Does Physics now have a complete description of Nature?

[Alex K]

And he's correct. The effects of the cutoff play basically no role in describing the physics behind what goes on around us - it's a Theory of almost everything, as someone put it once.

Just not any of everything if one go back close enough to the Big Bang.

That's among other things because the temperatures there will rise above any Lambda if you go back far enough, and setting lambda larger than the planck energy won't work.