Paper detail

A dark energy with higher order derivatives of $H$ in the modified gravity $f(R,T)$

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.