SEMICLASSICAL (QUANTUM FIELD THEORY) AND QUANTUM (STRING) DE SITTER REGIMES: NEW RESULTS

We compute the quantum string entropy Ss(m, H) from the microscopic string density of states ρs(m, H) of mass m in de Sitter space–time. We find for high m (high Hm → c/α') a new phase transition at the critical string temperature Ts = (1/2πkB)Lcl c2/α', higher than the flat space (Hagedorn) temperature ts (Lcl = c/H, the Hubble constant H acts at the transition, producing a smaller string constant α' and thus, a higher tension). Ts is the precise quantum dual of the semiclassical (QFT Hawking–Gibbons) de Sitter temperature Tsem = ħ c/(2πkBLcl). By precisely identifying the semiclassical and quantum (string) de Sitter regimes, we find a new formula for the full de Sitter entropy Ssem(H), as a function of the usual Bekenstein–Hawking entropy . For Lcl ≫ lPlanck, i.e. for low is the leading term, but for high H near c/lPlanck, a new phase transition operates and the whole entropy Ssem (H) is drastically different from the Bekenstein–Hawking entropy . We compute the string quantum emission cross-section σstring by a black hole in de Sitter (or asymptotically de Sitter) space–time (bhdS). For Tsem bhdS l Ts (early evaporation stage), it shows the QFT Hawking emission with temperature Tsem bhdS (semiclassical regime). For Tsem bhdS → Ts, σstring exhibits a phase transition into a string de Sitter state of size , , and string de Sitter temperature Ts. Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega–Sanchez transition). New bounds on the black hole radius rg emerge in the bhdS string regime: it can become rg = Ls/2, or it can reach a more quantum value, rg = 0.365 ls.