The Mukhanov–Sasaki equation is deduced from linear perturbations for a general scalar-tensor model with non-minimal coupling to curvature, to the Gauss–Bonnet invariant and non-minimal kinetic coupling to curvature. The general formulas for the power spectra of the primordial scalar and tensor fluctuations are obtained for arbitrary coupling functions. The results have been applied to models with power-law, exponential, natural and double-well potentials. It was found that the presence of these non-minimal couplings affect the inflationary observables leading to values favored by the latest observations, while some interesting results like sub-planckian symmetry breaking scale in natural inflation and sub-planckian v.e.v. of the scalar filed in the double-well potential were obtained. The consistency with the reheating process was discussed and some numerical cases were shown. The equivalence of the model to a sector of generalized Galileons was shown and the functions that establish the correspondence were found.

Mukhanov–Sasaki方程是从线性扰动推导的，该线性扰动是将非最小耦合到曲率的普通标量-张量模型转换为高斯-贝纳特不变且非最小耦合到曲率的动力学。对于任意耦合函数，可以获得原始标量和张量波动的功率谱的通用公式。结果已应用于具有幂律，指数势，自然势和双阱势的模型。发现这些非最小耦合的存在会影响通货膨胀的可观测值，从而导致最新观测值所支持的值，而一些有趣的结果，例如自然通货膨胀中的次普朗克对称性破坏尺度和标量的次普朗克维数则在获得了双阱势。讨论了与再加热过程的一致性，并给出了一些数值案例。显示了模型与广义伽利略扇形的等价性，并找到了建立对应关系的函数。