Ghost Dark Energy in Tsallis and Barrow Cosmology

According to the thermodynamics-gravity conjecture, any modification to the entropy expression leads to the modified cosmological field equations. Based on this, we investigate the cosmological consequences of the modified Friedmann equations when the entropy associated with the horizon is in the form of Tsallis/Barrow entropy and the dark energy (DE) component is in the form of ghost dark energy (GDE). We perform a dynamical system analysis and see that the Tsallis GDE(TGDE) and Barrow GDE(BGDE) can exhibit a correct phase space evolution for suitable range of the free parameters($0<\Delta<1$ for BGDE and $\beta<3/2$ for TGDE). We find that in BGDE and TGDE (with $Q=3b^2 H(\rho_D+\rho_m)$), there exist an early radiation dominated phase of expansion which is absent for GDE model in standard cosmology. It is worth mentioning that seeking an unstable phase of matter dominated in TGDE leads to a new constraint on $\beta$($<3/2$). Using the resulting range of free parameters from latter step we find that both models are capable to explain the cosmic evolution from deceleration to an accelerated phase. We observe that increasing $\Delta$ ($\beta$) parameters leads to a delay in the cosmic phase transition. We conclude that BGDE and TGDE are viable cosmological models which predict a consistent phase transition of the cosmic expansion for suitable ranges of the parameters. We also calculate the squared sound speed for both models and find out that they are unstable against perturbations...