  The string and brane tensions do not have to be put in by hand, they can be
dynamically generated, as in the case when we formulate string and brane
theories in the modified measure formalism. Then string and brane tensions
appears, but as an additional dynamical degree of freedom . It can be seen
however that these string or brane tensions are not universal, but rather each
string and each brane generates its own tension, which can have a different
value for each string or brane. We define a new background fields that can
couple to this new type of extended objects, the tension scalar is capable of
changing locally along the world sheet the value of the tension of the extended
object. When many 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 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 Einstein
equations and the consistency of these two Einstein equation determines the
tension scalar. The universal metric, common to both strings generically does
not satisfy Einstein equation . The problem is analyzed for Schwarzschild
background and for Kasner type space, for the Milne representation, for the
case of two types of string tensions, with solutions with negative string
tension at the early universe and a positive string tension that appears for
the late universe . The universal metric is not flat, instead it represents a
non singular bounce cosmology. The case in a warped space time where positive
and and negative string tensions are separated by a spontaneously generated
wall is also studied.
