Escaping the Hagedorn Temperature in Cosmology and Warped Spaces with Dynamical Tension Strings

In the modified measure formulation the string tension appear as an additional dynamical degree of freedom and these tensions are not universal, but rather each string generates its own tension, which can have a different value for each string. We consider new background field that can couple to these strings, the tension scalar is capable of changing locally along the world sheet the value of the tension of the extended object. When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For the case of two types of strings probing the same region of space with different dynamically generated tensions, there are two different metrics, associated to the different strings, that have to satisfy vacuum Einsteins equations and the consistency of these two equation determines the tension scalar. In a previous paper we studied solutions that completely avoid singularities, but with positive and negative tensions strings. In this paper we will consider only positive tension strings for the cosmological case and for warped space time . In both of these cases there is a region where the string tensions approach infinity, in the cosmological case this takes place in the early universe while in the warped case, for some value of the warping coordinate and since the Hagedorn temperature is proportional the the string tension, we get this way string scenarios with no limiting Hagedorn temperature in the early universe and this opens the possibility of a string cosmology without a Hgedorn phase transition through all of its history . Similar situation can take place in a warped space time, for this case, assuming the string have a tendency to avoid regions with lower Hagedorn temperature, we obtain a mechanism for condensation of strings into a surface at high temperatures.