where ρΛ ≡ λ/(8πGN ) is nothing but the vacuum energy
density. Since observation favours values of ΩΛ =
ρΛ/ρc of the order of 0.7, we deduce that Λ is of the order
of H−1
0 ∼ 1026 m. This is the size of the observable
Universe i.e. basically the size of our causal horizon.
This is thus a very natural value for an astrophysicist!
Now, the prospects look very different if one introduces
the quantum theory through its famous Planck
constant . One can then introduce a new length scale,
the Planck length