Recall from our discussions of the cosmological seesaw mechanism that the LHC scale, 1 TeV, is very close to the geometric average of the Planck scale and the cosmological constant scale (the fourth root of the observed vacuum energy).
A naive Planckian theory of quantum gravity would predict ρ to be of order ρ = Planckmass4. A naive (?) broken SUSY model at a TeV would predict ρ = 10-60 Planckmass4 which is better but we really need the observed ρ = 10-120 Planckmass4.
How do we fix the remaining 60 orders of magnitude?
Well, Gasperini borrows the old 1983 idea due to Rubakov and Shaposhnikov of "off-loading" of the gravitational effects of the cosmological constant into extra dimensions. Using the modern language, the idea is that the bulk is curved in the right way so that it compensates most of the vacuum energy on the brane. Yes, these guys were talking about the ADD-like braneworlds back in 1983.
The curvature scale L of the extra dimensions induced by this compensation technique for the brane-superpartner-induced TeV-scale vacuum energy must be given by Einstein's equations:
L-2 = 8πG TeV4 = millielectronVolt2This millielectronVolt bulk curvature induces SUSY breaking in the bulk and the vacuum energy of this SUSY breaking is no longer cancelled by anything. Consequently, it gives you
ρ = millielectronVolt4which is the observed value of the "dark energy" density. Things work well and besides the supersymmetry at a TeV, this scenario also predicts (marginally falsified) submillimeter extra dimensions. ;-)
Gasperini formulates the presentation as a proof of an inequality. Or a proof that we will see superpartners at the LHC or earlier, if you wish. ;-) The proof assumes that the brane-bulk compensation mechanism above is correct, of course.
I think it is a beautiful idea. The main problem so far is that in supergravity, the assumed cancellation between the brane and the bulk doesn't seem to occur. Of course, if someone proves that it does occur under mild enough assumptions, Gasperini's paper could very well be the right solution to the cosmological constant problem, including predictions of both SUSY and extra dimensions right behind the corner. ;-)
That's what I would call life on the edge. :-)