We investigate the scalar perturbations in a class of spatially covariant gravity theory with a dynamical lapse function. Generally, there are two scalar degrees of freedom due to the presence of the velocity of the lapse function. We treat the scalar perturbations as analogues of those in a two-field inflationary mode, in which one is light mode and the other is the heavy mode. This is justified by the fact that the scalar mode due to the dynamical lapse function becomes infinitely heavy in the limit when the lapse function reduces to be an auxiliary variable. The standard approaches of multiple filed perturbations can be applied to deal with our model. By integrating out the heavy mode and derive the effective theory for the single light field, we find the solution to the single mode in the form of plane waves. Then we calculate the corrections to the power spectrum of the light mode from the heavy mode, by making use of the standard perturbative method of field theory. At last, when the two fields are not weakly coupled, we find a power law mode for the coupled system in large scales.

我们研究了一类具有动态失效函数的空间协变引力理论中的标量扰动。通常，由于存在延迟函数的速度，存在两个标量自由度。我们将标量扰动视为类似于双场暴胀模式中的那些，其中一个是轻模式，另一个是重模式。这是由以下事实证明的：当失效函数减少为辅助变量时，由于动态失效函数导致的标量模式在极限中变得无限重。可以应用多场扰动的标准方法来处理我们的模型。通过对重模的积分，推导出单光场的有效理论，我们找到了平面波形式的单模的解。然后我们利用场论的标准微扰方法计算从重模式到轻模式的功率谱的校正。最后，当两个场不是弱耦合时，我们找到了大尺度耦合系统的幂律模式。