标题： 扩展的静质量引力理论 显示英文标题

标题： Extended minimal theories of massive gravity

摘要： 在本工作中，我们引入了一类扩展的最小引力质量理论（eMTMG），而无需事先要求该理论应具有与de Rham-Gabadadze-Tolley引力质量相同的均匀和各向同性宇宙学解。 该理论被构造为在引力领域中仅具有两个自由度。 为了完成这一步，我们首先引入一个具备一般引力子质量项的前体理论，在哈密顿量层面，我们添加两个额外约束以去除不需要的自由度，否则通常会导致鬼态和/或不稳定性。 在分析独立约束的数量和张量模式扰动的性质时，我们发现引力波是唯一获得非平凡质量的传播引力自由度，这是预期的结果。 为了理解该理论的有效引力作用方式，我们随后研究了在无压流体存在下的宇宙学标量扰动。 然后，我们通过在所有时间施加以下条件来限制整个模型类别：1）可以定义一个有效引力常数，$G_{{\rm eff}}$；2）值$G_{\text{eff}}/G_{N}$始终是有限的但并不总是等于单位（以便允许除质量张量模态以外的一些非平凡的引力修改）；3）引力子质量的平方始终为正。 这些约束自动使所有时间的ISW效应贡献保持有限。 最后，我们关注此类理论的一个简单子类，并表明它们已经可以提供丰富且有趣的物理现象。 显示英文摘要

摘要： In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{{\rm eff}}$; 2) the value $G_{\text{eff}}/G_{N}$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology.