Following a talk by Cumrum Vafa, I understood that light branes are important as he quoted the formula: $$m\sim \exp(-\alpha M/M_P)$$ and then, he stated that light massive particles AND extended objects (particle/p-brane species) are produced as we get $M>M_P$, where $M_P$ is the Planck mass. However, in Cosmology, we are commonly said that masses or arbitrarily number of states are not allowed since they would cause the Universe to collapse. Why light p-branes are not "problematic" for Cosmology? And secondly, is the above formula something related to Schwinger effect in string theory? Where does that formula comes from?
Extra clarification: what motivated my question is the fact that arXiv:1603.04583 shows the rate is, instead the formula by Vafa (I think they are similar but not the same): $\Gamma\sim\exp(-M_P^2/M_{3/2})$
Comment: it also remembers me the Hagedorn transition in string theory, but it is not the same at first sight!