On Einstein equations with cosmological constant in braneworld models

In this paper, we investigate the Einstein equations with cosmological constant for Randall–Sundrum (RS) and Dvali–Gabadadze–Porrati (DGP) models to determine warp functions in context of product spacetimes. RS model, it is shown that Einstein’s equation bulk reduced into brane as a vacuum equation, having solution, which not affected by bulk. DGP along extra dimension, where both are We have solved these subject vanishing constants on obtained exact solutions functions. The depend typical values well dimension brane. So, corresponding values, some exponential behaviors may be set represent inflation brane, other oscillating waves or branes dimension.