Was Our Universe Born In Chaos?
Our Universe appears similar in every location and direction we look, but that doesn’t mean it was always so.
“The design of the universe…is very magnificent and shouldn’t be taken for granted.” -Charles W. Misner
One of the longstanding questions in cosmology involves whether or not the universe has always been roughly similar in all directions — what cosmologists call “isotropic.” Today, on the largest scales, the Universe appears very similar in all directions, with the same average properties. But was this always true? Has there ever been a time when the cosmos was shaped irregularly, like a lump of a coal, only to be smoothed out by a dynamic process? The idea that the early cosmos was a haphazard jumble and somehow became regularized is called the ‘chaotic cosmology program.’ The idea was inspired by the sheer diversity of solutions to Einstein’s field equations in general relativity. (We are talking about solutions in classical general relativity; quantum gravity might be even more jumbled.) Why should we assume we’d have a simple cosmos if there are so many choices?
In 1964, when Arno Penzias and Robert Wilson discovered the cosmic microwave background (CMB) — the ‘hiss’ of the cooled-down radiation relic of the early universe — one of its most salient features was its uniformity. No matter which way the researchers pointed their horn antenna — the device they accidentally discovered the CMB with at Bell Labs in Holmdel, NJ — they found the same radiation profile. As the distribution of any form of radiation over various wavelengths depends on its temperature, that meant that each point in the sky had approximately the same temperature, around 2.73 degrees above absolute zero. (Subtle variations, at the 0.01% level or below, would be discovered much later through the launching of balloons and satellites designed to map out the CMB.)
Because of such uniformity of temperature at that particular value, Bob Dicke and his group at Princeton — including Jim Peebles and Dave Wilkinson — immediately identified that hiss as the “smoking gun” establishing the correctness of Big Bang cosmology. In its original incarnation, as developed by Belgian cleric and cosmologist Georges Lemaitre, Alexander Friedman, and later George Gamow, Ralph Alpher, and Robert Herman, that model envisioned a primordial ‘fireball’ expanding and cooling down continuously over time, in line with a simple, isotropic set of solutions of Einstein’s equations, called the Friedman-Lemaitre-Robertson-Walker (FLRW) metric. At a certain point in cosmic history, known as the recombination era, the formation of neutral atoms would release massive amounts of hot photons into space. Dicke calculated how the temperature of that photon gas would cool down over time, due to the growth of space, and found that what Penzias and Wilson found was roughly consistent with that prediction: within the same order of magnitude. (Gamow soon reminded Dicke that Alpher and Herman had made a similar prediction of cooled-down relic radiation back in 1948.)
In 1969, Charles Misner, a physicist at the University of Maryland who was a former student of John Wheeler, noted a major dilemma with the simple FLRW model of cosmic dynamics, called the “horizon problem.” Misner calculated that any two points in the sky separated by more than a 30 degree angle would have been completely out of causal contact (no way to have communicated) by the time of the era of recombination when the radiation that would eventually become the CMB was first released into empty space. By the time of the era of recombination, the points would have been so far apart that a light signal could not have traveled from one to the other. Given the lack of causal connection between those two points, it became a puzzle to explain the remarkable present-day temperature uniformity (more or less) in all parts of the sky. The near-sameness thereby presented either an astonishing coincidence or a flaw in the standard Big Bang theory.
We can picture the horizon problem by imagining that someday, in the near future, we manage to pick up the radio signals of a number of distantly separated extraterrestrial civilizations, and find that every one of them broadcasts in a language similar to one of Earth’s ancient languages, such as Sumerian. Each of those planets is so far away from us that they wouldn’t have had time to detect our signals. Without mutual communication, how could they have developed a common language? Because of the lack of causal connection, it would similarly seem too much of a coincidence. The logical conclusion would be that there must have been some unknown mutual interactions in the distant past. If, for example, a central “mother” civilization from millions of years ago sent out ships to all of the planets, and introduced the same language to each, that would explain it. (This is just an analogy, of course; we’re not saying that really happened!) Similarly, there must have been a mechanism to link up otherwise distant points in the early universe so that they could have coordinated their temperatures through thermal contact.
To “mix up” the early universe — such that otherwise remote regions could have been brought into contact at an earlier stage — and thus try to solve the horizon problem, Misner proposed the “Mixmaster universe,” named after a kitchen appliance popular at the time. He based his model on an anisotropic solution of Einstein’s field equations of general relativity with a special geometry (classified according to Italian mathematician Luigi Bianchi’s methods as ‘type IX’), which churned space in various directions for repeated oscillations, rather than steadily expanding like the isotropic FLRW solution. Misner imagined that the early universe started out anisotropic, underwent an era of mixing, smoothed itself out, and ultimately switched to isotropic growth.
The crazy part of the Mixmaster universe’s dynamics had to with its seemingly erratic behavior that was grounded, nevertheless, in deterministic equations. The model goes through successive intervals of oscillating in two directions while expanding in the third, something like an elevator shaking left and right, back and forth, as it steadily ascends for a number of floors. But then, after a certain number of cycles, called an “era,” one of the oscillating directions swaps places with the expanding direction, and the model begins to grow along a different direction. In the elevator analogy, that would be as if an ascending elevator started to move to the right instead. That transition inaugurates another era, which lasts for a particular number of cycles before switching behavior again to a third direction. Oddly if one writes down the number of cycles for each era, the sequence seems as random as successful dice tosses.
While, unfortunately the Mixmaster universe was not robust enough in its churning to eliminate the horizon problem, its introduction triggered a flurry of research about chaotic dynamics in cosmology. The term “chaotic” in this context, as coined by James Yorke of the University of Maryland in 1975, refers to a type of behavior that, while specified by a set of deterministic equations, is so highly sensitive to initial conditions that long-term prediction becomes effectively impossible. Any minute deviation in the initial values leads to huge differences in the long term behavior, rendering long terms forecasts inaccurate or even impossible.
A classic example of deterministic chaos is the weather. As meteorologist Edward Lorenz discovered, even a tiny change in atmospheric conditions, such as temperature, pressure, or wind velocity, can lead to a completely differently weather forecast. He found that out by making a slight mistake in entering data into a computer program, starting it up, and seeing it produce a drastically different printout. Noting that even the flapping of a butterfly’s wings in one region could affect others dramatically, he dubbed this the “butterfly effect.”
During the 1980s and 1990s, noted cosmologists such as John Barrow and Janna Levin explored the chaotic properties of the Mixmaster universe. Interestingly, tweaking the model with changes such as adding matter or changing the number of dimensions (instead of assuming a three-dimensional spatial vacuum) tended to suppress the chaotic behavior. Hence, like the weather, the universe itself offered a “test subject” for dynamic experiments — not necessarily the actual universe, but rather the enormous range of solutions to Einstein’s equations.
Today, the mainstream solution to the horizon dilemma is postulating an ultra-brief interval of inflation — ultra-rapid expansion — in the very early universe. That sudden and dramatic stretching takes any two proximate points and drastically separates them, explaining why their conditions are coordinated. Ultimately it explains why the CMB temperatures in opposite parts of the sky are so similar.
Why, then, study the Mixmaster universe and other anisotropic models? First and foremost, they represent valid solutions of Einstein’s equations of general relativity, and reveal much about how chaotic dynamics arises under certain circumstances, and not under others. Second, the jury is still out over whether or not the observable universe is isotropic at the largest scale or might have a slight anisotropy in a certain direction. Some researchers argue the latter because of an unusual cold spot found in the CMB data, or because of the so-called Axis of Evil. Finally, while we can measure the observable universe, we cannot, by definition, see beyond it. Therefore, the actual universe on a larger scale could well be anisotropic, with its irregularities long ago hurled beyond measurement due to spatial expansion.
The regularity of the nighttime sky might be a comforting thought, but the next time you see it, consider that what’s visible to you might only be a small, relatively tranquil patch of a greater, turbulent ocean.
Paul Halpern is the author of fifteen popular science books, including The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality.
Starts With A Bang is now on Forbes, and republished on Medium thanks to our Patreon supporters. Ethan has authored two books, Beyond The Galaxy, and Treknology: The Science of Star Trek from Tricorders to Warp Drive.
