Supersymmetric Hybrid Inflation with Non-Minimal Kahler potential

TL;DR

Minimal SUSY hybrid inflation with a minimal Kähler potential predicts $n_s \gtrsim 0.98$, in tension with the central value $n_s \approx 0.95$. The paper shows that a non-minimal Kähler potential, kept compatible with the same superpotential, together with the one-loop effective potential $\Delta \mathcal V_{\mathrm{1loop}}$, yields a red-tilted spectrum with $n_s$ around $0.95$ for plausible parameter choices, and a reduced inflation scale $M$. A crucial result is that the single parameter $\kappa_S$ controls the tilt via $n_s \simeq 1-2\kappa_S-2\delta$, with $\delta$ the 1-loop contribution, while slow-roll requires $\kappa_S<1$ and the normalization adjusts $M$ and $S$. The paper also discusses post-inflationary cosmology, showing two viable reheating/baryogenesis channels: non-thermal leptogenesis via right-handed neutrinos with $T_R \sim (10^{-1}-10^{-2}) M_N$, and leptogenesis in flipped $SU(5)$, both compatible with gravitino bounds. Overall, the approach preserves the attractive features of SUSY hybrid inflation while achieving $n_s$ in better agreement with observations and maintaining viable baryogenesis.

Abstract

Minimal supersymmetric hybrid inflation based on a minimal Kahler potential predicts a spectral index n_s\gsim 0.98. On the other hand, WMAP three year data prefers a central value n_s \approx 0.95. We propose a class of supersymmetric hybrid inflation models based on the same minimal superpotential but with a non-minimal Kahler potential. Including radiative corrections using the one-loop effective potential, we show that the prediction for the spectral index is sensitive to the small non-minimal corrections, and can lead to a significantly red-tilted spectrum, in agreement with WMAP.

Figures (5)

• Figure 1: Predicted value of the spectral index $n_s$ depending on the value of the coupling $\kappa$, for different values of ${\cal N}=1,2,8,10,16$. We have set $N_e = 50$. Varying the no. of e-folds up to say $N_e=60$ would increase the predicted value of $n_s$ by at most $0.005$.
• Figure 2: Ratio $S_{Re}/S_R^{max}$ versus $\kappa_S$, for different values of $\kappa$.
• Figure 3: Value of $M$ depending on $\kappa$, for different values of $\kappa_S$; from top to bottom $\kappa_S=0,\,0.005,\,0.01,\, 0.015,\,0.02$. (${\cal N}=1$)
• Figure 4: Non-Minimal Kähler potential: predicted value of the 1-loop contribution to the spectral index, $\delta$, depending on the value of the coupling $\kappa$, for different values of $\kappa_S$; from top to bottom $\kappa_S=0.02,\,0.015,\,0.01,\,0.005,\, 0$. (${\cal N}=1$).
• Figure 5: Non-Minimal Kähler potential: predicted value of the spectral index $n_s$ depending on the value of the coupling $\kappa$, for different values of $\kappa_S$. We have taken ${\cal N}=1$.