In order to make a nice, clear ice cube for your drinks, it’s important to consider quantum fields. First, boil to release dissolved gasses, then make sure the freezing extends through the cube from a single surface. If the crystallization
process starts from multiple nucleation points then there’ll be imperfections in the lattice
structure where the regions of spreading ice meet - what we call topological defects. So where do quantum fields come into all of this? Well, it turns out the universe is a gigantic ice cube, and the imperfect freezing of its quantum fields right after the Big Bang very likely left vast topological
defects stretching across the sky. These are cosmic strings, and many physicists think that they have to exist, and that we can find them. Reality has cracks in it. Universe-spanning
filaments of ancient Big Bang energy, formed from topological defects in the quantum fields, aka cosmic strings. They have subatomic thickness but prodigious mass and they lash
through space at a close to the speed of light. They could be the most bizarre undiscovered entities that probably actually exist. To understand cosmic strings, and to convince you that they probably do exist, we need to understand phase transitions in quantum fields - we need to see how a whole
universe can freeze like a badly-made ice cube.
Heat up ice and it melts, keep heating the water
and it vaporizes, more heat still and that water vapor ionizes into plasma. But that’s not the final
phase transition. Keep heating until you hit temperatures of the extremely early universe and a
phase transition occurs in the quantum fields that underlie all particles. Just as with water, a
field’s inherent temperature massively changes its behavior. For example, the force-carrying field of
the modern universe has a complicated structure. There are many different ways it can vibrate.
These modes manifest as different force-carrying particles moving in what we think of as separate
force fields. This gives us our familiar electromagnetic, strong and weak nuclear forces. But at very high temperatures, the complexities of the quantum fields sort of
get ironed out, a little like how the complex crystal structure of ice dissolves when it melts.
It seems pretty certain that in the first searing instant after the big bang, most of the modes
of vibration of the quantum fields vanished. The many force-carrying fields behaved as a
single field, generating a single master force. We know for sure that this is true of the
electromagnetic and weak nuclear forces - we’ve re-merged those in our particle colliders -
but it’s almost certainly the case for the strong nuclear force and the Higgs field also. That’s right, I said Higgs field. We think of the Higgs field and Higgs boson as giving elementary particles their masses, but we should also think of the Higgs as a fifth fundamental force, because
it arises from the same field structure as the other non-gravity forces. And it’s the freezing of this field that can give us our cosmic strings.
Now a quantum field is just some numerical
property that the fabric of space can have. The field at any point can oscillate around that value, and those oscillations can have quantized energy states. These vibrations can move through space, and we see them as particles. A field’s numerical value is called
its field strength and it depends on the amount of energy in the field, sometimes
in complex ways. In the absence of particles, a field will always drop to the nearest minimum
in energy - this is the vacuum state of the field. In the early universe, the Higgs field had
a very simple response to changes in energy, with a single minimum value, and even this
vacuum state still contained a lot of energy.
The shape of this so-called potential curve
depends on the temperature. As the universe expanded and things cooled down, the Higgs
field potential developed a bump. The lowest energy value was no longer a single number -
instead new minima appeared around the old value. Actually, the Higgs field is really characterized
by two numbers - a pair of field strengths, and so the new minimum formed a ring around the old minimum,
resembling an item of festive Mexican headwear. So, quite suddenly the Higgs
field everywhere in the universe found itself sitting at a higher energy than it
needed. It was momentarily stable at that point, just like a ball sitting at the top of a hill. But
the slightest quantum jiggle would send the ball, or the Higgs, rolling down in a random direction.
And that’s what happened. Here and there across the universe, the Higgs field started falling
towards the new vacuum state - we call this vacuum decay. Neighboring points in a field drag on each
other, pulling them towards the same value, just like how the magnetic dipoles in a ferromagnet
drag each other into alignment. So, when vacuum decay started at one point neighboring points were
dragged to the same part of the Higgs minimum. A bubble of this lower vacuum energy was
nucleated, and it expanded at the speed of light. Many bubbles would have started
at different places across the universe, and when the bubbles found each other and merged,
the old, high-energy vacuum was completely erased. Or mostly erased. Just as with ice, topological
defects should have formed where these bubbles met. Our ice cube forms sheets, but our
Higgs field formed strings. Remember that the vacuum decayed in a random
direction towards this circular valley. That means we can ascribe an angle to
every point in space defining the relative value of the two components of the Higgs
field. We’ll call that the phase angle.
Across a single expanding region of decaying vacuum, the phase angle would have been similar because these points were all pulled in the
direction of the initial nucleation event. But independent bubbles may have very different phase angles. When bubbles met, the Higgs phase angle at the boundary tried to rotate to line up. This led to textures of slowly shifting phase angles across the universe. But if multiple bubbles join with
different phase angles then sometimes the lowest energy approach to lining up the phase angles
is for them to vary smoothly around a loop - a 2-pi rotation of the phase angle around the
intersection. And that left a knot somewhere inside the loop where the fields couldn’t align.
The Higgs field at the center of that knot was forced to take on the Higgs value at the top
of the potential hill rather than the valley. It became a fossil of the ancient, high-energy vacuum
that would persists into the modern universe. This sort of swirly topological defect is called
a vortex, and we see 2-D versions everywhere from cyclones to swirls of hair on your head. But
in a 3-D space, like, you know, actual space, this sort of defect manifests as a
cylindrical swirl around a central line. And that central line is our cosmic string.
Other topological defects may be possible. For example, a zero-dimensional, point-like
topological defect would be a magnetic monopoles, which we talked about recently. There are also
ways to produce 2-D defects called domain walls, but that’s for another time. OK, so we’ve managed to freeze the quantum fields amidst the first bawlings of the baby universe and woven some cosmic strings. What do they look like and what do they do? Those
phase angles really do prefer to line up, which means the loops around the defect tighten as much
as they can. The filament of high vacuum energy is squeezed it down to one-ten-trillionth the width
of a proton. And yet it still holds an incredible amount of energy, which gives it the mass of the planet Mars for every 100 meters of length. And these things are long. They started as long
as light can travel between the nucleation event and the completion of vacuum decay and then the
expanding universe stretched them up to the size of the observable universe. We actually expect
multiple nucleation events in each causal horizon, potentially leading to dozens of cosmic
strings in a network across the universe.
Unlike the topological defects in ice,
cosmic strings move and vibrate. They are also under pretty insane tension, so vibrations
travel along them at near the speed of light. This inevitably leads to collisions
between segments of strings–either two distinct strings or two sections of the
same string. When this happens either the two segments pass straight through each other,
or they switch partners - they intercommute.
If a straight string collides with itself it can
cut out a loop. Then, if the loop intersects with itself again, it forms two smaller loops, chopping
up into smaller and smaller loops. But larger and larger loops keep forming from the original giant
cosmic strings. Over time, the size of the largest loops increases, while at the same time populating
the universe with their chopped-up offspring. Once intercommutation occurs, a pair of “kinks” is formed in each of the newly formed strings speed away from each other along the string at near the
speed of light. They’re whipped back and forth by the oscillating string, and the incredible mass in the kinks causes them to radiate gravitational waves. In this way cosmic strings
shed energy, and so they slowly decay away. Eventually they vanish as the Higgs field smooths
itself out across the filament. The smaller the loop size the quicker they evaporate, so the
breaking up of loops accelerates their demise.
OK, that’s what cosmic strings do. Now, how do we
find them, assuming they exist? Well let’s start with these gravitational waves. That radiation
should be emitted in beams in the direction of oscillation of the string, so we might see flashes
as these beams pass over our gravitational wave observatories. These are likely too weak to be seen at our current detectors such as LIGO, but future detectors such as LISA might be
sensitive enough. Then there’s the Pulsar Timing Array - as we’ve described previously,
it detects gravitational waves by looking for irregularities in the period of the fantastically
regular flashes of light from pulsars. It also has the potential to spot the tell-tale signals from gravitationally radiating kinks in cosmic strings.
The other way to spot cosmic strings also
relies on a gravitational effect: gravitational lensing - which is the warping of background light sources due to the space-time warping effect of gravity. When a massive object sits between
us and a distant light source, it bends all passing rays of light inwards, so focusing them
towards us. We can see multiple images or even a ring surrounding that lens. A cosmic string would also deflect light towards itself, but that can only lead to a pair of split images, and that could potential leave a chain of split images across the sky. No such chain has yet been detected,
but upcoming gigantic all-sky surveys may give us the data that we need to find these. Now if we do find a cosmic string, there’s one other point of confusion we’d need to settle.
Is this a cosmic string, or is it a cosmic superstring? You’ve probably heard of string
theory - we’ve certainly talked about it enough on this show. It’s perhaps the most established
candidate for a theory of everything - a theory that brings together all physics as we know it.
The fundamental building blocks of the theory are these subatomic 1-dimensional filaments called,
fittingly, strings. The strings of string theory have nothing to do with the cosmic strings that I described. For one thing, they’re ridiculously tiny instead of universe-sized. However the
universe may have found a way to confuse the two.
Many physicists think that in the extremely early
universe the so-called inflationary epoch expanded the subatomic into the cosmic. Some of these
string-theoretic strings may have been stretched to universe-size by that event. Now those are called cosmic superstrings, and annoyingly they behave like “regular” cosmic strings in many ways -
like the gravitational waves and the lensing.
But there are differences. While cosmic strings
almost always intercommute when they collide, cosmic superstrings are far more likely
to pass straight through each other, which reduces the rate of chopping up. They can also form junctions, specifically where two different types of superstring meet and combine
to form a third, connected string which is, in a sense, a combination of the two. This gives us a potential way to distinguish our cosmic string-type. If one of these superstring
junctions does any gravitational lensing, it should produce a six-part image, perhaps
with a parade of split pairs approaching it. Observation of such a junction would be the
best - dare I say only - evidence to date in support of string theory. We also expect
cosmic superstrings to decay less quickly because they don’t chop into loops as fast.
That means they should result in a stronger gravitational wave background, and possibly
a distinct gravitational wave signature.
Now we haven’t actually found cosmic strings or superstrings … yet. But our searches have given us bounds on the range of allowed
tensions–and therefore energies–of these things. And we have to keep looking, because it’s very
possible that the universe is riddled with veins of its primordial vacuum. If we can find one who
knows what we’ll learn? We may discover truths about the origins of the universe, or the nature
of quantum fields, or the validity of string theory. Many murky mysteries may become as clear
as a well-made ice cube. I mean, what better way to see its inner workings of the universe than
to find a crack in the fabric of spacetime.
