On the origin of brane cosmological constant in two-brane warped geometry model

In the backdrop of generalised Randall-Sundrum braneworld scenario, we look for the possible origin of an effective four dimensional cosmological constant ($\Omega_{vis}$) on the visible 3-brane due to the effects of bulk curvature and the modulus field that can either be a constant or dependent on extra dimensional co-ordinate $y$ or a time dependent quantity. In case of constant or $y$ dependent modulus field, the induced $\Omega_{vis}$ leads to an exponentially expanding Universe. For such modulus fields the presence of vacuum energy densities on either of the 3-branes as well as a non-vanishing bulk curvature $l$ ($l \sim {\Lambda_5}^{-1}$) are essential to generate an effective $\Omega_{vis}$. In particular for constant modulus field the Hubble constant turns out to be equal to the visible brane cosmological constant which agrees with the present result. In an alternative scenario, a time dependent modulus field is found to be capable of accelerating the Universe. The Hubble parameter in this case is determined for a slowly time-varying modulus field.