Quote by Haelfix
"it is not even remotely defined on spacetime"
You better believe the cosmological constant is defined on spacetime, its true in general relativity,.. .

the cosmological constant is simply a constant in the Einst. Field Eqn.
since it is independent of time and position is not, except in a trivial sense, a function defined on spacetime
the cosmological constant is very different from what is normally understood by a "quintessence field"
which varies with time typically has w different from 1. It is apt to mislead people if you try to blur the distinction
between the cosmological constant and a quintessence field.
You do know what the improved renormalization group is right?..

Good. Let's move on to discuss Reuter and Saueressig paper developing the RG equation and plotting the flow trajectories.
You seem to think there is some connection with COSMOLOGY. My impression is that their work on the renormalization group for gravity does not depend on cosmology except for the measured constant value of Lambda at low k.
But we will see.
the paper you need to read now is
http://arxiv.org/hepth/0110054
or some more recent survey, like the Loops 07 talk, that covers it.
I'd opt for the 2007 survey talk here:
http://www.matmor.unam.mx/eventos/lo...PL3/Reuter.pdf
http://www.matmor.unam.mx/eventos/lo...PL3/Reuter.mp3