coincidence? weirder still

Last week we’ve discussed that the Einstein-Hilbert-action \(S = \int\mathrm{d}^4x\:\sqrt{-\mathrm{det}g}\:\left(R - 2\Lambda\right)\) has the curious property that both terms \(R\) and \(\Lambda\) for a FLRW-universe today have the same value. If you extrapolate into the future, will it be the case that \(S\) approaches zero? What’s the physical interpretation of this?