the largest scales, one patch of universe just so happens to look like any other patch? When did they exchange memos to start coordinating? When was the note passed around the cosmic classroom so everybody knew that in 13.8 billion years, we all need to look the same?
The answer: before inflation. When the universe was just a tiny little nugget, there was plenty of time for everyone to compare notes, settle into equilibrium, and agree on what their future course ought to look like. Then swoosh, inflation kicked in, sending bits of the universe zooming apart, never to talk again.
Direct communication is no longer possible from one distant corner of the universe to another—they're just too far apart, and only getting farther. But they still look and act relatively the same. The only way to resolve this paradox is inflation.
There's another problem that inflation handily solves—the flatness problem—but describing “flatness” belongs to another chapter, so we'll leave it at that.
But wait—there's more!
Inflation has one more trick up its quantum sleeve, One more reason to think that hey, maybe this isn't such a harebrained, cockeyed concept after all. And that concerns you and me. That's right: you. And me.
Imagine a ball rolling down a gentle slope to the bottom of a valley. It starts with a lot of potential energy, and as it rolls, it converts that potential energy into kinetic energy, speeding up in the process. Maybe there's a little friction as the ball rubs up against the grass. That's fine. Once the ball reaches the bottom of the valley, however, its story isn't over. It will wiggle around, sloshing playfully back and forth in the grass before finally settling down.
The grass underneath that ball will get rubbed, over and over, as the ball continues its wiggling. In the end, the ball transfers all of its energy into the irritated grass underneath it.
I want you to imagine the process of inflation—of the stupendous expansion of the early universe powered by an exotic quantum field—as a cute little ball slowly rolling down a hill in a sunlit meadow. When inflation is done, after that fraction of a second, the field has nearly expended nearly all its energy to swell the volume of the universe and is now settling into a comfortable retirement.
Inflation has done its job—it flung the monopoles as far apart as inhumanly possible—but it did its job a little too well. Not only did it separate any possible monopoles, it also separated everything else. If there was any matter at all in that hot second, it's been cooled and spread way too thin after the sudden expansion.
But like I said, inflation isn't done. Before the field responsible for driving the process completely settles down, it wiggles. Just a bit is all it takes. Strictly speaking, it oscillates perturbatively within its potential, but for us the word “wiggle” will suffice. And that wiggle breathes life into the newly cold universe.
According to our best understanding (which, I should admit, isn't all that best), the field driving inflation decays, transforming itself into a flood of particles, the fundamental particles that make up our everyday existence. That last-minute wiggling does all the work—in a final selfless gift to the universe, the inflaton (the vaguely cool-sounding name we give to the inflation field) does settle down into the background, never again to play a significant role in the rest of the history of the universe.
But its children inherit the universe that inflation shaped: one that is large, free of defects, empty, and ready for settling. Ready for a flood of particles, forces, and fields: the same characters that still inhabit the cosmos and are responsible for star formation, nuclear physics, magnetic fields, dodgeball, and life.
I know this chapter must be almost as frustrating to read as it was to write, what with all the what-ifs and maybes and perhapses, but that's the way it is. The universe is a fantastically complicated place, and as you can tell, that goes more so in its heady early days. But don't worry; we'll return again to the topic of inflation and reveal its true power—and some evidence.
So much happens in that first slice of an instant, and so much of that is inaccessible to us, both in observations and in theory. We don't have the gear or the mathematics to fully study this epoch of our universe. We're doing our best, though, so cut us some slack. Besides, at this point in the story, our entire universe is still only a few centimeters across and has a temperature of ten trillion billion degrees. And things are only going to get more interesting from here.