AI 中文总结
本文研究双度量宇宙学模型，利用随时间变化的α(t)关联不同度量，分析其动力学引力参数、奇点性质及引力减弱的物理效应，为共形循环宇宙学及标量-张量引力理论研究提供了新的动机。
AI 中文摘要
我们研究一种双度量宇宙学模型，其中引力和物质部分由不同的度量描述，二者通过随时间变化的函数α(t)关联。这种关联导致引力参数具有动力学特性，其中G(t)∝α⁻³，c_grav(t)∝α⁻¹，c_grav表示引力相互作用的传播速度。我们考虑一类解，在有限宇宙时间处α→∞，导致G→0且c_grav→0。对于一个解析可处理的解，我们证明最终奇点出现在有限共形时间处，且具有与连续宇宙学周期之间可能过渡相容的共形结构。Tipler和Królak准则表明该奇点是强奇点。我们进一步讨论引力相互作用减弱的物理后果，包括引力束缚结构的瓦解和黑洞视界的收缩。这些效应表明存在一种可能的机制，可导向有效辐射主导的最终状态，这可能与共形循环宇宙学相关。研究结果为将分析扩展到更一般的标量-张量引力理论提供了动机。
英文摘要
We investigate a bimetric cosmological model in which the gravitational and matter sectors are described by distinct metrics related through a time-dependent function $α(t)$. This relation leads to dynamical gravitational parameters, with $G(t)\proptoα^{-3}$ and $c_{\rm grav}(t)\proptoα^{-1}$, where $c_{\rm grav}$ denotes the propagation speed of gravitational interactions. We consider a class of solutions for which $α\rightarrow\infty$ at a finite cosmic time, resulting in $G\rightarrow0$ and $c_{\rm grav}\rightarrow0$. For an analytically tractable solution, we show that the final singularity occurs at finite conformal time and possesses a conformal structure compatible with a possible transition between successive cosmological cycles. The Tipler and Królak criteria indicate that the singularity is strong. We further discuss the physical consequences of the weakening gravitational interaction, including the dissolution of gravitationally bound structures and the shrinking of black-hole horizons. These effects suggest a possible mechanism leading toward an effectively radiation-dominated final state, which may be relevant for Conformal Cyclic Cosmology. The results provide a motivation for extending the analysis to more general scalar--tensor theories of gravity.
