In the first part of this note, we observe that a non-Riemannian piece in the affine connection (a “dark connection”) leads to an algebraically determined, conserved, symmetric 2-tensor in the Einstein field equations that is a natural dark matter candidate. The only other effect it has, is through its coupling to standard model fermions via covariant derivatives. If the local dark matter density is the result of a background classical dark connection, these Yukawa-like mass corrections are minuscule ( ∼ 10−31eV for terrestrial fermions) and none of the tests of general relativity or the equivalence principle are affected. In the second part of the note, we give dynamics to the dark connection and show how it can be re-interpreted in terms of conventional dark matter particles. The simplest way to do this is to treat it as a composite field involving scalars or vectors. The (pseudo-)scalar model naturally has a perturbative shift-symmetry and leads to versions of the Fuzzy Dark Matter (FDM) scenario that has recently become popular (e.g. arXiv:1610.08297) as an alternative to WIMPs. A vector model with a 𝒵2-parity falls into the Planckian Interacting Dark Matter (PIDM) paradigm, introduced in arXiv:1511.03278. It is possible to construct versions of these theories that yield the correct relic density, fit with inflation and are falsifiable in the next round of CMB experiments. Our work is an explicit demonstration that the meaningful distinction is not between gravity modification and dark matter, but between theories with extra fields and those without.

中文翻译：

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来自暗连接的暗物质

在本笔记的第一部分，我们观察到仿射连接（“暗连接”）中的非黎曼部分导致爱因斯坦场方程中代数确定的、守恒的、对称的 2-张量，它是一种天然暗物质候选人。它唯一的其他影响是通过协变导数与标准模型费米子耦合。如果局部暗物质密度是背景经典暗连接的结果，那么这些类似 Yukawa 的质量校正是微不足道的（ ～ 10-31电子伏特对于陆地费米子）和没有广义相对论或等价原理的检验受到影响。在笔记的第二部分，我们给出了暗连接的动力学，并展示了如何根据传统的暗物质粒子来重新解释它。最简单的方法是将其视为涉及标量或向量的复合场。（伪）标量模型自然具有微扰移位对称性，并导致最近流行的模糊暗物质（FDM）场景的版本（例如arXiv:1610.08297)作为 WIMP 的替代品。一个向量模型𝒵2-parity 属于普朗克相互作用暗物质 (PIDM) 范式，在arXiv：1511.03278。有可能构建这些理论的版本，以产生正确的遗迹密度、适合膨胀​​并且在下一轮 CMB 实验中是可证伪的。我们的工作明确表明，有意义的区别不是引力修改和暗物质之间的区别，而是具有额外场的理论和没有场的理论之间的区别。