当引力是动力学的时候，宇宙能改变时空符号吗？
Can the Universe Change Signature When Gravity is Dynamical?
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中文总结 AI 辅助
本文在标量-张量引力中研究动力学引力耦合下的时空符号转变，通过爱因斯坦框架构造解并施加Jordan框架全测地性，发现符号转变在爱因斯坦引力之外依然存在，且正则性与有效宇宙学行为对框架敏感。
中文摘要 AI 辅助
当一个引力耦合本身是动力学的时候，宇宙能否经历一个正则的欧几里得-洛伦兹时空符号转变？我们在具有非最小耦合$F(\phi)R$的标量-张量引力中探讨这个问题。尽管空间平坦的Friedmann-Lemaitre-Robertson-Walker（FLRW）扇区在$F>0$且标量场重新定义非退化的情况下可以映射到爱因斯坦框架，但并非所有转变性质都是框架无关的。对于有限、正且足够正则的共形因子，类型改变的存在性和横向特征得以保留，而外在几何则不然。因此，我们将爱因斯坦框架用作解生成表示，并在物理的Jordan框架中施加全测地性。我们构造了两类精确可积的解。在振子-鬼-振子分支中，标量场在转变处是静止的，且在共形因子的适当正则性假设下，Jordan框架的全测地性得以满足。在临界指数势分支中，标量场通常是非静止的，全测地性反而要求\begin{equation*} H_E\big|_\Sigma = \frac12 \left( \frac{d\ln F}{d\psi} \right)_\Sigma \dot\psi_\Sigma. \end{equation*} 我们还将此条件与Kossowski-Kriele型横向度量的更强光滑性要求区分开来。最后，虽然正则的爱因斯坦框架标量不允许有效的幻影演化，但当所选振子分支满足$\left(\frac{d\ln F}{d\psi}\right)_\Sigma>0$时，动力学非最小耦合可以在转变附近产生局部的超加速Jordan框架区域。因此，时空符号转变在爱因斯坦引力之外依然存在，其正则性和有效宇宙学行为本质上仍对框架敏感。
英文摘要
Can a universe undergo a regular Euclidean-Lorentzian signature transition when the gravitational coupling itself is dynamical? We address this question in scalar-tensor gravity with nonminimal coupling $F(ϕ)R$. Although the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) sector can be mapped to the Einstein frame for $F>0$ and a nondegenerate scalar redefinition, not all transition properties are frame independent. For a finite, positive, and sufficiently regular conformal factor, the existence and transverse character of the type change are preserved, whereas the extrinsic geometry is not. We therefore use the Einstein frame as a solution-generating representation and impose total geodesy in the physical Jordan frame. We construct two exactly integrable classes of solutions. In the oscillator-ghost-oscillator branch, the scalar field is stationary at the transition and Jordan-frame total geodesy follows under suitable regularity assumptions on the conformal factor. In the critical exponential-potential branch, the scalar is generically nonstationary and total geodesy instead requires \begin{equation*} H_E\big|_Σ= \frac12 \left( \frac{d\ln F}{dψ} \right)_Σ\dotψ_Σ. \end{equation*} We also distinguish this condition from the stronger smoothness requirements of a Kossowski-Kriele-type transverse metric. Finally, while the canonical Einstein-frame scalar does not allow effective phantom evolution, the dynamical nonminimal coupling can generate a locally superaccelerating Jordan-frame regime near the transition when $\left(\frac{d\ln F}{dψ}\right)_Σ>0$ for the chosen oscillator branch. Thus signature change persists beyond Einstein gravity, with regularity and effective cosmological behavior remaining intrinsically frame sensitive.
发表机构
- Bilkent University（比尔肯特大学）
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