No-go theorems for ekpyrosis from ten-dimensional supergravity

Kunihito Uzawa

doi:10.1088/1742-6596/1275/1/012058

Abstract

We study whether the new ekpyrotic scenario can be embedded into tendimensional supergravity. We use that the scalar potential obtained from flux compactifications of type II supergravity with sources has a universal scaling with respect to the dilaton and the volume mode. Similar to the investigation of inflationary models, we obtain very strong constraints ruling out ekpyrosis from analysing the fast-roll conditions. We conclude that flux compactifications tend to provide potentials that are neither too flat and positive (inflation) nor too steep and negative (ekpyrosis).

Highlights

In this note we investigate whether the new ekpyrotic scenario can be embedded into ten-dimensional supergravity
We study the dynamics of two scalar fields in the four-dimensional effective theory after a compactification in string theory
The terms coupling the scalar fields to the scalar curvature of the internal space and orientifold plane contribute the negative value to the potential in the string theory, we find that the potential does not satisfy the fastroll condition in general

Summary

No-Go theorem of the ekpyrotic scenario in the type II theory

We consider compactifications of the type II theory to four-dimensional spacetime on compact manifold Y. The moduli potential arises from the compactification of the terms in ten-dimensional action (2.1) associated with the various field strengths, Dp-branes and Op-planes as well as the gravity and the dilaton. VOp(τ , ρ) = −AOp exp −κ (2.12a) (2.12b) (2.12c) dp−3x√gp−3 , (2.12d) dp−3x√gp−3 , (2.12e) where AY , AH , Ap , ADp , and AOp are coefficients to scale with fluxes and numbers of Op-planes and Dp-branes These coefficients in general depend on the choice of flux integers hΣ , fC(p) , and the function of the moduli of the internal space Y. If four-dimensional effective action is described by Kahler moduli, complex structure moduli, and axions as well as volume moduli (breathing mode), the moduli potential will be modified We will discuss these in the end of this section. The stabilization mechanisms of all the geometric moduli and many axions in type II string theory have been discussed in [36, 37, 38, 39]

Type IIA compactification

Type IIB compactification

Discussions

Scalar potential in four-dimensional effective theory