"The cyclic universe model is a simple mechanism for solving the cosmological constant problem"
The search for a single theory of everything has led scientists to propose a surprising, new and non-intuitive description of our Universe. Stephen Hawking and Thomas Hertog have just proposed a model based on the no-boundary hypothesis, in which the Universe is a closed surface and has no beginning in time .
Before the summer break, we interviewed Paul Steinhardt, physicist at the Department of Physics at Princeton University, USA, and co-author of a report published in Science in which he shows that the small and positive value of the cosmological constant, the vacuum energy, can be understood within a cyclic Universe model .
Paul Steinhardt, how would you define the cosmological constant?
The cosmological constant is a surname for what we call vacuum energy, the energy of empty space. What we mean by empty is without particle, radiation, or any object. There can still be energy, there can still be fields, like electric or magnetic fields, in it but all particles or objects are missing from it.
Even though itís empty, there can still be energy, and thatís what we call the cosmological constant.
Based on the observation, what have we learned about this cosmological constant?
The cosmological constant, because the value is so small, because it doesnít change with time, has almost no observable consequences, except for one thing: it affects the expansion of the Universe. If the vacuum energy is greater than all the other forms of energy, like the energy of the matter or radiation, then it causes the expansion of the Universe to speed up. This effect has been observed. When we look at the motion of distant galaxies compared to more nearby galaxies, we can observe that the expansion of the Universe has been speeding up the last 4 or 5 billion years. Thatís the sign that there is a small and positive vacuum energy.
Why is it so surprising?
We think we understand many of the things that contribute to the vacuum energy of the Universe. For example, we think there are quantum effects associated with gravity which contribute a certain amount to the cosmological constant. We can estimate what that quantity is, roughly. And we find that itís huge, enormously bigger than the cosmological constant that we actually observe, more than a googol times bigger (more than 10100 times bigger). Thatís one contribution. There are other contributions we know which have to do with the effects of the electromagnetic forces and the effects of the strong nuclear forces. They also contribute to the cosmological constant or vacuum energy. Not as much of the first contribution I mentioned, but maybe 1060 or 1040 of power, a huge, enormous amount, much bigger than what we actually observe. So the peculiar thing is that when we add up all these contributions, somehow, for reasons we donít understand, we end up with something which is very small. The different contributions must cancel to nearly perfection, more than a hundred decimal places, in order to explain the value we see.
In the past decades of effort to try to understand why that cancellation might occur, there have been no good ideas, no winning ideas.
What about the so called ďanthropic selectionĒ?
What physicists have tried to do over the decades is to find fundamental reasons why there would be this cancellation of these large contributions to the vacuum energy. And they had various ideas to doing it, but all these ideas have failed. A fall back idea that some had proposed in the past - but now it has become more popular as desperation has increased - has been the idea of anthropic selection. The idea of anthropic selection is that in the Universe as a whole, the cosmological constant is big, as big as you might guess based on these very large contributions. Maybe in most places of the Universe, itís large, but there maybe a few packets where itís small and those are the only places where we can live, because in places where the cosmological constant is big the expansion of the Universe is speeding up so much that you can never form galaxies and stars. So the idea is that the cosmological constant is small in very rare places in the Universe, and we happen to live in one of them because thatís central for our existence.
This idea has been around for a number of years. Most cosmologists didnít give it weight because it makes assumptions about part of the Universe that we can never see. However, interest in this idea has risen because of progress in string theory, which is an attempt to unify the fundamental forces of nature. String theory tends to give you various possibilities that the Universe might take in different regions and most of which will give you a large cosmological constant and only rare one which will give you a small cosmological constant. So the string theory sort of reengineered interest in anthropic selection.
In your report  you propose an alternate explanation for the smallness of the cosmological constantÖ
Our idea is the melding of an older idea and a new idea. An idea that people talked about before was what we call ďrelaxationĒ. As we said before, there are many things that contribute to the vacuum energy: quantum gravity, strong nuclear forces, magnetic forcesÖ Some of those contributions are constant. They donít change with time. If there were some contributions that did change with time, when you summed up the whole thing, the whole thing would be changing with time. So the idea of relaxation is to say that although there are many contributions that we know are constants, there might be yet another contribution which is actually slowly decreasing in time. And when you add them all up, its effect acts to slowly cancel the contributions from the constant pieces that we know have to be there. People had this idea Ė particularly 25 years ago people were playing with this idea Ė but they had a problem. Relaxation process tends to be so slow that by the time the cosmological constant gets small, the Universe is nearly empty. It contains no galaxies or stars. So they gave it up.
Now we come to more recent idea, the idea of what we call the cyclic Universe. The reason why the process was too slow is because people were thinking about a standard big bang Universe, where the Universe was born in a big bang 14 billion years ago. So you only had 14 billion years to make the cosmological constant relax from the large value that you would expect to the small value that you actually observe.
Recently, Dr. Turok, from Cambridge University and I have explored the idea of a cyclic Universe, one of which the bang is not the beginning of space and time but is really a distant event in which a lot of matter and radiation is created and a new period of expansion and cooling takes place. Every trillion years or so thereís a bang that creates new matter and radiation followed with a period of expansion and cooling. This repeats itself maybe forever in the past, we donít really know, it could be a very long time in the past. In this picture, the first thing we have, which is essential, is that Universe is much older. So now, we can begin to think of the idea that the cosmological constant is relaxing slowly with time, but we have much more time than we imagined. But you donít want the Universe to be empty. It doesnít happen in the cyclic model because every trillion years, itís creating new matter and radiation which make new galaxies and stars. So even if the cosmological constant takes a very long time to relax, if youíre patient and wait long enough, eventually, it will reach a value which is small and positive like we observe it today, and yet thereíre also galaxies and stars.
There are various ways you can get this slowly relaxing cosmological constant. We actually took an idea that L. Abbott proposed 20 years ago . Itís a nice idea because the way the relaxation works in his model is that as the cosmological constant gets smaller, the Universe spends more and more time at each value. So the cosmological constant is initially big but the Universe doesnít spend much time in this state, it spends almost all the time when the cosmological constant is small and positive, in accordance with what we see today.
Is this cyclic universe hypothesis widely accepted?
Itís a new idea. I think most cosmologists today still believe in the standard big bang model with addition of inflation, which make the Universe smooth and flat, and with the addition of dark energy to explain its expansion. However, the basis on which they make that decision is because that theory agrees with observation, and the cyclic model that weíve been developing turns out also to agree to the same observations. So if, based on the observations alone, you really canít tell from what we know at present which of these 2 models is correct.
Now the 2 ways to separate them are : 1/ to make an observation that can distinguish them. Weíve been studying different kinds of observation one can do in the future that might distinguish them. 2/ to see if you can use one of them to explain certain pictures of the Universe which the other one can not explain. Thatís where we come to the cosmological constant. Itís very important and interesting that the cyclic model is a simple mechanism for solving the cosmological constant problem, and that mechanism couldnít work in the standard model. And the key reason being because of this difference in how old the Universe is - the cyclic Universe being very old and the standard model Universe being only 14 billion years old. So itís interesting that this difference relies precisely on the key difference between the 2 conceptual pictures.
What are the next steps now?
First of all, weíd like to elaborate a relaxation mechanism so that we can understand whether or not one can get this mechanism out of a larger framework like string theory in a natural way. Weíd like to look for more clues of the cyclic model, I mean to test the cyclic model hypothesis versus the standard big bang inflationary picture. Weíd like to understand more clearly what happens at each of the big bangs that occur in our model.
Finally, what this new idea of the cosmological constant suggests is that by having a Universe which is much older, you can solve fine-tuning problems which before neither the big bang inflationary picture nor the original cyclic model could explain. There are other fine-tuning problems which are not explained at the moment, and we were thinking about whether or not they can be explained by actually the same idea. For example we donít understand why the ratio of matter to antimatter in the Universe is as it is, why there is much more matter than antimatter. We know itís crucial for our existence, but we donít understand why it has that particular ratio. We donít understand the ratio of dark matter to ordinary matter, and we donít understand neither the ratio of the dark energy to dark matter and to ordinary matter. Thereíre various things we donít understand in either models, and one might be able to use the same idea of a sort of gradual relaxation to solve all of them, to show how they might be related to one another, and that would be a very exciting and elegant idea.
Paul Steinhardt, thank you.
 Hawking, S.W. & Hertog, T., Phys. Rev. D 73, 123527 (2006)
 Steinhardt, P.J. & Turok, N., Science 312, 1180 (2006)
 Abbott, L. Phys. Lett. B 150, 427 (1985)
Paul Steinhardt is a physicist at the Department of Physics at Princeton University, USA.
Interview by Gilles Prigent
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