Why does the oldest light in the sky have the same temperature in every direction?
Light from opposite sides of the sky comes from regions that, without inflation, never had time to exchange heat. Yet their temperatures agree to about 1 part in 100,000.
Inflation proposes that a small region expanded fast enough to become everything we can see. In many versions of the theory, that expansion keeps going elsewhere, forming new universes.
The Big Bang
About 13.8 billion years ago, everything in the observable universe was packed into a very hot, very dense state. Since then, space has expanded and everything in it has cooled. As it cooled, the first atomic nuclei formed, then atoms, then stars and galaxies. That story is the Big Bang theory, and it's supported by a lot of evidence, including the cosmic microwave background (the CMB) itself. It describes how the universe expanded and cooled from that state, but it doesn't say what started it.
Puzzle one: the horizon problem
Comparison: a cup of hot coffee cools toward room temperature because it exchanges heat with the air. Heat exchange can explain why two things end up at the same temperature.
That explanation needs time. Heat and information can't travel faster than light, so regions that never exchanged a signal couldn't have equalized their temperatures this way.
Without inflation, the expanding Big Bang model leaves too little time. The CMB was released when the universe was about 380,000 years old. Regions more than about 2 degrees apart in our sky hadn't been able to exchange signals, yet their temperatures nearly match.
The horizon problem is explaining that uniform temperature. The model can start with it, but it gives no reason for that starting condition.
Puzzle two: the flatness problem
Space is close to flat as far as we can measure. During expansion dominated by matter or radiation, a small departure from flatness grows in importance. For space to remain this close to flat, it had to start much closer still. Physicists call this the flatness problem.
Inflation
In December 1979, a young physicist named Alan Guth worked out an idea that solves both puzzles at once. On the morning of 7 December, he wrote "SPECTACULAR REALIZATION" at the top of a page in his notebook. His paper came out in January 1981 in Physical Review D, titled Inflationary universe: A possible solution to the horizon and flatness problems.
Inflation is the idea that, in its first tiny fraction of a second, the universe went through a burst of extremely fast expansion. NASA's WMAP overview describes it as expansion by "more than a trillion trillion fold in less than a trillionth of a trillionth of a second". Guth puts the minimum at about 60 steps of growth by a factor of e, which works out to about 1026.
A factor of 1026 is what you get when you double a length about 86 times in a row. A proton is about 1.7 × 10−15 meters across. Stretched by 1026, it would be about 1.7 × 1011 meters across, a bit more than the distance from the Earth to the Sun. A grain of sand one millimeter across would end up about 10 million light years across, four times the distance to the Andromeda galaxy.
What drives it
Inflation needs something to push space apart that fast. In the theory, the push comes from a field: a quantity that has a value at every point in space, the way temperature has a value at every point in a room. The field that drives inflation is called the inflaton.
In inflation models, the inflaton's stored energy per unit volume stays nearly constant as space expands. Its pressure is negative, which can make expansion accelerate under general relativity. When the field releases that energy into particles, the region heats up and enters the hot Big Bang phase.
How it solves the two puzzles
The horizon problem changes if our observable universe grew from one small region. Before inflation stretched it, that region could have been small enough for its parts to exchange heat. Opposite sides of our sky could once have been neighbors.
Comparison: an ant on a balloon the size of the Earth would see nearly flat ground. The balloon's curve extends much farther than the ant can explore. Inflation stretches spatial curvature in a similar way, leaving a region that looks flat even if the larger space is curved.
What the measurements support
Planck's measurements, combined with galaxy data, are consistent with flat space. Inflation also predicts small differences in the early density of matter. Quantum fluctuations get stretched to cosmic distances, where they can become the seeds of galaxies.
The spectral index describes how the strength of those initial fluctuations changes with scale. A value of 1 means the strength is the same across scales. Planck measured 0.9649, with an uncertainty of 0.0042, about eight standard deviations below 1. That small departure agrees with many inflation models. The Planck team's analysis of inflation also found the data compatible with models where the inflaton rolls slowly down a gentle slope.
Inflation models also predict primordial gravitational waves, ripples in space from the early universe. Their strength depends on the model. They could affect the CMB's polarization, the direction in which the light's electric field vibrates. A twisting pattern in those directions across the sky is called a B mode.
On 17 March 2014, a team using the BICEP2 telescope at the South Pole announced that they had found that signal. In February 2015, a joint analysis with the Planck team found "strong evidence for dust and no statistically significant evidence" for the gravitational waves. Dust in our own galaxy could explain the pattern, so the claim was dropped.
The experiments instead set upper limits. The number r compares the strength of primordial gravitational waves with the strength of the initial density fluctuations. In 2021, BICEP and Keck put r below 0.036 at 95 percent confidence. An analysis combining several data sets tightened the limit to about 0.032.
The BICEP2 story happened in 2014, the same year my interest in parallel universes started.
How inflation can keep going
Quantum jitter in the inflaton
Comparison: imagine the field's energy as a hill, and the value of the field as a ball on that hill. While the ball sits high up, the stored energy is large, and space inflates. As the ball rolls down to the valley at the bottom, the energy is released, and inflation ends in that region.
The inflaton is a quantum field, though, so its value jitters at random everywhere. Most of the time the ball rolls down anyway, but in some regions the jitter pushes it back up the hill for a while.
A region that stays high on the hill keeps expanding. Even while inflation ends in some places, the places still inflating can grow fast enough to increase their total volume. In Guth's simplified calculation, one region expands into about 20 regions during a characteristic expansion time. If more than about 1 in 20 stays high on the hill, the inflating volume can keep growing.
The idea is called eternal inflation. Alexander Vilenkin described it in 1983, and Andrei Linde developed it in 1986.
Bubble universes
Comparison: think of a lake freezing. Normally, patches of ice form, grow, join together, and soon the whole lake is frozen. Now imagine the liquid water between the patches keeps expanding, faster than the ice can spread. New ice patches keep forming forever, but the water between them grows so fast that the patches never join.
In eternal inflation, the patches are regions where inflation has ended. Inside each one, the inflaton released its energy, the region filled with hot particles, and an ordinary Big Bang history started. Physicists call these regions bubble universes or pocket universes. Our entire observable universe sits inside one of them.
In this picture, space between the pockets keeps inflating. New pockets form while the distances between most existing ones grow too fast for a signal to cross.
That's a Level II parallel universe, in Max Tegmark's map: another bubble, born from the same inflating space, cut off from ours.
Inside a bubble
In some bubble models, space inside a bubble can be infinite at a given cosmic time. The result follows from the geometry of the bubble, with roots in Sidney Coleman and Frank De Luccia's 1980 calculation. Such a bubble could contain Level I copies if its matter also satisfies the statistical assumptions in that argument.
Different laws in different bubbles
A theory with one final state gives every pocket the same physics. A theory with several possible final states allows more variety. Different pockets could settle into states with different particles, force strengths, or numbers of large spatial dimensions.
In that case, a neighboring bubble could be nothing like ours, with no atoms or no stable stars at all. The laws you'd measure there would look different, even though the deeper theory is the same.
String theory is one proposal for where those different states could come from.
Could we ever see another bubble?
If another bubble formed close enough to ours, the two could have collided. Some models predict a disk shaped mark in the CMB from such a collision, with a temperature pattern that astronomers can search for.
In 2011, Stephen Feeney and colleagues searched WMAP data and found no need to add bubble collisions to the standard model. They put the average number of detectable collisions across the sky below 1.6 at 68 percent confidence. A 2015 forecast found little improvement from better temperature maps, but estimated that adding polarization could improve detectability by about 30 percent.
A collision could be too faint or outside our observable region. The search constrains collisions with a detectable signal; it doesn't rule out all other bubbles.
The debate over eternal inflation
Paul Steinhardt helped develop inflation in the early 1980s. In February 2017, he and two colleagues, Anna Ijjas and Abraham Loeb, wrote an article in Scientific American called Pop Goes the Universe. They argued that if eternal inflation makes an infinite number of bubbles, every possible outcome happens somewhere, so the theory can explain any observation at all. A theory that can explain anything predicts nothing, which to them means it isn't science.
In May 2017, 33 physicists, including Alan Guth, Andrei Linde, Stephen Hawking, and Steven Weinberg, replied with a letter called A Cosmic Controversy that defended inflation as a tested scientific theory. They pointed out that inflation's predictions were confirmed, and that specific models can still be tested and ruled out.
The measure problem concerns probabilities when outcomes occur infinitely many times. Calculating which outcomes are common needs a rule for comparing infinite sets. Different rules can give different predictions about a typical bubble.
What I think
The CMB measurements give me a reason to take inflation seriously. Eternal inflation needs more: a model in which quantum fluctuations keep enough space inflating, and a way to calculate probabilities across its pockets.
I think parallel universes exist. The fact that many inflation models keep producing new pockets is one of my reasons.
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