Title: Dark Energy Oscillations in Mimetic $F(R)$ Gravity Show Chinese title

Title: 暗能量在拟态$F(R)$引力中的振荡

Abstract: In this paper we address the problem of dark energy oscillations in the context of mimetic $F(R)$ gravity with potential. The issue of dark energy oscillations can be a problem in some models of ordinary $F(R)$ gravity and a remedy that can make the oscillations milder is to introduce additional modifications in the functional form of the $F(R)$ gravity. As we demonstrate the power-law modifications are not necessary in the mimetic $F(R)$ case, and by appropriately choosing the mimetic potential and the Lagrange multiplier, it is possible to make the oscillations almost to vanish at the end of the matter domination era and during the late-time acceleration era. We examine the behavior of the dark energy equation of state parameter and of the total effective equation of state parameter as functions of the redshift and we compare the resulting picture with the ordinary $F(R)$ gravity case. As we also show, the present day values of the dark energy equation of state parameter and of the total effective equation of state parameter are in better agreement with the observational data, in comparison to the ordinary $F(R)$ gravity case. Finally, we study the evolution of the growth factor as a function of the redshift for all the mimetic models we shall use. Show Chinese abstract

Abstract: 在本文中，我们研究了在具有势能的模仿 $F(R)$ 引力背景下暗能量振荡的问题。 暗能量振荡问题在普通 $F(R)$ 引力的一些模型中可能是一个问题，一种可以减轻振荡的补救方法是在 $F(R)$ 引力的功能形式中引入额外的修改。 正如我们所展示的，在模仿 $F(R)$ 的情况下，幂律修改是不必要的，并且通过适当选择模仿势能和拉格朗日乘子，可以在物质主导时代结束时以及晚期加速时代使振荡几乎消失。 我们研究了暗能量状态方程参数和总有效状态方程参数作为红移函数的行为，并将得到的结果与普通 $F(R)$ 引力的情况进行比较。 正如我们还展示的那样，暗能量状态方程参数和总有效状态方程参数的当前值与观测数据的符合程度优于普通 $F(R)$ 引力的情况。 最后，我们研究了所有我们将使用的模仿模型中增长因子作为红移函数的演化情况。