Extra-dimensional curvature suppression of the effective four-dimensional vacuum energy density

DOI10.1088/0264-9381/29/10/105007zbMATH Open1242.83104arXiv1201.6213OpenAlexW3098717778MaRDI QIDQ2896897

Publication date: 5 July 2012

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Abstract: Considering a very large number of extra dimensions,

N i g h t a r r o w i n f t y

, 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

L a m b d a

, 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.

Full work available at URL: https://arxiv.org/abs/1201.6213

Mathematics Subject Classification ID

Unified quantum theories (81V22) Relativistic cosmology (83F05) Kaluza-Klein and other higher-dimensional theories (83E15) Exact solutions to problems in general relativity and gravitational theory (83C15)