Atick-Witten Hagedorn Conjecture, near scale-invariant matter and blue-tilted gravity power spectrum

We will provide an interesting new mechanism to generate almost scale invariant seed density perturbations with a red spectrum, while keeping the gravitational wave spectrum blue-tilted in a stringy thermal contracting phase at temperatures beyond the Hagedorn temperature. This phase is often referred to as the Hagedorn phase where the free energy has been conjectured by Atick and Witten to grow more slowly than ordinary radiation. The primordial fluctuations are created by the statistical thermal fluctuations determined by the partition function, rather than quantum vacuum driven fluid dynamical fluctuations. In order for our mechanism to work we require a non-singular bouncing cosmology.