Question

Following on Jim Graber's answer to: Can "big rip" rip apart an atomic nucleus?

If the cosmological constant is large enough, even the ground state of a hydrogen atom can be affected. So why is the energy scale for quantum gravity set by the planck mass and not by the cosmological constant? Is it because the cosmological constant can be associated with other theories (inflatons, or vacuum energies of the matter fields, etc.) and thus is just considered an ingredient and not gravity itself? If this does come down to a semantics issue, I'd still be interested to hear if the scale set by the cosmological constant suggests we may be able to see interesting quantum effects at that scale depending on what the cosmological constant 'is'.

Answer 1

A very good question. The cosmological constant has been taken to be the natural scale in various not-quite-mainstream papers such as those written by my ex-adviser Tom Banks, starting from e.g.

http://arxiv.org/abs/hep-th/0007146

More generally, the cosmological constant scale is extremely long in our Universe - it's the millimeter scale when you calculate the energy scale from the energy density; and the Hubble scale when you calculate it from the curvature of the vacuum.

Particle physics has this habit of thinking about short-distance physics as the fundamental physics; the long-distance physics is the derived discipline. It's because one can derive how big objects behave if he knows how the small ones do; but it is not possible in the opposite direction.

Consequently, the most fundamental scale has to be the shortest distance scale where "interesting things happen". Because the Planck scale - the radius of the smallest black holes and many other things - is much shorter than the cosmological constant scale, it has to be more fundamental.