Laws of Logic Lead to New Restrictions on the Big Bang

Patterns in the ever-expanding arrangement of galaxies might reveal secrets of the universe’s first moments. Dave Whyte for Quanta Magazine

Physicists are translating commonsense principles into strict mathematical constraints on how our universe must have behaved at the beginning of time.

by Charlie Wood Staff Writer

For over 20 years, physicists have had reason to feel envious of certain fictional fish: specifically, the fish inhabiting the fantastic space of M.C. Escher’s Circle Limit III woodcut, which shrink to points as they approach the circular boundary of their ocean world. If only our universe had the same warped shape, theorists lament, they might have a much easier time understanding it.

Escher’s fish lucked out because their world comes with a cheat sheet — its edge. On the boundary of an Escher-esque ocean, anything complicated happening inside the sea casts a kind of shadow, which can be described in relatively simple terms. In particular, theories addressing the quantum nature of gravity can be reformulated on the edge in well-understood ways. The technique gives researchers a back door for studying otherwise impossibly complicated questions. Physicists have spent decades exploring this tantalizing link.

Inconveniently, the real universe looks more like the Escher world turned inside out. This “de Sitter” space has a positive curvature; it expands continuously everywhere. With no obvious boundary on which to study the straightforward shadow theories, theoretical physicists have been unable to transfer their breakthroughs from the Escher world.

Illustration of an Escher pattern.
M.C. Escher’s Circle Limit III (1959).M.C. Escher

“The closer we get to the real world, the fewer tools we have and the less we understand the rules of the game,” said Daniel Baumann, a cosmologist at the University of Amsterdam.

But some Escher advances may finally be starting to bleed through. The universe’s first moments have always been a mysterious era when the quantum nature of gravity would have been on full display. Now multiple groups are converging on a novel way to indirectly evaluate descriptions of that flash of creation. The key is a new notion of a cherished law of reality known as unitarity, the expectation that all probabilities must add up to 100%. By determining what fingerprints a unitary birth of the universe should have left behind, researchers are developing powerful tools to check which theories clear this lowest of bars in our shifty and expanding space-time.

Unitarity in de Sitter space “was not understood at all,” said Massimo Taronna, a theoretical physicist at the National Institute for Nuclear Physics in Italy. “There is a huge jump that has happened in the last couple of years.”

Spoiler Alert

The unfathomable ocean that theorists aim to plumb is a brief but dramatic stretch of space and time that many cosmologists believe set the stage for all we see today. During this hypothetical era, known as inflation, the infant universe would have ballooned at a truly incomprehensible rate, inflated by an unknown entity akin to dark energy.

Cosmologists are dying to know exactly how inflation might have happened and what exotic fields might have driven it, but this era of cosmic history remains hidden. Astronomers can see only the output of inflation — the arrangement of matter hundreds of thousands of years after the Big Bang, as revealed by the cosmos’s earliest light. Their challenge is that countless inflationary theories match the final observable state. Cosmologists are like film buffs struggling to narrow down the possible plots of Thelma and Louise from its final frame: the Thunderbird hanging frozen in midair.

The final frame of Thelma and Louise (left) and the cosmic microwave background radiation (right) both depict the last instant of an epic saga.Roland Neveu / PictureLux / The Hollywood Archive / Alamy Stock Photo; ESA, Planck Collaboration

Yet the task may not be impossible. Just as currents in the Escher-like ocean can be deciphered from their shadows on its boundary, perhaps theorists can read the inflationary story from its final cosmic scene. In recent years, Baumann and other physicists have sought to do just that with a strategy called bootstrapping.

Cosmic bootstrappers strive to winnow the crowded field of inflationary theories with little more than logic. The general idea is to disqualify theories that fly in the face of common sense — as translated into stringent mathematical requirements. In this way, they “hoist themselves up by their bootstraps,” using math to evaluate theories that can’t be distinguished using current astronomical observations…


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