1201.6213 (E. I. Guendelman)

Extra Dimensional Curvature Supression of the Effective Four Dimensional
Vacuum Energy Density    [PDF]

E. I. Guendelman

Considering a very large number of extra dimensions, $N\rightarrow \infty$,
we show that in the effective four dimensional picture, to leading order in
$N$, both the cosmological constant in $N+4$ dimensions and the curvature of
the extra dimensions (curved as spheres) give the same type of contributions.
Furthermore in this limit, the extra dimensional curvature naturally supress
the effect of a positive Cosmological Constant, so that the resulting effective
potential governing the vacuum energy in the effective $4-D$ picture has a
leading 1/N dependence (i.e. vanishing in the large $N$ limit). We can
understand qualitatively this effect in a heuristic picture, by thinking that
all dimensions, both visible and extra have an equal sharing of the curvature
caused by $\Lambda$, in this case when increasing the overall number of
dimensions by adding $N$ extra dimensions, then if $N$ is large, the visible
dimensions do not have to curve too much, hence a small four dimensional vacuum
energy follows. In the large $N$ picture the potential can be also stabilized
by a small (i.e. vanishing at large $N$) expectaction value of a four index
field strength.

View original: http://arxiv.org/abs/1201.6213