Logamediate inflation on the Swiss-cheese brane with varying cosmological constant

Abstract: The existence of Schwarzchild black holes in the structure of Swiss-cheese brane-world led to the conclusion that this specific brane-world scenario is more realistic than the FLRW branes. In this paper, we show that a Logamediate inflation on the Swiss-cheese brane with time-dependent cosmological constant $\Lambda(H)$ leads to a positive kinetic term and a negative potential with AdS minimum. The cosmic pressure $p$ is always positive but the energy density $\rho$ starts to get negative after a finite time. However, there is a time interval where they both are positive. Although this behavior of $\rho$ can be considered as a drawback of Swiss-cheese brane where positive energy dominates the present universe, it has been suggested that the presence of some source of negative energy could have played a significant role in early cosmic expansion. The model suffers from the eternal inflation problem which appears from the evolution of the first slow-roll parameter $\epsilon$. Due to the existence of $\rho^2$ term, we have tested the new nonlinear energy conditions. The slow-roll parameters have been investigated and compared to Planck 15 results.