  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.
