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. Next, we proceed the statefinder analysis and see that both models are significantly distinct from Lambda CDM as well as with respect to each other at past epochs, while both of them catch the standard cosmology at far future. We also explore the impacts of the non-extensive parameters on the density perturbations and find out that the pattern of density contrast (delta) evolution in TGDE/BGDE is distinct from GDE in standard cosmology.