镜像引力的理论景观：全面综述
The Theoretical Landscape of Mimetic Gravity: A Comprehensive Review
AI总结：
镜像引力通过重新参数化引力场，产生模仿冷暗物质的纵向自由度，用于构建统一的宇宙学模型并解决宇宙学奇点问题。
摘要：
镜像引力作为一种广义相对论（GR）的有力扩展，最初受到试图隔离引力场规范自由度的尝试启发。通过将物理度规用辅助度规和标量场重新参数化，该理论自然产生了一个纵向自由度，其行为模仿冷暗物质。本文综述了镜像引力的理论景观及其在宇宙学和高能物理中的多种应用。我们首先考察了原始公式，并探讨其等效于GR的基本问题，强调单一的反形变变换如何引入新的物理自由度。随后，我们探索了最小的扩展，导致统一的宇宙学模型，包括镜像物质情景和扩展到f(R, ϕ)引力，允许重建任何期望的膨胀历史。对“极限曲率”假说通过f(□ϕ)修改给予了显著关注，提供了一种经典机制来解决宇宙学和黑洞奇点。我们批判性地评估了该理论面临的挑战，特别是宇宙学扰动中发现的梯度和鬼不稳定问题，并讨论了现代解决方案，如无鬼镜像质量引力和协变的霍尔瓦重力公式化。最后，我们讨论了镜像场在早期宇宙中的作用，特别是在渐近自由引力和解决膨胀中的自复制问题中的作用。
英文摘要：
Mimetic gravity has emerged as a compelling extension of General Relativity (GR), originally motivated by the attempt to isolate the conformal degree of freedom of the gravitational field. By reparametrizing the physical metric in terms of an auxiliary metric and a scalar field, the theory naturally gives rise to a longitudinal degree of freedom that mimics the behavior of cold dark matter. This review provides a comprehensive survey of the theoretical landscape of mimetic gravity and its multifaceted applications to cosmology and high-energy physics. We begin by examining the original formulation and addressing the fundamental question of its equivalence to GR, highlighting how a singular disformal transformation introduces new physical degrees of freedom. We then explore minimal generalizations that lead to unified cosmological models, including mimetic matter scenarios and extensions into $f(R, ϕ)$ gravity, which allow for the reconstruction of any desired expansion history. Significant attention is given to the ``limiting curvature'' hypothesis through $f(\Box ϕ)$ modifications, providing a classical mechanism for resolving cosmological and black hole singularities. We critically assess the challenges facing the theory, specifically the gradient and ghost instabilities identified in cosmological perturbations, and discuss modern resolutions such as ghost-free mimetic massive gravity and covariant formulations of Hořava gravity. Finally, we discuss the role of the mimetic field in the early universe, specifically in the context of asymptotically free gravity and the resolution of the self-reproduction problem in inflation.
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