The Universe Within (17 page)

A beautiful feature of the Hartle–Hawking proposal is that it does not impose an arbitrary initial condition on the laws of physics. Instead, the laws themselves define their own quantum starting point. According to the Hartle–Hawking proposal, the universe can start out with
any
value for the inflationary energy. Their proposal predicts the probability for each one of these possible starting values. It turns out that this calculation agrees with the estimate of gravitational entropy I mentioned earlier: the probability of getting realistic inflationary initial conditions is around one in 10 to the power of 10 to the power of 120. The most probable starting point, by far, is the one with the smallest possible value of the inflationary energy, that is, today's vacuum energy. There would be no period of inflation, no matter or radiation. Hartle and Hawking's proposal is a wonderful theory, but at least in the most straightforward interpretation, it predicts an empty universe.

Hartle and Hawking and their collaborator Thomas Hertog, of the University of Leuven, propose to avoid this prediction by invoking the “anthropic principle” — the idea that one should select universes according to their ability to form galaxies and life.

It is not a new notion that the properties of the universe around us were somehow “selected” by the fact that we are here. The idea has grown increasingly popular as theory has found it more and more difficult to explain the specific observed properties of the universe. The problem is that the anthropic arguments are vague: in order to make them meaningful, one needs a theory of the set of possible universes and also the precise condition for us to be located in one of them. Neither of these requirements are yet close to being met. Nevertheless, Hartle, Hawking, and Hertog argue that even if
a priori
an empty universe is the most likely, the predictions of the Hartle–Hawking proposal, supplemented by anthropic selection, are consistent with what we observe. In principle, I have no objection to this kind of argument, as long as it can really be carried through.

However, a realistic universe like ours has a minuscule
a priori
probability in this setup, of one in 10 raised to the power of 10 raised to the power of 120 (the same tiny number mentioned earlier). Anthropic selection has to eliminate
all
of the other possible universes, and this seems an extremely tall order. A universe in which ours was the only galaxy, surrounded by empty space, would seem to be quite capable of supporting us. And, according to the Hartle–Hawking proposal, it would be vastly more likely than the universe we observe, which is teeming with galaxies (Hartle, Hawking, and Hertog exclude such a universe by
fiat
in their discussion). When the
a priori
probabilities are so heavily stacked against a universe like ours, as they are with the Hartle–Hawking proposal, it seems to me very unlikely that anthropic arguments will save the day.

A THEORY THAT PREDICTS
a universe like ours
a priori
, without any need for anthropic selection, would seem vastly preferred. Even if anthropic selection
could
rescue Hartle and Hawking's theory (which seems to me unlikely), the non-anthropic theory would be statistically favoured over the anthropic one by a huge factor, of 10 raised to the power of 10 raised to the power of 120.

For the past decade, with Paul Steinhardt of Princeton University and other collaborators, I have been trying to develop such theories as an alternative to inflation. Our starting point is to tackle the big bang singularity. What if it was not the beginning of time, but instead was a gateway to a pre–big bang universe? If there was a universe like ours before the singularity, could it have directly produced the initial ball of light, and if it did, would there be any need for a period of inflation?

Most of the universe today is very smooth and uniform on scales of a millimetre, and we have no problem understanding why. Matter and radiation tend to spread themselves out through space, and the vacuum energy is completely uniform anyway. Let us imagine following our universe forward into the future. The galaxies and all the radiation will be diluted away by the expansion: the universe will become a cold, empty place, dominated by the vacuum energy. Now imagine that for some reason the vacuum energy is not absolutely stable. It could start to slowly decay, tens of billions of years into our future. We can easily build mathematical models where it declines in this way, becoming smaller and smaller and then going negative. Its repulsive gravity would become attractive, and the universe would start to collapse.

When we studied this idea, we discovered that the pressure of the unstable energy would become large and positive, and it would quickly dominate everything else. As the universe collapsed, this large positive pressure would quickly make the universe very smooth and flat.When the universe shrunk down to zero size, it would hit a singularity. Then, plausibly, the universe would rebound, fill with radiation, and start expanding again. In fact, immediately after the bounce we would have conditions just like those in our millimetre-sized ball of light: the very initial conditions that were needed to explain the hot big bang.

Much to our surprise, we found that during the collapse initiated by the unstable vacuum energy, our high-pressure matter develops quantum variations of exactly the form required to fit observations. So in this picture, we can reproduce inflationary theory's successes, but with no need for initial inflationary conditions.

Our scenario is far more ambitious than inflation in attempting to incorporate and explain the big bang singularity. We have based our attempts on M-theory, a promising but still developing framework for unifying all the laws of physics. M-theory is the most mathematical theory in all of physics, and I won't even try to describe it here.

Einstein used the mathematics of curved space to describe the universe. M-theory uses the same mathematics to describe everything
within
the universe as well. For example, string theory, which is a part of M-theory, describes a set of one-dimensional universes — pieces of string — moving within higher-­dimensional space. Some strings describe force-carrier particles like photons, gluons, or gravitons, while others describe matter particles like electrons, quarks, or neutrinos. As well as strings,
M-theory includes two-dimensional universes, called “membranes,” and three-dimensional universes, called “3-branes,” and so on. According to M-theory, all of these smaller universes are embedded within a universe with ten space dimensions and one time dimension, which seems more than rich enough to contain everything we see.

In the best current versions of M-theory, three of the ten space dimensions — the familiar dimensions of space — are very large, while the remaining seven are very small. Six of them are curled up in a tiny little ball whose size and shape determine the pattern of particles and forces we see at low energies. And the seventh, most mysterious dimension, known as the “M-theory dimension,” is just a tiny gap between two three-dimensional parallel worlds.

Until our work, most M-theorists interested in explaining the laws of particle physics today had assumed that all the extra, hidden dimensions of space were static. Our new insight was to realize that the extra dimensions could change near the big bang, and that the higher-dimensional setting would cast the big bang singularity in a new light.

What we found was that, according to M-theory, the big bang was just a collision between the two three-dimensional worlds living at the end of the M-theory dimension. And when these worlds collide, they do
not
shrink to a point — from the point of view of M-theory, the three-dimensional worlds are like two giant parallel plates running into each other. What our work showed was that, within M-theory, the big bang singularity was, after all, not as singular as it might first appear, and most physical quantities, like the density of matter and radiation, remain completely finite.

Recently, we have discovered another, very powerful way to describe how the universe passes through the singularity, which turns out not to rely on all the details of M-theory. The trick uses the same idea of imaginary time which Hartle and Hawking used to describe the beginning of spacetime. But now we use imaginary time to circumvent the singularity, passing from a pre-bang collapsing universe to a post-bang expanding universe like the one we see today. We are close to finding a consistent and unique description of this process and to opening a new window on the pre-bang world.

If the universe can pass through a singularity once, then it can do so again and again. We have developed the picture into a cyclic universe scenario, consisting of an infinite sequence of big bangs, each followed by expansion and then collapse, with the universe growing in size and producing more and more matter and radiation in every cycle. In this picture of the universe, space is infinite and so too is time: there is no beginning and there is no end. We called this an “endless universe.”
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A cyclical universe model may, in its evolution, settle down to a state in which it repeats the same evolution, in its broad properties, over and over again. In this way, the vast majority of space would possess the physical properties of the universe we see. There would be no need for anthropic arguments, and the theoretical predictions would be clearer.

IF THERE IS ONE
rule in basic physics, I would say it is “in the long run, crime does not pay.” Cosmology in the twentieth century was, by and large, based on ignoring the big bang singularity. Yet the singularity represents a serious flaw in the theory, one which it is possible to ignore only by making arbitrary assumptions, which, in the end, may have little foundation. By continuing to ignore the singularity, we are in danger of building castles of sand. The singularity may just be our greatest clue as to where the universe really came from. Our work on the cyclic universe model has shown that all of the successes of the inflationary model can be reproduced in a universe that passes through the singularity without undergoing any inflation at all.

The competition between the cyclic and inflationary universe models highlights one of the most basic questions in cosmology: did the universe begin? There are only two possible answers: yes or no. The inflationary and cyclic scenarios provide examples of each possibility. The two theories could not be more different: inflation assumes a huge burst of exponential expansion, whereas the cyclic model assumes a long period of slow collapse. Both models have their weak points, mathematically, and time will tell whether these are resolved or prove fatal. Most exciting, the models make different observational predictions which can be tested in the not-too-distant future.

At the time of writing, the European Space Agency's Planck satellite is deep in space, mapping the cosmic background radiation with unprecedented precision. I have already discussed how inflation can create density variations in the universe. The same mechanism — the burst of inflationary expansion — amplifies tiny quantum gravitational waves into giant, long-wavelength ripples in spacetime, which could be detectable today. One of the Planck satellite's main goals is to detect these very long wavelength gravitational waves though their effects on the temperature and polarization of the cosmic background radiation across the sky. In many inflationary models, including the simplest ones, the effect is large enough to be observed.

Throughout his career, Stephen Hawking has enjoyed making bets. It's a great way of focusing attention on a problem and encouraging people to think about it. When I gave my first talk on the cyclic model in Cambridge, I emphasized that it could be observationally distinguished from inflation because, unlike inflation, it did
not
produce long wavelength gravitational waves. Stephen immediately bet me that the Planck satellite would see the signal of inflationary gravitational waves. I accepted at once, and offered to make the bet at even odds for any sum he would care to name. So far we haven't agreed on the terms, but we will do so before Planck announces its result, which may be as soon as 2013. Another leading inflationary theorist, Eva Silverstein of Stanford University, has agreed to a similar, though more cautious bet: the winner will get either a pair of ice skates (from me, in Canada) or a pair of rollerblades (she being from California).

· · ·

LOOKING BACK OVER PAST
millennia, we have to feel privileged to be alive at a time when such profound questions about the universe are being tackled, and when the answers seem finally within reach. In ancient Greece, there was a debate that in many ways prefigured the current inflationary/cyclic competition. Parmenides of Elea held the view — later echoed by Plato — that ideas are real and sensations are illusory, precisely the opposite of the views later espoused by David Hume. If thought is reality, then anything one can conceive of must exist. Parmenides reasoned that since you cannot think of something not existing without first thinking of the thing itself, then it is logically impossible for anything to come into existence. Hence he believed all change must be an illusion: everything that happens must already be implicit in the world. This is a fairly accurate description of Hartle and Hawking's “no boundary” proposal. To work out the predictions of their proposal, one works in “imaginary time” — in the primordial, quantum region of spacetime where everything that happens subsequently in the universe is implicit, and one continues the predictions into real time to see what they mean for today's observations.

On the other hand, Heraclitus of Ephesus, like Anaximander before him, held the opposite point of view. “All is flux” was his dictum: the world is in constant tension between its opposing tendencies. Everything changes and nothing endures. The goal of philosophy, he argued, is to understand how things change, both in society and in the universe. Starting with Zeno, the Stoic philosophers introduced the concept of
ekpyrosis
, meaning “out of fire,” to describe how the universe begins and ends in a giant conflagration, with a period of normal evolution in between. In his treatise
On the Nature of the Gods
, Cicero explains, “There will ultimately occur a conflagration of the whole world . . . nothing will remain but fire, by which, as a living being and a god, once again a new world may be created and the ordered universe restored as before.”
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There were similar ideas in ancient Hindu cosmology, which presented a detailed cyclic history of the universe.