Successfully combining SUGRA hybrid inflation and moduli stabilisation

Abstract

Inflation and moduli stabilisation mechanisms work well independently, and many string-motivated supergravity models have been proposed for them. However a complete theory will contain both, and there will be (gravitational) interactions between the two sectors. These give corrections to the inflaton potential, which generically ruin inflation. This holds true even for fine-tuned moduli stabilisation schemes. Following a suggestion by 0712.3460, we show that a viable combined model can be obtained if it is the Kahler functions (G= K+\ln |W|^2) of the two sectors that are added, rather than the superpotentials (as is usually done). Interaction between the two sectors does still impose some restrictions on the moduli stabilisation mechanism, which are derived. Significantly, we find that the (post-inflation) moduli stabilisation scale no longer needs to be above the inflationary energy scale.

Figures (1)

• Figure 1: Parameter space in $\{ \log_{10}(m), \log_{10}(\mathcal{M})\}$ for (a) $\lambda = 0.1$ and (b) $\lambda = 10^{-4}$. In the white region the model reduces to SUSY hybrid inflation. Regions I-IV are excluded, because I: the modulus mass dominates the 1-loop potential, II: the gravitino mass is too large, III: the modulus is tachyonic during inflation, and IV: the modulus potential property $m \lesssim \mathcal{M}$ is not satisfied. The dashed lines correspond to $H_*=\mathcal{M}$