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In this letter, we apply the Randall-Sundrum (RS) model, a scenario based oncompactifications, to control the UV divergence of the zero-point energydensity equation for the vacuum fluctuations, which has been unsuccessfullyaddressed to the cosmological constant (CC) due to a heavy discrepancy betweentheory and observation. Historically, the problem of CC has been shelved in theRS point of view, having few or non literature on the subject. In this senseand as done with the hierarchy problem, we apply the RS model to solve thisdifference via extra dimensions; we also describe how brane effects could bethe solution to this substantial difference. It should be noticed that thisproblem is studied assuming first Minkoswki type branes, and then followed bycosmologically more realistic FLRW type branes. We finally find some remarkablyinteresting consequences in the RS scenario: The CC problem can be solved viacompactification of the extra dimension and the compactification radius turnsout to be approximately twice the one used to solve the hierarchy problem inthe $\beta\pi r$ factor by Randall and Sundrum, suggesting that this subtledifference in both problems could be caused by corrections that comes fromquantum gravity effects. We also estimate the corresponding scale where,according to this results, we should begin to notice subtle deviations to theinverse square law of gravitation due to the presence of the extra dimension.

Cosmological constant problem in a scenario with compactifications (RS-I model)