We propose a new cosmological framework in which the strength of the gravitational force acted on dark matter at late time can be weaker than that on the standard matter fields without introducing extra gravitational degrees of freedom. The framework integrates dark matter into a type-II minimally modified gravity that was recently proposed as a dark energy mimicker. The idea that makes such a framework possible consists of coupling a dark matter Lagrangian and a cosmological constant to the metric in a canonically transformed frame of general relativity (GR). On imposing a gauge fixing constraint, which explicitly breaks the temporal diffeomorphism invariance, we keep the number of gravitational degrees of freedom to be two, as in GR. We then make the inverse canonical transformation to bring the theory back to the original frame, where one can add the standard matter fields. This framework contains two free functions of time which specify the generating functional of the above mentioned canonical transformation and which are then used in order to realize desired time evolutions of both the Hubble expansion rate H(z) and the effective gravitational constant for dark matter G_eff(z). The aim of this paper is therefore to provide a new framework to address the two puzzles present in today's cosmology, i.e. the H₀ tension and the S₈ tension, simultaneously. When the dark matter is cold in this framework, we dub the corresponding cosmological model the V Canonical Cold Dark Matter (VCCDM), as the cosmological constant Λ in the standard ΛCDM is replaced by a function V(ϕ) of an auxiliary field ϕ and the CDM is minimally coupled to the metric in a canonically transformed frame.

我们提出了一个新的宇宙学框架，其中在不引入额外的引力自由度的情况下，后期作用在暗物质上的引力强度可以弱于标准物质场上的引力强度。该框架将暗物质整合到最近被提议作为暗能量模拟物的 II 型最小修改重力中。使这种框架成为可能的想法包括将暗物质拉格朗日和宇宙学常数与广义相对论 (GR) 的规范变换框架中的度量耦合。在施加规范固定约束时，它明确打破了时间微分同胚不变性，我们将重力自由度的数量保持为两个，就像在 GR 中一样。然后我们进行逆规范变换，使理论回到原来的框架，可以在其中添加标准事项字段。该框架包含两个自由时间函数，它们指定上述规范变换的生成函数，然后用于实现哈勃膨胀率 H(z) 和暗物质有效引力常数 G 的所需时间演化_效率(z)。因此，本文的目的是提供一个新的框架来同时解决当今宇宙学中存在的两个难题，即 H ₀张力和 S ₈张力。当暗物质在这个框架中很冷时，我们将相应的宇宙模型称为 V 典型冷暗物质 (VCCDM)，因为标准 ΛCDM 中的宇宙学常数 Λ 被辅助场 φ 的函数 V(φ) 代替， CDM 最小地耦合到规范变换框架中的度量。