修正引力$f(R,T)$中$H$高阶导数的暗能量
A dark energy with higher order derivatives of $H$ in the modified gravity $f(R,T)$
摘要：
在本文中，我们考虑了最近提出的包含三项的暗能量（DE）模型（一个正比于哈勃参数的平方，一个正比于哈勃参数相对于宇宙时间的一阶导数，一个正比于哈勃参数相对于宇宙时间的二阶导数），考虑到特定的模型$f\left(R,T \right)$，具有$μ$和$ν$两个自由正常参数。这里$R$和$T$分别是曲率标量和挠率标量。在这项工作中，我们已经发现，哈勃参数$H$表现出衰减的行为，直到红移的顺序为$z\approx-0.5$（当它开始增加）和哈勃参数的时间导数从负值到正值的不同的红移。DE的状态方程（EoS）参数和有效EoS参数表现出从$ω<-1$到$ω>-1$的转变（然后EoS参数具有类似五等分的行为）。我们还发现，该模型可以达到宇宙的晚期加速相。利用状态探测器参数$r$和$s$，我们推导出所考虑的模型可以达到宇宙的$Λ$ CDM相，并且可以在尘埃和宇宙的$Λ$ CDM相之间进行插值。最后，通过研究声速的平方$v_s^2$，我们看到，所考虑的模型在宇宙的早期阶段是经典稳定的，但在当前阶段是经典不稳定的。
英文摘要：
In this paper, we consider a recently proposed model of Dark Energy (DE) which contains three terms (one proportional to the squared Hubble parameter, one to the first derivative with respect to the cosmic time of the Hubble parameter and one proportional to the second derivative with respect to the cosmic time of the Hubble parameter) in the light of the $f\left(R,T \right)$ model of modified gravity, considering the particular model $f\left(R,T \right) = μR + νT$, with $μ$ and $ν$ two free positive constant parameters. Here $R$ and $T$ are the curvature and torsion scalars, respectively. In this work, we have found that the Hubble parameter $H$ exhibits a decaying behavior until redshifts of the order of $z\approx-0.5$ (when it starts to increase) and the time derivative of the Hubble parameter goes from negative to positive values for different redshifts. The equation of state (EoS) parameter of DE and the effective EoS parameter exhibit a transition from $ω<-1$ to $ω>-1$ (then the EoS parameters have a quintom-like behavior). We have also found that the said model can attain the late time accelerated phase of the universe. Using the statefinder parameters $r$ and $s$, we derived that the considered model can attaining the $Λ$CDM phase of the universe and can interpolate between dust and $Λ$CDM phase of the universe. Finally, studying the squared speed of sound $v_s^2$, we have seen that the model under consideration is classically stable in the earlier stage of the universe, but classically unstable in the current stage.
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