The anthropic argument and the multiverse — and where the course begins

In a quantum field theory the vacuum energy gets both positive and negative contributions, so across the landscape we would expect values spread from roughly $-10^{120}$ to $+10^{120}$ times the observed value. (Asked why exactly $10^{120}$: it simply restates the mismatch, which is itself uncertain by a few orders of magnitude — $10^{123}$ is probably closer.) Our value would be a thin slice in the middle, about $10^{-120}$ of the range. With $10^{500}$ vacua,

So finding such vacua is no problem. The puzzle is why we should live in one, if they are so rare.

Guth starts with an example where a selection effect is surely right. The matter around us has a density of about 1 g/cm³, give or take a factor of 10. The average density of the visible universe is about $10^{-30}$ g/cm³ — emptier than the best vacuum we can make in a laboratory. So we live where the density is about $10^{30}$ times the average: a very atypical place. Chance? Luck? Divine providence? Most of us would call it a selection effect: life happens only in such rare places, like the surface of a planet.

If that is acceptable within our visible universe, it is not much of a stretch to apply it within the multiverse. Steven Weinberg emphasised this in 1987 — not the first to say it, Guth notes, but the first to be sometimes believed. There is physics behind it. Vacuum energy drives acceleration: if it were much larger and positive, the universe would fly apart before galaxies could form; if large and negative, it would collapse very quickly — perhaps in as little as $10^{-20}$ s. Assuming galaxies are needed for life, Weinberg and his collaborators (Martel, Shapiro and Weinberg, 1998) calculated that galaxies form only if the vacuum energy is about the observed value or less, within a factor of about 5. So it is a possible explanation.

It is controversial. Many physicists find it ridiculous — you can explain almost anything by saying it is needed for life — and there is some truth in that. Guth's recommendation: treat anthropic explanations as the explanation of last resort. Until we understand the landscape and what it takes to create life, they are only plausibility arguments, attractive when the search for more deterministic explanations has failed. For the vacuum energy, people have tried very hard for years to find a particle-physics reason, without anything widely accepted. So, Guth concludes, the selection effect deserves to be taken seriously; as things stand, he finds no known explanation more plausible. (Anthropic arguments are also discussed for other quantities, such as the Higgs and top-quark masses and the size of the primordial density ripples.)

Three winds blowing us towards the multiverse

1. Almost all inflationary models are eternal into the future, producing pocket universes forever.
2. The universe is accelerating, probably because of a non-zero vacuum energy far smaller than we can understand.
3. String theorists mostly agree there is no unique vacuum but a landscape of perhaps $10^{500}$; with the multiverse, a small vacuum energy can be explained as a selection effect.

Do physicists take this seriously? Guth tells of a conference discussion: Martin Rees, Britain's Astronomer Royal, said he was confident enough in the multiverse to bet his dog's life on it; Andrei Linde said he would bet his own life. Steven Weinberg, hearing of it, wrote that he had just enough confidence to bet the lives of Linde and Rees's dog.

Guth answers many questions — a first batch while reviewing Lecture 1, before the landscape counting, and a second after the Rees–Linde–Weinberg story. They are gathered here; the main points:

• Shape of pocket universes: they are predicted to be open, because of how they form, but those with a lot of inflation are indistinguishable from flat.
• Repulsive gravity is not reversed ordinary gravity: it comes from the negative pressure of the space between objects, and pushes them apart at a rate independent of their masses. Whether space expands or objects move through it is a matter of viewpoint in relativity; cosmologists usually take space to expand with the matter.
• Zero total energy: a closed universe — possible even if very nearly flat — has exactly zero energy.
• Is the universe "speckled" on huge scales? If the multiverse is right, yes: other pocket universes are very different. Before inflation, uniformity was simply postulated; now that it comes from a dynamical process, it is natural to ask on what scale it holds — far larger than we can observe.
• Does everything expand? No: galaxies get farther apart, but atoms and rulers don't grow. Most of today's expansion is coasting from the Big Bang.
• The future: our pocket universe will thin out until life is impossible, and will probably decay in places — a "Swiss cheese" — while still expanding faster than it decays. Decays inside it would make new pocket universes; the multiverse as a whole would go on generating them forever. A cyclic universe is possible, but Guth sees no evidence for it and no reasonable theory of the bounce.
• What distinguishes vacua? String theory has nine dimensions of space; six are curled up so small we can't see them, in very many different ways. Different curlings give different particles, constants, even different numbers of visible dimensions.
• Particles and energy: during inflation the energy is in fields rather than particles; it grows (balanced by negative gravitational energy), and the decay creates vastly more particles than were there at the start. Energy conservation alone does not decide what happens — nothing happening would conserve energy too.
• Carbon-based life? Life unlike ours is a real weakness of anthropic arguments. Guth's view, controversial: condition only on what is needed to ask the question, and prefer theories in which most observers asking it get our answer.
• Separate pocket universes form in rapidly expanding space, so most never meet; but if two form close enough they can collide, and astronomers have looked (without definite results) for signs of such a collision in our past — which means the multiverse is not, in principle, untestable.
• Is it science, if other pockets can't be seen? We accept theories once enough of their predictions are tested; then we should take seriously their other implications, as with untested consequences of Newtonian gravity.
• Accelerated observers see a warm bath of particles where an inertial observer sees vacuum [this is the Unruh effect]. Guth's answer: we tend to adopt the philosophy that freely falling (geodesic) observers define reality, and on the cosmic scale we are essentially geodesic.
• Stability of vacua: there is a trend for higher-energy vacua to be less stable, with wide variations. "Long-lived" here means long compared with the age of our universe, about $10^{10}$ years. A vacuum with as small an energy as ours might be longer-lived than most, but over an infinite future decays still happen.

After housekeeping (office hours), Guth starts the course proper with Hubble's law:

where $v$ is the recession velocity of a typical galaxy and $r$ its distance. It is not exact — individual galaxies deviate — and $H$ is better called the Hubble expansion rate than Hubble's constant: it is constant over the lifetime of an astronomer, not of the universe (and its estimated value has changed by about a factor of 10 since Hubble's own).

Hubble or Lemaître?

Guth's old notes said Hubble discovered the law in 1929, but that has become controversial. Georges Lemaître, a Belgian priest — and an MIT PhD of 1927, who did most of the work at the Harvard College Observatory, which granted no degrees — published a 1927 paper in French on an expanding universe. The English-speaking world knew it from a 1931 translation, from which paragraphs about the Hubble constant were missing, and for a while Hubble or his friends were suspected of suppressing them. Mario Livio found in the archives that Lemaître himself had cut them, since by 1931 Hubble had published a better estimate. Lemaître understood the linear law theoretically and estimated $H$ by dividing an average velocity by an average distance, admitting the data couldn't show linearity. Hubble was the first to argue — weakly at first, then more strongly — from observations that the relation is linear. So it will probably stay Hubble's law.

Measuring v and r

Distances come from standard candles — objects whose intrinsic brightness we think we know, so that apparent brightness gives distance (well described in Weinberg's The First Three Minutes). Velocities come from the Doppler shift, the subject of the first lecture notes. Guth sets up the first case — a moving source of sound and a stationary observer, with the air at rest — and notes that because each wave crest from a receding source travels a little farther, the observed period is longer than the emitted one. The calculation, and the relativistic versions, follow in the next lecture. (The cosmological redshift, which includes gravity, comes later in the course; like Hubble, the first lectures ignore gravity, which is fine for nearby galaxies [Guth says "nearby stars"].)

• Of perhaps $10^{500}$ landscape vacua, about $10^{380}$ might have a vacuum energy as small as ours.
• A selection effect — life only where the vacuum energy is tiny — could explain why we see one, just as we live where the density is $10^{30}$ times the average. Weinberg (1987) and Martel, Shapiro & Weinberg (1998) made this quantitative.
• Guth calls anthropic reasoning the explanation of last resort, but thinks it is now the most plausible explanation known for the vacuum energy.
• The course proper starts with Hubble's law, $v = Hr$; Lemaître understood it in 1927 but Hubble first argued for it from data. Velocities come from the Doppler shift.