How big is the universe?

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).

The
closed geometry would mean the Universe is finite,
while the other two would mean the Universe is,
theoretically, infinite.

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.{%recommended 5317%}

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. 

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.

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.”