AI 中文总结
构建最小修正引力理论，通过耦合辅助约束消除模糊性，研究特定子类，耦合规范暴胀子后，唯一传播标量模式为暴胀子涨落，给出标量谱指数及张量与标量比变化关系，参数区域需超光速张量速度。
AI 中文摘要
我们构建了一种最小修正引力理论，它在空间平坦的弗里德曼 - 勒梅特 - 罗伯逊 - 沃克（FLRW）背景下仅传播两个张量引力自由度，并允许一个可预测的宇宙学微扰理论。首先表明，在原始的四约束构造中，拉格朗日乘子的均匀值未完全确定且进入二次张量作用，阻碍了宇宙学可预测性。通过将辅助约束与乘子的空间拉普拉斯耦合消除了这种模糊性。乘子部分从均匀背景方程中消失，同时继续约束非均匀标量部分。张量色散关系通常包含$k^{2}$和$k^{4}$贡献，而在约束约化非退化的一般分支上不存在传播的引力矢量或标量模式。随后研究了一个子类，其引力哈密顿密度与消逝因子成比例且包含立方动量不变量。在这个子类中，$k^{4}$张量项消失，消逝因子可在背景水平上被吸收到时间重新定义中。耦合一个规范暴胀子后，唯一传播的标量模式是暴胀子涨落，声速为单位 1。对于二次势，与广义相对论的偏差会使标量谱指数发生偏移，而张量速度$c_{T}>1$会根据$r = 16\epsilon_{s}/c_{T}$抑制张量与标量比。与本工作采用的观测界限兼容的参数区域需要超光速张量速度；然而，非常大的$c_{T}$同时会降低张量动力学系数并可能降低微扰截断，尽管确定实际的强耦合尺度需要非线性分析。
英文摘要
We construct a minimally modified gravity theory that propagates only two tensorial gravitational degrees of freedom around a spatially flat Friedmann--Lemaître--Robertson--Walker (FLRW) background and admits a predictive cosmological perturbation theory. We first show that, in the original four-constraint construction, the homogeneous values of the Lagrange multipliers are not fully determined and nevertheless enter the quadratic tensor action, thereby obstructing cosmological predictivity. We remove this ambiguity by coupling the auxiliary constraints to spatial Laplacians of the multipliers. The multiplier sector then drops out of the homogeneous background equations while continuing to constrain the inhomogeneous scalar sector. The tensor dispersion relation generically contains both $k^{2}$ and $k^{4}$ contributions, whereas no propagating gravitational vector or scalar mode is present on the generic branch for which the constraint reduction is nondegenerate. We subsequently study a subclass whose gravitational Hamiltonian density is proportional to the lapse and contains cubic momentum invariants. In this subclass the $k^{4}$ tensor term vanishes and the lapse can be absorbed into a time redefinition at the background level. After coupling a canonical inflaton, the only propagating scalar mode is the inflaton fluctuation, with unit sound speed. For a quadratic potential, departures from general relativity shift the scalar spectral index, while a tensor speed $c_{T}>1$ suppresses the tensor-to-scalar ratio according to $r=16ε_{s}/c_{T}$. The parameter regions compatible with the observational bounds adopted in this work require a superluminal tensor speed; however, very large $c_{T}$ simultaneously reduces the tensor kinetic coefficient and may lower the perturbative cutoff, although determining the actual strong-coupling scale requires a nonlinear analysis.
Comments16 pages, 4 figures
