A Scale at 10 MeV, Gravitational Topological Vacuum, and Large Extra Dimensions

Abstract

Abstract:We discuss a possible scale of gravitational origin at around 10 MeV, or 10 −12 cm, which arises in the MacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago. A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to the MacDowell-Mansouri formulation. We particularly draw attention to the intriguing incident that the existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of 10 −12 cm, as the compactification scale. The presence of six such extra dimensions is also in remarkable consistency with the MacDowell-Mansouri formalism; it provides a possible explanation for the factor of ∼10 120 multiplying the Gauss-Bonnet term in the action. We also comment on the relevant implications of such a scale regarding the thermal history of the universe motivated by the fact that it is considerably close to 1-2 MeV below which the weak interactions freeze out, leading to Big Bang Nucleosynthesis.

String Theory Bounds on the Cosmological Constant, the Higgs Mass, and the Quark and Lepton Masses

“…By comparison, a similar mass value has been argued [53] to be natural by examining a dimension-6 analogue of Weinberg's operator, where a neutrino could acquires its mass from a fermionic condensate controlled by the Bjorken-Zeldovich scale, with the electroweak cutoff scale:…”

“…analogously to the relation (23), for the first of the Heisenberg algebras in (53). The holographic bound [11,12] for the effective spacetime associated with the vacuum energy is N Λ = l 2 Λ /l 2 P , which with (54) produces…”

Beyond the Standard Model with Six-Dimensional Spinors

“…Given the difficulties of finding UV-finite quantum gravity and its small coupling constant, GUTs were proposed to unify all of the fundamental forces besides gravity. Recently, it has been suggested that torsion allows for UV-complete fermions [110][111][112], while the Gauss-Bonnet term allows for two-loop graviton scattering [113], both of which are related to the MacDowell-Mansouri formalism [114][115][116][117] studied in various graviGUT models [61,118]. Grand unified theory has been studied in a supersymmetry or supergravity context [6,18,21,24,29,36,45,47,48,52,54].…”

Beyond the standard model with six-dimensional spacetime

“…Given the difficulties of finding UV-finite quantum gravity and its small coupling constant, GUTs were proposed to unify all of the fundamental forces besides gravity. Recently, it has been suggested that torsion allows for UVcomplete fermions [110][111][112], while the Gauss-Bonnet term allows for two-loop graviton scattering [113], both of which are related to the MacDowell-Mansouri formalism [114][115][116][117] studied in various graviGUT models [61,118].…”