Logamediate Inflation on the Swiss-Cheese Brane with Varying Cosmological Constant

The existence of Schwarzschild black holes in the structure of a Swiss-cheese brane world has led to the conclusion that this specific brane-world scenario is more realistic than the FLRW branes. In this paper, we show that Logamediate inflation on the Swiss-cheese brane with a 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 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 the 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 the 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 the \(\rho^{2}\) term, we have tested the new nonlinear energy conditions. The slow-roll parameters have been investigated and compared to Planck 15 results.