Abstract
We propose a mechanism for the natural inflation with and without modulation in the framework of type IIB string theory on toroidal orientifold or orbifold. We explicitly construct the stabilization potential of complex structure, dilaton and K\"ahler moduli, where one of the imaginary component of complex structure moduli becomes light which is identified as the inflaton. The inflaton potential is generated by the gaugino-condensation term which receives the one-loop threshold corrections determined by the field value of complex structure moduli and the axion decay constant of inflaton is enhanced by the inverse of one-loop factor. We also find the threshold corrections can also induce the modulations to the original scalar potential for the natural inflation. Depending on these modulations, we can predict several sizes of tensor-to-scalar ratio as well as the other cosmological observables reported by WMAP, Planck and/or BICEP2 collaborations.
Highlights
We propose a mechanism for the natural inflation with and without modulation in the framework of type IIB string theory on toroidal orientifold or orbifold
In the case of type IIA string theory on toroidal orientifold or orbifold with O-planes and D6-branes wrapping on a supersymmetric three-cycle of the internal tori, the gauge threshold corrections are explicitly computed by an exact CFT method via the cylinder and Mobius diagram [28]. (There are similar computations in type IIB string theory and F-theory on the local geometric cycle with fractional Dbranes [31, 32].) When we consider the T-dual picture, they correspond to the setup of D3/D7-branes or D5/D9-branes in type IIB orientifold or orbifold which depend on the choice of T-duality
We proposed a mechanism for the natural inflation with and without modulations in the framework of type IIB string theory on toroidal orientifold or orbifold
Summary
We briefly review the one-loop stringy threshold corrections to the gauge couplings on D-. In type II string theory, in general, the charged open strings between two stacks of D-branes or O-planes contribute to the gauge couplings on D-branes as the threshold corrections ∆a which are mostly moduli-dependent [30]. We propose the moduli stabilization and inflation scenario in the framework of type IIB string theory on toroidal orientifold or orbifold such as T 2/Z2 or T 2/(Z2 × Z2) with D-branes. Where Ω is the holomorphic three-form of the CY manifold and G3 = F3−i SH3 is the threeform flux determined by Ramond-Ramond (RR) three-form flux F3 and Neveu-Schwarz (NS) three-form flux H3 Such flux-induced superpotential can stabilize the dilaton and all complex structure moduli at the perturbative level [34]. In order to show the essential idea of our scenario, as mentioned above, we consider the type IIB string on the simple toroidal orientifold or orbifold such as T 2/Z2 or T 2/(Z2 × Z2) whose moduli are characterized by dilaton S, three complex structure moduli U 1, U 2, U 3 and single overall Kahler modulus T .1 In order to obtain the desired inflation potential, we follow a similar step to the KKLT scenario [27] for stabilizing all the moduli other than Im U 2 which is identified as the inflaton field
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