Potential for the slow-roll inflation, mass-scale hierarchy and dark energy from type IIAsupergravity

Abstract

The magnetic fluxbrane solution with a strongly warped throat is studied in typeIIA supergravity theory with a co-dimension one local source which is theZ2-symmetric UV boundary of the throat. The overall volume of extra space may bestabilized since the introduction of the local source breaks the no-scale structure of thetheory and evades the no-go theorem. The radion field is defined as the position of the UVboundary ‘moved’ from its stable value fixed by the anisotropic Israel junction conditions.The analytical expression for the radion effective potential is found. The potential decreasesexponentially (the exponent is equal to 0.21 in Planck units) in the slow-roll region andapparently meets other demands of the early inflation. Thus the radion potential serves aninflaton. Reissner–Nordstrom type deformation of the elementary fluxbrane solutionpermits us to construct the IR end of the throat and results in a tiny positive non-zerovalue of the radion potential in its extremal point seen today as dark energy densityρDE. Expressions for themass-scale hierarchy m/MPl and for the ‘acceleration hierarchy’ found in this paper give the physically interesting relation between twohierarchies: ρDE∼m8/MPl4.