## From COSMOS: “How big is the universe?”

17 July 2017

Cathal O’Connell

“Space is big. You just won’t believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.” – Douglas Adams, *Hitchhikers Guide to the Galaxy*.

In one sense the edge of the universe is easy to mark out: it’s the distance a beam of light could have travelled since the beginning of time. Anything beyond is impossible for us to observe, and so outside our so-called ‘observable universe’. You might guess that the distance from the centre of the universe to the edge is simply the age of the universe (13.8 billion years) multiplied by the speed of light: 13.8 billion light years.

But space has been stretching all this time; and just as an airport walkway extends the stride of a walking passenger, the moving walkway of space extends the stride of light beams. It turns out that in the 13.8 billion years since the beginning of time, a light beam could have travelled 46.3 billion light years from its point of origin in the Big Bang. If you imagine this beam tracing a radius, the observable universe is a sphere whose diameter is double that: 92.6 billion light years.

“Since nothing is faster than light, absolutely anything could in principle happen outside the observable universe,” says Andrew Liddle, an astronomer at the University of Edinburgh. “It could end and we’d have no way of knowing.”

But we have good reasons to suspect the entire Universe (capitalised now to distinguish from the merely observable universe) goes on a lot further than the part we can observe – and that it is possibly infinite. So how can we know what goes on beyond the observable universe?

Imagine a bacterium swimming in a fishbowl. How could it know the true extent of its seemingly infinite world? Well, distortions of light from the curvature of the glass might give it a clue. In the same way, the curvature of the universe tells us about its ultimate size.

“The geometry of the universe can be of three different kinds,” says Robert Trotta, an astrophysicist at Imperial College London. It could be closed (like a sphere), open (like a saddle) or flat (like a table).

Universal geometry: the universe could be closed like sphere, open like a saddle or flat like a table. The first option would make it finite; the other two, infinite.

*Cosmos Magazine*.

The key to measuring its curvature is the cosmic microwave background (CMB) radiation – a wash of light given out by the fireball of plasma that pervaded the universe 400,000 years after the Big Bang. It’s our snapshot of the universe when it was very young and about 1,000 times smaller than it is today.

Just as ancient geographers once used the curviness of the Earth’s horizon to work out the size of our planet, astronomers are using the curvinesss of the CMB at our cosmic horizon to estimate the size of the universe.

The key is to use satellites to measure the temperature of different features in the CMB. The way these features distort across the CMB landscape is used to calculate its geometry. “So determining the size and geometry, of the Universe helps us determine what happened right after its birth,” Trotta says.

Since the late 1980s, three generations of satellites have mapped the CMB with ever improving resolution, generating better and better estimates of the universe’s curvature. The latest data, released in March 2013, came from the European Space Agency’s Planck telescope. It estimated the curvature to be completely flat, at least to within a measurement certainty of plus or minus 0.4%.

The extreme flatness of the universe supports the theory of cosmic inflation. This theory holds that in a fraction of a second (10−36 second to be precise) just after its birth, the universe inflated like a balloon, expanding many orders of magnitude while stretching and flattening its surface features.

Perfect flatness would mean the universe is infinite, though the plus or minus 0.4% margin of error means we can’t be sure. It might still be finite but very big. Using the Planck data, Trotta and his colleagues worked out the minimum size of the actual Universe would have to be at least 250 times greater than the observable universe.

The next generation of telescopes should improve on the data from the Planck telescope. Whether they will give us a definitive answer about the size of the universe remains to be seen. “I imagine that we will still treat the universe as very nearly flat and still not know well enough to rule out open or closed for a long time to come,” says Charles Bennet, head of the new CLASS array of microwave telescopes in Chile.

As it turns out, owing to background noise there are fundamental limits to how well we can ever measure the curvature, no matter how good the telescopes get. In July 2016, physicists at Oxford worked out we cannot possibly measure a curvature below about 0.01%. So we still have a ways to go, though measurements so far, and the evidence from inflation theory, has most physicists weighing toward the view the universe is probably infinite. An impassioned minority, however, have had a serious problem with that.

Getting rid of infinity, the great British physicist Paul Dirac said, is the most important challenge in physics. “No infinity has ever been observed in nature,” notes Columbia University astrophysicist Janna Levin in her 2001 memoir *How the Universe got its Spots*. “Nor is infinity tolerated in a scientific theory.”

So how come physicists keep allowing that the universe itself may be infinite? The idea goes back to the founding fathers of physics. Newton, for example, reasoned that the universe must be infinite based on his law of gravitation. It held that everything in the universe attracted everything else. But if that were so, eventually the universe would be pulled towards a single point, in the way that a star eventually collapses under its own weight. This was at odds with his firm belief the universe had always existed. So, he figured, the only explanation was infinity – the equal pull in all directions would keep the universe static, and eternal.

Albert Einstein, 250 years later at the start of the 20th century, similarly envisioned an eternal and infinite universe. General relativity, his theory of the universe on the grandest scales, plays out on an infinite landscape of spacetime.

Mathematically speaking, it is easier to propose a universe that goes on forever than to have to deal with the edges. Yet to be infinite is to be unreal – a hyperbole, an absurdity.

In his short story *The Library of Babel*, Argentinian writer Jorge Luis Borges imagines an infinite library containing every possible book of exactly 410 pages: “…for every sensible line of straightforward statement, there are leagues of senseless cacophonies, verbal jumbles and incoherences.” Because there are only so many possible arrangements of letters, the possible number of books is limited, and so the library is destined to repeat itself.

An infinite Universe leads to similar conclusions. Because there are only so many ways that atoms can be arranged in space (even within a region 93 billion light years across), an infinite Universe requires that there must be, out there, another huge region of space identical to ours in every respect. That means another Milky Way, another Earth, another version of you and another of me.

Physicist Max Tegmark, of the Massachusetts Institute of Technology, has run the numbers. He estimates that, in an infinite Universe, patches of space identical to ours would tend to come along about every 1010115 metres (an insanely huge number, one with more zeroes after it than there are atoms in the observable universe). So no danger of bumping into your twin self down at the shops; but still Levin does not accept it: “Is it arrogance or logic that makes me believe this is wrong? There’s just one me, one you. The universe can’t be infinite.”

Levin was one of the first theorists to approach general relativity from a new perspective. Rather than thinking about geometry, which describes the shape of space, she looked at its topology: the way it was connected.

All those assumptions about flat, closed or open universes were only valid for huge, spherical universes, she argued. Other shapes could be topologically ‘flat’ and still finite.

“Your idea of a donut-shaped universe is intriguing, Homer,” says Stephen Hawking in a 1999 episode of *The Simpsons*. “I may have to steal it.” Actually, the show’s writers had already stolen the idea from Levin—who published her analysis of a donut-shaped universe in 1998.

A donut, she noted, actually had – “topologically speaking” – zero curvature because the negative curvature on the inside is balanced by the positive curvature on the outside. The (near) zero curvature measured in the CMB was therefore as consistent with a donut as with a flat surface.

One ring theory to rule them all: CMB data doesn’t rule out a donut-shape, but it would be an awfully big one. Mehau Kulyk / Getty Images.

In such a universe, Levin realised, you might cross the cosmos in a spaceship, the way sailors crossed the globe, and find yourself back where you started. This idea inspired Australian physicist Neil Cornish, now based at Montana State University, to think about how the very oldest light, from the CMB, might have circumnavigated the cosmos. If the donut universe were below a threshold size, that would create a telltale signature, which Cornish called “circles in the sky”. Alas, when CMB data came back from the Wilkinson Microwave Anisotropy Probe (WMAP) in 2001, no such signatures were found. That doesn’t rule out the donut theory entirely; but it does mean that the universe, if it is a donut, is an awfully big one.

Attempts to directly prove or disprove the infinity of the universe seem to lead us to a dead-end, at least with current technology. But we might do it by inference, Cornish believes. Inflation theory does a compelling job of explaining the key features of our universe; and one of the offshoots of inflation is the multiverse theory.

It’s the kind of theory that, when you first hear it, seems to have sprung from the mind of a science-fiction author indulging in mind-expanding substances. Actually it was first proposed by influential Stanford physicist Andrei Linde in the 1980s. Linde – together with Alan Guth at MIT and Alexei Starobinsky at Russia’s Landau Institute for Theoretical Physics – was one of the architects of inflation theory.

Guth and Starobinsky’s original ideas had inflation petering out in the first split second after the big bang; Linde, however, had it going on and on, with new universes sprouting off like an everlasting ginger root.

Linde has since showed that “eternal inflation” is probably an inevitable part of any inflation model. This eternal inflation, or multiverse, model is attractive to Linde because it solves the greatest mystery of all: why the laws of physics seem fine-tuned to allow our existence.

The strength of gravity is just enough to allow stable stars to form and burn, the electromagnetic and nuclear forces are just the right strength to allow atoms to form, for complex molecules to evolve, and for us to come to be.

In each newly sprouted universe these constants get assigned randomly. In some, gravity might be so strong that the universe recollapses immediately after its big bang. In others, gravity would be so weak that atoms of hydrogen would never condense into stars or galaxies. With an infinite number of new universes sprouting into and out of existence, by chance one will pop up that is fit for life to evolve.

Infinite variety: in the the eternal inflation model, new universes sprout off like an everlasting ginger root. Andrei Linde.

The multiverse theory has its critics, notably another co-founder of inflation theory, Paul Steinhardt. who told Scientific American in 2014: “Scientific ideas should be simple, explanatory, predictive. The inflationary multiverse as currently understood appears to have none of those properties.” Meanwhile Paul Davies at the University of Arizona wrote in The New York Times that “invoking an infinity of unseen universes to explain the unusual features of the one we do see is just as ad hoc as invoking an unseen creator”.

But in another sense the multiverse is the simpler of the two inflation models. In a few lines of equations, or just a few sentences of speech, the multiverse gives us a mechanism to explain the origin of our universe, just as Charles Darwin’s theory of natural selection explained the origin of species. As Max Tegmark puts it: “Our judgment therefore comes down to which we find more wasteful and inelegant: many worlds or many words.”

To settle the issue, we will need to know more about what went down in the first split-second of the universe. Perhaps gravitational waves will be the answer, a way to ‘hear’ the vibrations of the big bang itself.

Whether infinite or finite, stand-alone or one of an endless multitude, the universe is surely a mindbending place. Which brings us back to *The Hitchhiker’s Guide to the Galaxy*: “If there’s any real truth, it’s that the entire multidimensional infinity of the Universe is almost certainly being run by a bunch of maniacs.”

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