Eternal inflation, dark energy and the landscape

The repulsive-gravity material is metastable: it decays. Watch any one place where inflation is happening, and the probability that it is still inflating a little later falls exponentially, halving every half-life. But meanwhile the volume of any inflating region grows exponentially too — and in any successful inflationary model, much faster than the decay. Wait one half-life: half of the volume has stopped inflating, by definition, but what is left is far bigger than the region you began with.

So the inflating volume grows forever, even though the material is decaying: inflation becomes eternal. ("Eternal" means forever into the future, not the past: inflation would still start at some finite time.) Wherever a piece of the inflating region decays, it looks locally like a Big Bang, producing a pocket universe. Our universe would be one of them — "pocket" because there are many, though each may be as large as our whole universe. Instead of one universe, inflation produces infinitely many: a multiverse. The word is used in other theories too, but inflation is probably the most plausible route, and what most cosmologists mean by it.

In 1998 two groups of astronomers discovered independently that the expansion is accelerating, and has been for roughly the last 5 billion years of the universe's 14-billion-year history. The implication: inflation is happening today, driven, as inflation was, by something with negative pressure. That stuff, whatever it is, is called dark energy. What is it? Who knows. But the most plausible candidate is vacuum energy — the energy of nothingness, also known as a cosmological constant — which fits everything we can measure about the expansion.

Why only in the last 5 billion years? Vacuum energy, like the inflating material, is constant, while ordinary matter thins out as the universe expands. Matter dominated until about 5 billion years ago, and its attraction slowed the expansion; then it thinned enough for the vacuum energy's repulsion, present all along, to take over.

Why can nothing weigh something?

The quantum vacuum, unlike the classical one, is far from empty: it is a jumble of fluctuations. The electromagnetic field oscillates constantly because of the uncertainty principle, and the Higgs field has a non-zero average value even in the vacuum. So there is no reason for the vacuum's energy to be zero. The real problem is why it is so small.

In quantum field theory the fluctuations come in every wavelength, each contributing to the vacuum energy. A box has a longest wavelength but no shortest, so the calculated energy density diverges. Quantum theory works superbly in the laboratory, so presumably something happens at very short wavelengths — perhaps quantum gravity — to cut it off. Cutting off at the Planck length, about $10^{-33}$ cm, gives a finite answer — too large by 120 orders of magnitude. There is a way out in principle: the electron field (like other fermion fields) contributes negative energy, so the pieces could cancel, almost exactly — but nobody knows why they should.

For many years string theorists searched for the vacuum of string theory, without success. A little more than ten years before this lecture, many converged on the idea that there is no unique vacuum. Instead there may be a colossal number — perhaps $10^{500}$ — of long-lived metastable states, any of which could serve as the vacuum of a pocket universe for a long time before decaying or tunnelling into another. This is the landscape of string theory.

Combine it with eternal inflation, and the multiverse would probably contain pocket universes of every type, their vacua chosen at random as they break off from the inflating "backbone". String theory would govern everything, but the physics we see is low-energy physics: small oscillations about our particular vacuum. So the observed laws would differ from pocket to pocket — the particles (electrons and quarks may be peculiar to our pocket), the "constants" of nature, and the vacuum energy density. That variability is a possible answer to why ours is so small. Guth ran out of time here; the next lecture continues.

• The inflating material decays exponentially, but its volume grows exponentially faster, so inflation is eternal, continually producing pocket universes: a multiverse.
• Since 1998 we know the expansion is accelerating — inflation happening today — driven by dark energy, most plausibly vacuum energy.
• The quantum vacuum naturally has energy; the puzzle is its size: a Planck-scale cutoff overshoots by about 120 orders of magnitude.
• String theory's landscape of perhaps $10^{500}$ vacua, populated by eternal inflation, would give each pocket universe its own physics and vacuum energy — opening a possible explanation.