Superconformal D-Term Inflation

TL;DR

This work shows that superconformal supergravity disfavors F-term hybrid inflation due to tachyonic inflaton masses, while D-term hybrid inflation, augmented by a holomorphic Kähler deformation that breaks the symmetry, yields a two-field inflation model with an inflationary slope generated by quantum corrections. The single-field limit can reproduce a near-scale-invariant spectrum with n_s ≈ 0.99–1, but incorporating a cosmic-string contribution lowers n_s toward ~0.97; two-field trajectories further modify P_s and n_s, offering regions where A_s and n_s can fit current data within 2σ, albeit with tension against the cosmic-string bound. The study highlights the role of the FI-term, frame-function breaking, and multi-field dynamics in reconciling D-term inflation with observations, while also stressing the theoretical uncertainties in cosmic-string bounds and the potential need for embedding in broader frameworks. Overall, superconformal D-term inflation can account for the primordial power spectrum and yield n_s down to ~0.96, but cosmic-string constraints and model-building alternatives will be decisive for its viability.

Abstract

We study models of hybrid inflation in the framework of supergravity with superconformal matter. F-term hybrid inflation is not viable since the inflaton acquires a large tachyonic mass. On the contrary, D-term hybrid inflation can successfully account for the amplitude of the primordial power spectrum. It is a two-field inflation model which, depending on parameters, yields values of the scalar spectral index down to n_s ~ 0.96. Generically, there is a tension between a small spectral index and the cosmic string bound albeit, within 2-sigma uncertainty, the current observational bounds can be simultaneously fulfilled.

Figures (5)

• Figure 1: Normalization condition and cosmic string bound for $\chi = -15$, $q = 2$, $g^2 = 1/2$ and $N_* = 50$. The blue line shows the relationship between $\xi$ and $\lambda$ imposed by the correct normalization of the amplitude of the primordial fluctuations. The black lines denote the cosmic string bound for $G \mu \times 10^7 < 2, 4.2$ and $7$, respectively; the darker shaded regions on the left are in agreement with the constraint. The dashed lines show contours of constant scalar spectral index. The white region to the bottom right must be excluded since there is no positive solution to $m^2_{+}(\sigma_c) = 0$.
• Figure 2: Spectral index and total amplitude for $\sqrt{\xi} = 4.3 \times 10^{15}$ GeV, $\lambda = 4 \times 10^{-3}$, $q = 2$, $g^2 = 1/2$, $N_* = 50$. The solid lines show the numerical results, the dashed lines the analytical ones. The values of $\xi$ and $\lambda$ are chosen such as to be compatible with the cosmic string bound as well as the normalization constraint for $\chi = -15$ (c.f. Fig. \ref{['fig_cobe_strings']}).
• Figure 3: Inflationary trajectories in ($\sigma, \tau$) field space for $\chi = -15$, $\lambda = 4 \times 10^{-3}$, $\sqrt{\xi} = 4.3 \times 10^{15}$ GeV, $g^2 = 1/2$ and $q = 2$. Contour lines of the scalar potential are denoted by dashed lines. The dashed blue line marks the $m_+ = 0$ condition, the green solid lines show several examples of inflationary trajectories. The blue lines show contours of the number of e-folds $N$, from $N= 0$ to $N = N_* = 50$. The single field case discussed in Section \ref{['sec_single_field']} corresponds to the trajectory coinciding with the $\sigma$-axis.
• Figure 4: Spectral index and total amplitude resulting from different inflationary trajectories for the same values of model parameters as in the single-field case depicted in Fig. \ref{['fig_ns_P']}, i.e. $\sqrt{\xi} = 4.3 \times 10^{15}$ GeV, $\lambda = 4 \times 10^{-3}$, $q = 2$, $g^2 = 1/2$, $N_* = 50$.
• Figure 5: Possible values of the spectral index $n_s$ as a function of $\chi$. The shaded region bounded by a curve with a given stroke style shows the range of possible $n_s$ values achieved by varying the inflationary trajectory for a given value of $\lambda$, while constraining the corresponding values of the amplitude to the 3-sigma range of the observed value $A_s^0$. For $\lambda = 0.005$, the region to the top left, bounded by the gray solid-dashed curve, is in accordance with the cosmic string bound.