The Quantum Structure of Space and Time (293 pages)

Cosmology 217

I will discuss these in turn.

6.1.1.1 Faxed-A theories

The basic problem here is that we know that our vaciiiim is a rather nontrivial state,
and we can identify several contributions to its energy density that are of the order

of particle physics scales. It is sufficient to focus on one of them; let us choose the

electron zero point energy, since we know a lot about electrons. In particular, they
are weakly coupled and pointlike up to an energy scale M of at least 100 GeV. Thus
we can calculate the electron zero point energy up to this scale from the graphs of
Fig. 1 [5],

pv = o(M~) + 0(~’mm,2) + o(m2 lnM/me) , (1)

which is at least 55 orders of magnitude too large.

Fig. 6.1
cosmological constant.

An electron vacuum loop and its coupling to external gravitons generate an effective

So we must understand why this contribution actually vanishes, or is cancelled.
To sharpen the issue, we know that electron vacuum energy does gravitate in some
situations. Fig. 2a shows the famous Lamb shift, now coupled to an external gravi-

P e

I\ I\

a a

Fig. 6.2
static energy of a nucleus, coupled to an external graviton.

a) The Lamb shift, coupled to an external graviton. b) A loop correction to the electro-