发表机构
Instituto de Física Teórica, Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从两个视角研究AdS和dS时空中标量场的半经典反作用，发现有效宇宙学常数形式为Λ_eff=A/ℓ²+B/ℓ⁴，且解析延拓ℓ→iℓ不能正确映射量子贡献，表明半经典反作用依赖全局信息。
AI 中文摘要
我们从两个互补的视角研究了四维反德西特（AdS）和德西特（dS）时空中量子化标量场的半经典反作用。首先，我们确定了自洽场参数，使得在裸宇宙学常数固定为其经典几何值的情况下，给定的几何结构仍然是精确解。其次，我们保留规定背景上的重整化真空应力-能量张量，并研究其对有效宇宙学常数的贡献。在AdS中，自洽解依赖于允许的边界条件，而相应的dS解是在Bunch-Davies态中获得的，揭示了对全局和态依赖信息的敏感性。对于无质量构型，有效宇宙学常数采取普遍形式 $\Lambda_{\rm eff}=A/\ell^{2}+B/\ell^{4}$，从而可以比较经典贡献和量子贡献，并识别它们相对重要性发生变化的特征曲率尺度。然后，我们通过形式延拓 $\ell\rightarrow i\ell$ 检验AdS与dS之间的经典关系是否延伸到量子层面。尽管经典曲率项被正确映射，但量子贡献并非如此：对于最小耦合，AdS和dS系数之比为 $29/61$，而对于共形耦合，它们具有相等的大小和相反的符号。这些差异表明，半经典反作用并非仅由局部曲率决定，而是保留了关于量子态、边界条件和全局结构的信息。这些结果阐明了解析延拓作为AdS和dS半经典量子理论之间映射的局限性。
英文摘要
We investigate semiclassical backreaction of a quantized scalar field in four-dimensional anti-de Sitter (AdS) and de Sitter (dS) spacetimes from two complementary perspectives. First, we determine self-consistent field parameters for which the prescribed geometry remains an exact solution with the bare cosmological constant fixed to its classical geometric value. Second, we retain the renormalized vacuum stress--energy tensor on the prescribed background and study its contribution to the effective cosmological constant. In AdS, the self-consistent solutions depend on the admissible boundary conditions, while the corresponding dS solutions are obtained within the Bunch--Davies state, revealing sensitivity to global and state-dependent information. For massless configurations, the effective cosmological constant takes the universal form $Λ_{\rm eff}=A/\ell^{2}+B/\ell^{4}$, allowing comparison of classical and quantum contributions and identification of the characteristic curvature scales at which their relative importance changes. We then test whether the classical relation between AdS and dS extends to the quantum level through the formal continuation $\ell\rightarrow i\ell$. Although the classical curvature term is mapped correctly, the quantum contribution is not: for minimal coupling the AdS and dS coefficients are in the ratio $29/61$, while for conformal coupling they have equal magnitude and opposite sign. These discrepancies show that semiclassical backreaction is not determined by local curvature alone, but retains information about the quantum state, boundary conditions, and global structure. The results clarify the limitations of analytic continuation as a map between the semiclassical quantum theories of AdS and dS.
Comments27 pages, 3 figures
