BPS branes in cosmology

The possibility to study the M or string theory cosmology via 5D bulk and brane action is investigated. The role of the 4-form field in the theory of Bogomol’nyi-Prasad-Sommerfield (BPS) branes in 5D is clarified. We describe arguments suggesting that the effective 4D description of the universe in the ekpyrotic scenario should lead to contraction rather than expansion of the universe. To verify these arguments, we study the full 5D action prior to its integration over the fifth dimension. We show that if one adds the potential $V\left(Y\right)\mathrm{}$ to the action of the bulk brane, then the metric ansatz used in the ekpyrotic scenario does not solve the dilaton and gravitational equations. To find a consistent cosmological solution one must use a more general metric ansatz and a complete 5D description of the brane interaction instead of simply adding an effective 4D bulk brane potential $V\left(Y\right).$