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Where does string theory fit in?

   A big complicating factor in understanding string cosmology is understanding string theories. String theories and M theory appear to be limiting cases of some bigger, more fundamental theory. Until that's sorted out, anything we think we know today is potentially up for grabs.
   That being said, there are some basic issues in string theory cosmology:

1. Can string theory make any cosmological predictions relevant to Big Bang physics?
2. What happens to the extra dimensions?
3. Is there Inflation in string theory?
3. What can string theory tell us about quantum gravity and cosmology?

Low energy string cosmology

   Most of the mass in our Universe appears to occur in the form of dark matter. One leading candidate for the composition of this dark matter is something called a WIMP, a Weakly Interacting Massive Particle. One strong candidate for the WIMP comes from supersymmetry.
   The Minimal Supersymmetric Standard Model (MSSM) predicts the existence of spin 1/2 fermions called neutralinos that are the fermionic superpartners of the neutral gauge bosons and Higgs scalars. Neutralinos would have a high mass but interact very weakly with other particles. They could make up a significant portion of the mass density of the Universe without emitting light, so that makes them good candidates for the mysterious source of dark matter in the Universe.
   String theories require supersymmetry, so in principle, if neutralinos were discovered to make up cosmic dark matter, that would be good. But if supersymmetry were unbroken, fermions and bosons would be exactly matched in the Universe, and that's not the way things are. The really hard part of any supersymmetric theory is to break the supersymmetry without losing all the advantages of having had the supersymmetry to begin with. (It's very much one of those proverbial cake situations.)
    One of the reasons particle and string physicists have liked supersymmetric theories is that they predict zero total vacuum energy, because the fermion and boson vacuum energies cancel each other out. When supersymmetry is broken, the fermions and bosons don't exactly match any more, the cancellation doesn't occur any more.
   There seems to be pretty good evidence from the red shifts of distant supernovae that the expansion of our Universe is accelerating due to something like a vacuum energy or a cosmological constant. So whatever path by which supersymmetry is broken in string theory needs to lead at the end to the right amount of vacuum energy to account for this observed acceleration. This is a theoretical challenge, because supersymmetry breaking seems to give too large a contribution.

Cosmology and extra dimensions

   Superstring cosmology is enormously complicated by the presence of those pesky six (or seven in the case of M theory) extra space dimensions that are required for quantum consistency of the theory. Extra dimensions that just sit there are challenging enough to deal with in string theory, but in the framework of cosmology, the extra dimensions are evolving in time according to the physics of the Big Bang and whatever happened before it. So what keeps the extra dimensions from expanding to get as big as the three space dimensions that we observe and measure in our Universe?
   But wait - there's a complicating factor to the complicating factor: a superstring duality symmetry known as T duality. When a space dimension is rolled up in a circle of radius R, the resulting string theory ends up being equivalent to another string theory with a space dimension rolled up in a circle of radius Lst2/R, where Lst is the string length scale. For many of these theories, when the extra dimension radius R satisfies the condition R = Lst, the string theory has an enhanced symmetry with some massive particles becoming massless. This is called the self dual point and has special significance for many reasons.
   This duality symmetry has led to an interesting proposal for pre-Big Bang cosmology where the stringy Universe starts out flat, cold and very large instead of curved, hot and very small. This early Universe is unstable and starts to collapse and contract until it reaches the self dual point, where it heats up and starts to expand to give the expanding Universe we observe today. One advantage to this model is that it incorporates the very stringy behavior of T duality and the self dual point, so it is a very inherently stringy cosmology.

Inflation vs. the giant brane collision

   What does string theory predict for the source of the vacuum energy and pressure necessary to drive the inflationary period of accelerating expansion? Scalar fields that could inflate Universe at GUT scale could also be involved in breaking supersymmetry at just above electroweak scale, determining coupling strengths of gauge fields, and maybe even providing the vacuum energy for a cosmological constant. String theory contains the ingredients to build models with supersymmetry breaking and inflation or quintessence, but the trick is to get all the ingredients to work together, and that is still, as they say, an active area of research.
   A current alternative model to inflation is the giant brain collision model, also known as the Ekpyrotic Universe, or the Big Splat. This intriguing model starts out with a cold, static five-dimensional spacetime that is close to being perfectly supersymmetric. The four space dimensions are bounded by two three-dimensional walls or three branes, and one of those three-dimensional walls makes up the space that we live on. The other brane is hidden from our perception.
   According to this theory, there is a third three brane loose between the two bounding branes of the four dimensional bulk, and when this brane hits the brane we live on, the energy from the collision heats up our brane and the Big Bang occurs in our visible Universe as described elsewhere in this site.
   This proposal is quite new, and it remains to be seen whether it will survive careful scrutiny.

The problem with acceleration

   There is a problem with an accelerating Universe that is fundamentally challenging to string theory, and even to traditional particle theory. In eternal inflation models and most quintessence models, the expansion of the Universe accelerates indefinitely. This indefinite acceleration leads to situation where a hypothetical observer traveling forever through the Universe will be eternally blocked from seeing any evidence of most of the Universe.
   The boundary of the region beyond which an observer can never see is called that observer's event horizon. In cosmology, the event horizon is like the particle horizon, except that it is in the future and not in the past.
   From the point of view of human philosophy or the internal consistency of Einstein's theory of relativity, there is no problem with a cosmological event horizon. So what if we can't ever see some parts of the Universe, even if we were to live forever?
   But a cosmological event horizon is a major technical problem in high energy physics, because of the definition of relativistic quantum theory in terms of the collection of scattering amplitudes called the S Matrix. One of the fundamental assumptions of quantum relativistic theories of particles and strings is that when incoming and outgoing states are infinitely separated in time, they behave as free noninteracting states.
   But the presence of an event horizon implies a finite Hawking temperature and the conditions for defining the S Matrix cannot be fulfilled. This lack of an S Matrix is a formal mathematical problem not only in string theory but also in particle theories.
   One recent attempt to address this problem invokes quantum geometry and a varying speed of light. This remains, as they say, an active area of research. But most experts doubt that anything so radical is required.


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