论文标题
汉密尔顿 - 雅各比的动力学优势和PSI系数
Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models
论文作者
论文摘要
动力学优势时期的单场通气模型接纳了由普遍的渐近扩张所提供的正式解决方案，称为PSI系列。我们提出了一种计算Hubble参数PSI序列的方法，这是汉密尔顿 - 雅各比（Hamilton-Jacobi）模型公式中的Aftraton场的函数。也得出了相似的PSI序列，也得出了量表因子，保形时间和哈勃半径。当通货膨胀期开始时，它们用于确定充气场的值，并估算动力学优势周期的贡献以计算通货膨胀持续时间。这些PSI系列还用于获得奇异性附近的显式两项截短的PSI系列，以获得Mukhanov-Sasaki方程的电势用于曲率和张量的扰动。该方法用广泛的充气模型家族进行了说明，该家族由结合多项式和指数函数以及广义的Starobinsky模型的潜在功能决定。
Single-field inflaton models in the kinetic dominance period admit formal solutions given by generalized asymptotic expansions called psi series. We present a method for computing psi series for the Hubble parameter as a function of the inflaton field in the Hamilton-Jacobi formulation of inflaton models. Similar psi series for the scale factor, the conformal time and the Hubble radius are also derived. They are applied to determine the value of the inflaton field when the inflation period starts and to estimate the contribution of the kinetic dominance period to calculate the duration of inflation. These psi series are also used to obtain explicit two-term truncated psi series near the singularity for the potentials of the Mukhanov-Sasaki equation for curvature and tensor perturbations. The method is illustrated with wide families of inflaton models determined by potential functions combining polynomial and exponential functions as well as with generalized Starobinsky models.
