Moduli Corrections to D-term Inflation

TL;DR

This work embeds D-term hybrid inflation into supergravity with stabilised moduli by using an uplifting $D$-term to generate an effective FI-term and a no-scale, shift-symmetric Kähler potential to preserve flatness. The resulting potential combines moduli and inflation sectors, with one-loop corrections providing the slow-roll slope and moduli-induced corrections controlled by the parameter $\alpha$, which governs the ratio of moduli to inflation scales. The analysis shows inflation can occur only in restricted parameter regions; moduli corrections generally reduce the spectral index $n_s$, potentially bringing it in line with WMAP3, but cosmic-string constraints remain a major challenge, often requiring very small $\lambda$ or alternative string-inspired constructions such as semilocal strings. Overall, the study clarifies how moduli stabilisation reshapes inflationary predictions and topological defect phenomenology in string-motivated D-term inflation, highlighting both viable regimes and tensions with observations.

Abstract

We present a D-term hybrid inflation model, embedded in supergravity with moduli stabilisation. Its novel features allow us to overcome the serious challenges of combining D-term inflation and moduli fields within the same string-motivated theory. One salient point of the model is the positive definite uplifting D-term arising from the moduli stabilisation sector. By coupling this D-term to the inflationary sector, we generate an effective Fayet-Iliopoulos term. Moduli corrections to the inflationary dynamics are also obtained. Successful inflation is achieved for a limited range of parameter values with spectral index compatible with the WMAP3 data. Cosmic D-term strings are also formed at the end of inflation; these are no longer Bogomol'nyi-Prasad-Sommerfeld (BPS) objects. The properties of the strings are studied.

Figures (2)

• Figure 1: $V/V_0$ as a function of $x=\varphi/\varphi_1$. In figure (a) the curves correspond to parameter choices with $\mathcal{B}>1$ (upper, green), $\mathcal{B}=1$ (middle, red), and $\mathcal{B} <1$ (lower, blue). Figure (b) is for $\alpha \xi = 1$.
• Figure 2: Contour plot of $n_s$ for $\ln \mathcal{B}$ vs. $\ln u$. The upper contour is $n_s=1$, and the lower one is $n_s=0.9$. The 1-$\sigma$ WMAP3 results correspond to the dark (blue) region in between. Parameters to the right of the black line below the contours satisfy the cosmic string bound on $\xi$.