引力热理论：从早期暗能量到各类引力现象
Gravitational caloric theory: From early dark energy to a wide variety of gravitational phenomena
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中文总结 AI 辅助
本研究提出广义相对论延伸理论引力热理论（GCT），其含与流体非最小耦合的矢量场$S_μ$，可解决早期暗能量巧合问题，还能提供暴胀替代方案并适配强场等多类引力场景。
中文摘要 AI 辅助
我们提出引力热理论（gravitational caloric theory, GCT）——这是广义相对论的一种延伸，其核心特征是存在一个矢量场$S_μ$，该场由流体部分提供源并与流体部分非最小耦合，同时保持标准流体能量-动量张量的协变守恒。我们的最初动机是利用编码了宇宙辐射-物质转变的总流体状态方程来触发早期暗能量（early dark energy, EDE），这一机制为EDE的巧合问题提供了自然的解决方案。我们通过将演化方程转化为动力系统形式，并在相关的简化情形下使用庞加莱紧化来揭示对应的全局相空间结构，详细分析了宇宙学背景动力学。除EDE之外，GCT还拥有两种与无穷远临界点相关的全新宇宙学应用，二者均源自一类能量抵消解——在这类解中，常规能量组分优先激发$S_μ$，而非为时空曲率提供源。其中一种是Λ抵消解，它可实现针对旧宇宙学常数问题的自调节机制，但目前仍不完善。另一种是流体抵消解，它是我们提出的“早期静态热宇宙”的基础。在该情形下，$S_μ$抵消了普通热气体的引力效应，产生了准静态膨胀，且伴随共动哈勃半径减小，能够解决视界问题，为暴胀提供了替代方案。此外，其“热”的特性将该情形与其他准静态早期宇宙模型区分开来，并且可能在原初涨落中留下可观测的特征。为了探究GCT在宇宙学之外的可行性，我们进一步分析了闵可夫斯基时空的线性微扰，并研究了静态球对称（强场）系统。（摘要因arXiv篇幅限制有所删减。）
英文摘要
We propose gravitational caloric theory (GCT) --- an extension of general relativity that features a vector field $S_μ$ sourced by and non-minimally coupled to the fluid sector while preserving covariant conservation of the standard fluid energy-momentum tensor. Our initial motivation is to trigger early dark energy (EDE) using the total fluid equation of state that encodes the cosmic radiation-matter transition. This mechanism provides a natural resolution of the EDE coincidence problem. The cosmological background dynamics are analyzed in detail by casting the evolution equations into dynamical-system form and, in relevant reduced cases, using Poincaré compactification to uncover the corresponding global phase-space structure. Beyond EDE, GCT admits two novel cosmological applications associated with critical points at infinity. Both arise from a class of energy-cancelling solutions in which conventional energy components preferentially excite $S_μ$ rather than source spacetime curvature. One is a $Λ$-cancelling solution that realizes the self-tuning mechanism for the old cosmological constant problem. Yet it remains incomplete. The other is a fluid-cancelling solution that serves as the basis for our proposed \textit{early static hot Universe}. In this scenario, $S_μ$ offsets the gravitational effect of ordinary hot gas, yielding quasi-static expansion with a decreasing comoving Hubble radius that can address the horizon problem. This offers an alternative to inflation. Furthermore, its \textit{hot} ingredient distinguishes this scenario from other quasi-static early Universe models and may leave observable signatures in primordial fluctuations. To probe the viability of GCT beyond cosmology, we further analyze linear perturbations about Minkowski spacetime and investigate static spherically symmetric (strong-field) systems. (Abstract abridged to meet arXiv limits.)
