Narrow Results

We propose a new type of cosmological model in which it is postulated that not only the temperature but also the curvature is limited by the mass scale of the Hagedorn temperature. We find that the big bang of this universe is smoothly connected to the big crunch of the previous universe through a Hagedorn universe, in which the temperature and curvature remain very close to their limiting values. In this way, we obtain the picture of a cyclic universe. By estimating the entropy gained in each big crunch and big bang, we reach the conclusion that our universe has repeated this process about forty times after it was created at the Planck scale. We also show that the model gives a scale-invariant spectrum of curvature perturbations.

Atick and Witten have proposed the Hagedorn transition of closed strings via condensation of 'winding tachyon'. But we have not known the stable minimum of this tachyon potential yet. On the other hand, we have previously shown that a phase transition occurs near the Hagedorn temperature and D9-brane– -brane pairs become stable. We present a conjecture that D9-brane– -brane pairs are created by the Hagedorn transition of closed strings. We will show some circumstantial evidences for this conjecture.

The string tension does not have to be put in by hand, it can be dynamically generated, as in the case when we formulate string theory in the modified measure formalism, and other formulations as well. Then string tension appears, but as an additional dynamical degree of freedom. It can be seen however that this string tension is not universal, but rather each string generates its own string tension, which can have a different value for each string. We also define a new Tension scalar background field which change locally the value of the string tension along the world sheets of the strings. When there are many strings with different string tensions this Tension field can be determined from the requirement of world sheet conformal invariance and for two types of string tensions depending on the relative sign of the tensions we obtain nonsingular cosmologies and warp space scenarios and when the two string tensions are positive, we obtain scenarios where the Hagedorn temperature is avoided in the early universe or in regions of warped space time where the string tensions become very big.