超越成对相互作用的多引力宇宙学

中文摘要 AI 辅助

我们为哈桑 - 施密特 - 梅多引力发展了宇宙学框架，这是一种无鬼双度规理论扩展，具有多个自旋 - 2 场的真正非成对相互作用。对于同时均匀且各向同性的度规，背景动力学简化为修正的弗里德曼方程，并辅以比例因子比的耦合四次多项式方程组。自旋 - 2 相互作用作为额外有效流体对弗里德曼方程有贡献。我们识别出接近标准辐射或物质主导宇宙的正则高密度分支，以及接近比例真空解的正则低密度分支，其中相互作用充当宇宙常数，对有效自旋 - 2 能量密度的主要修正提供额外物质贡献。我们还确定了相对零锥结构：在正则高密度分支上，额外零锥比物质耦合零锥开口角更宽，而在真空极限下所有零锥重合。在一阶时，我们求解确定非度规 vielbein 微扰的代数方程，推导一阶一致性方程及其标量和矢量投影，并得到耦合张量微扰方程的完整系统。这些结果为研究超越双度规理论及其成对相互作用扩展的无鬼多引力中的宇宙学解和微扰建立了框架。

英文摘要

We develop the cosmological framework for Hassan--Schmidt-May multi-gravity, a ghost-free extension of bimetric theory with genuinely non-pairwise interactions of multiple spin-2 fields. For metrics that are simultaneously homogeneous and isotropic, the background dynamics reduce to a modified Friedmann equation supplemented by a system of coupled quartic polynomial equations for the scale-factor ratios. The spin-2 interaction contributes to the Friedmann equation as an additional effective fluid. We identify a regular high-density branch that approaches the standard radiation- or matter-dominated Universe, while regular low-density branches approach proportional vacuum solutions, where the interaction acts as a cosmological constant and the leading correction to the effective spin-2 energy density provides an additional matter contribution. We also determine the relative null-cone structure: on the regular high-density branch, the additional null cones approach wider opening angles than the matter-coupled null cone, while all null cones coincide in the vacuum limit. At linear order, we solve the algebraic equations determining the non-metric vielbein perturbations, derive the first-order consistency equations and their scalar and vector projections, and obtain the complete system of coupled tensor perturbation equations. These results establish a framework for studying cosmological solutions and perturbations in ghost-free multi-gravity beyond bimetric theory and its pairwise-interacting extensions.

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29 pages