Ultimate Temperature and the Early Universe

Abstract

The early history of the universe is disc density of particle states.

Hagedorn inflation of D-branes

“…From here we get the standard result [3,4]. We have (2.14) in D effectively non-compact space-time dimensions, and 2.15) in an effectively compact space.…”

“…If not then the system is said to be non-limiting. Already the simple canonical ensemble above indicates that the Hagedorn temperature is a limiting temperature for the b ≤ 2 cases [3]. The remaining systems seem to be non-limiting, and until recently it was thought that this might imply some kind of Hagedorn phase transition (drawing strongly on the analogy with the quark-hadron phase transition) to more fundamental degrees of freedom.…”

“…Thus we are generally prohibited from examining the NL systems since adjacent patches will not be in equilibrium. 3 The random walk argument proceeds as before with one change. The factor that corrects for the translation of the walk in the excluded volume is not V /W but rather V /W for the L[-1] system.…”

“…To date applications of this phase have been quite limited in string cosmology [3] because the thermodynamics is governed by the finite temperature partition function. A rigorous analysis therefore requires nothing less than solving the string system in a cosmological setting, a difficult problem that might at best be tractable only in a few special cases.…”

“…At sufficiently high temperatures and densities fundamental strings enter a curious 'long string ' Hagedorn phase [2,3,4,5,6,7]. To date applications of this phase have been quite limited in string cosmology [3] because the thermodynamics is governed by the finite temperature partition function.…”