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By Root 1920 0

shape is attached to every point in the familiar three large dimensions of space, much as circular loops of pile attach to every point on the large extended base of a carpet, the energy the shape contains would uniformly fill the three large dimensions, much as soaking the individual fibers in a carpet’s pile would make the entire carpet backing uniformly heavy. Thus, should one or another of the 10500 different dressed-up Calabi-Yau shapes constitute the requisite extra dimensions, the energy it contains would contribute to the cosmological constant. Results obtained by Raphael Bousso and Joe Polchinski made this observation quantitative. They argued that the various cosmological constants supplied by the 10500 or so different possible forms for the extra dimensions are distributed uniformly across a broad range of values.

This is just what the doctor ordered. Having 10500 tick marks distributed across a range from 0 to 1 ensures that many of them lie extremely close to the value of the cosmological constant astronomers have measured during the past decade. It may be hard to find the explicit examples among the 10500 possibilities, because even if today’s fastest computers took a single second to analyze each form for the extra dimensions, after a billion years only a paltry 1032 examples would have been examined. But this reasoning suggests strongly that they exist.

Certainly, a collection of 10500 different possible forms for the extra dimensions is about as far from a unique universe as anyone imagined string theory research would ever take us. And for those who’ve held strongly to Einstein’s dream of finding a unified theory describing one single universe—ours—these developments came with significant discomfort. But analysis of the cosmological constant casts the situation in a different light. Rather than despair because a unique universe seems not to emerge, we are encouraged to celebrate: string theory makes the least plausible part of Weinberg’s explanation of the cosmological constant—the requirement that there be many more than 10124 different universes—suddenly seem plausible.

The Final Step, in Brief

The elements of a tantalizing story seem to be coming together. But a gap remains in the reasoning. It’s one thing for string theory to allow for a huge number of possible distinct universes. It’s another to claim that string theory ensures that all of the possible universes to which it can give rise are actually out there, parallel worlds populating a vast multiverse. As emphasized most emphatically by Leonard Susskind—who was inspired by the pioneering work of Shamit Kachru, Renata Kallosh, Andrei Linde, and Sandip Trivedi—if we weave eternal inflation into the tapestry, the gap can be filled.15

I’ll now explain this final step, but in case you’re reaching saturation and just want the punch line, here’s a three-sentence summary. The Inflationary Multiverse—the ever-expanding Swiss cheese cosmos—contains a vast, ever-increasing number of bubble universes. The idea is that when inflationary cosmology and string theory are melded, the process of eternal inflation sprinkles string theory’s 10500 possible forms for the extra dimensions across the bubbles—one form for the extra dimensions per bubble universe—providing a cosmological framework that realizes all possibilities. By this reasoning, we live in that bubble whose extra dimensions yield a universe, cosmological constant and all, that’s hospitable to our form of life and whose properties agree with observations.

In the remainder of the chapter, I will flesh out the details, but if you’re ready to move on, feel free to jump ahead to the chapter’s last section.

The String Landscape

In explaining inflationary cosmology back in Chapter 3, I used a variation on a common metaphor. A mountain’s peak represents the highest value of energy contained in an inflaton field suffusing space. The act of rolling down the mountain and coming to rest at a low point in the terrain represents the inflaton shedding this energy, which in the process is converted to particles