K-动量理论的小尺度非线性动力学
Small-scale Nonlinear Dynamics of K-mouflage Theories
摘要：
我们研究了由动力学项的一般函数$K(χ)$定义的K-模型的小尺度静态构型。如果$K'(χ)$对于大的负$χ$增长得足够快，则第五种力被非线性K-移动机制屏蔽。在一般的非球对称情况下，第五种力与牛顿力不一致。对于球对称静态物质密度分布，结果取决于势函数$W_{-}(y) = y K'(-y^2/2)$，对于$y \geq 0$，势函数必须单调增加到$+\infty$，以保证对于任何物质密度分布，在整个空间中存在单个解。这些静态轮廓周围的小的径向扰动作为行波以大于光速的速度传播。从消失的初始条件的标量场和随时间变化的物质密度对应的形成的超密度，我们数值检查的标量场收敛到静态解决方案。如果$W_{-}$是有界的，对于高密度的物体，在整个空间中没有静态解，但是仍然可以定义一个限制在大半径的静态解。我们的动力学研究表明，标量场松弛到这个静态的解决方案在大半径，而空间梯度保持增长随着时间在较小的半径。如果$W_{-}$不是有界的而是非单调的，则存在无穷多个不连续静态解，但它们不是物理的，并且这些模型在理论上是不合理的。这样的K-运动方案提供了一个例子，理论可以出现在宇宙学水平上可行的宇宙学背景和微扰分析，而在非线性水平上的小尺度配置是毫无意义的。这表明了筛选模型的小尺度非线性分析的重要性。
英文摘要：
We investigate the small-scale static configurations of K-mouflage models defined by a general function $K(χ)$ of the kinetic terms. The fifth force is screened by the nonlinear K-mouflage mechanism if $K'(χ)$ grows sufficiently fast for large negative $χ$. In the general non-spherically symmetric case, the fifth force is not aligned with the Newtonian force. For spherically symmetric static matter density profiles, the results depend on the potential function $W_{-}(y) = y K'(-y^2/2)$, which must be monotonically increasing to $+\infty$ for $y \geq 0$ to guarantee the existence of a single solution throughout space for any matter density profile. Small radial perturbations around these static profiles propagate as traveling waves with a velocity greater than the speed of light. Starting from vanishing initial conditions for the scalar field and for a time-dependent matter density corresponding to the formation of an overdensity, we numerically check that the scalar field converges to the static solution. If $W_{-}$ is bounded, for high-density objects there are no static solutions throughout space, but one can still define a static solution restricted to large radii. Our dynamical study shows that the scalar field relaxes to this static solution at large radii, whereas spatial gradients keep growing with time at smaller radii. If $W_{-}$ is not bounded but non-monotonic, there is an infinite number of discontinuous static solutions but they are not physical and these models are not theoretically sound. Such K-mouflage scenarios provide an example of theories that can appear viable at the cosmological level, for the cosmological background and perturbative analysis, while being meaningless at a nonlinear level for small-scale configurations. This shows the importance of small-scale nonlinear analysis of screening models.
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