D-term Uplifted Racetrack Inflation

TL;DR

The paper presents a racetrack inflation model embedded in moduli stabilization with a supersymmetric D-term uplift, yielding a complete effective supergravity description. Inflation occurs near a saddle of the racetrack potential, with the inflaton dominated by the imaginary part of the volume modulus and gaugino condensates evolving during inflation, yielding a scalar spectrum with $n_s \approx 0.95$ and negligible tensor modes. An equivalent simplified single-field potential $V_y$ reproduces the full model's predictions, indicating a universal racetrack behavior across variants of the Kähler potential and field content. The work discusses prospects for string-theoretic embedding and potential extensions to address uplift tuning, such as additional cancelling fields.

Abstract

It is shown that racetrack inflation can be implemented in a moduli stabilisation scenario with a supersymmetric uplifting D-term. The resulting model is completely described by an effective supergravity theory, in contrast to the original racetrack models. We study the inflationary dynamics and show that the gaugino condensates vary during inflation. The resulting spectral index is n_s = 0.95 as in the original racetrack inflation model. Hence extra fields do not appear to alter the predictions of the model. An equivalent, simplified model with just a single field is presented.

Figures (3)

• Figure 1: Plot of potential $V(X,Y)$, minimised with respect to $\phi$ at each point. The colour of the shading corresponds the the value of $\phi$. The line corresponds to the inflationary trajectory.
• Figure 2: Evolution of the (rescaled) fields as function of the number of $e$-folds $N$ before the end of inflation. COBE scales leave the horizon at $N_* \sim 55$. Left plot also shows the spectral index $n_s$. This and all other plots for parameters par1 and the top line of table \ref{['tab']}.
• Figure 3: (a) Variation of spectral index $n_s$ and the initial value of slow-roll parameter $\eta_{\rm sad}$ as a function of $W_0$. (b) The spectral index $n_s$ as a function of the value of $\eta_{\rm sad}$ at the saddle for the racetrack model (solid green) and the simplified potential Vy (dashed blue). The parameters are chosen as in par1.