  In this letter, we apply the Randall-Sundrum (RS) model, a scenario based on
compactifications, to control the UV divergence of the zero-point energy
density equation for the vacuum fluctuations, which has been unsuccessfully
addressed to the cosmological constant (CC) due to a heavy discrepancy between
theory and observation. Historically, the problem of CC has been shelved in the
RS point of view, having few or non literature on the subject. In this sense
and as done with the hierarchy problem, we apply the RS model to solve this
difference via extra dimensions; we also describe how brane effects could be
the solution to this substantial difference. It should be noticed that this
problem is studied assuming first Minkoswki type branes, and then followed by
cosmologically more realistic FLRW type branes. We finally find some remarkably
interesting consequences in the RS scenario: The CC problem can be solved via
compactification of the extra dimension and the compactification radius turns
out to be approximately twice the one used to solve the hierarchy problem in
the $\beta\pi r$ factor by Randall and Sundrum, suggesting that this subtle
difference in both problems could be caused by corrections that comes from
quantum gravity effects. We also estimate the corresponding scale where,
according to this results, we should begin to notice subtle deviations to the
inverse square law of gravitation due to the presence of the extra dimension.
