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arXiv 0908.1881hep-th
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弦热有效势的宇宙相

Cosmological Phases of the String Thermal Effective Potential

Francois Bourliot, John Estes, Costas Kounnas, Herve Partouche

摘要:

在超弦框架中,一旦超对称性通过几何通量自发破缺,自由能量密度F可以在全弦水平上明确地确定。我们明确地表明,只有与超对称性破缺相关的模量可能给出相关的贡献。对于相对较小的温度T和超对称破缺尺度M,所有其他旁观者模量μ_I都给出指数抑制的贡献。更简洁地说,对于μ_I > T和M,F具有F(T,M; μ_I)=F(T,M)+O[exp(- {μ_I \over T}),exp(- {μ_I \over M})]我们研究了T和M低于Hagedorn温标T_H的宇宙学体系.在这种情况下,F对旁观者模μ_I的任何值都是有限的。我们广泛地研究了内部紧化维数的半径模场R_d对应于一个旁观者模μ_d的情形。我们发现,它的热有效势承认五个阶段,每一个可以描述一个独特的,但不同的有效场论。在宇宙学晚期,宇宙被吸引到一个“类辐射演化”,M(t)~ T(t)~ 1/a(t)~ t^{-2/d}。旁观者模量μ(t)要么稳定在弦增强对称点R_d=1,要么固定在任意常数μ_0>T,M。对于任意的边界条件,在某个初始时刻,t_E,μ(t)在最终吸引之前可能经过不止一个有效场论阶段。

英文摘要:

In a superstring framework, the free energy density, F, can be determined unambiguously at the full string level once supersymmetry is spontaneously broken via geometrical fluxes. We show explicitly that only the moduli associated to the supersymmetry breaking may give relevant contributions. All other spectator moduli μ_I give exponentially suppressed contributions for relatively small (as compared to the string scale) temperature, T, and supersymmetry breaking scale, M. More concisely, for μ_I > T and M, F takes the form F(T,M; μ_I)=F(T,M)+O[exp(- {μ_I\over T}), exp(- {μ_I\over M})] We study the cosmological regime where T and M are below the Hagedorn temperature scale T_H. In this regime, F remains finite for any values of the spectator moduli μ_I. We investigate extensively the case of one spectator modulus μ_d corresponding to R_d, the radius-modulus field of an internal compactified dimension. We show that its thermal effective potential admits five phases, each of which can be described by a distinct but different effective field theory. For late cosmological times, the Universe is attracted to a "Radiation-like evolution" with M(t) ~ T(t)~ 1/a(t)~ t^{-2/d}. The spectator modulus μ(t) is stabilized either to the stringy enhanced symmetry point where R_d=1, or fixed at an arbitrary constant μ_0>T,M. For arbitrary boundary conditions at some initial time, t_E, μ(t) may pass through more than one effective field theory phase before its final attraction.

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