$\overline{D3}$ Induced Geometric Inflation

TL;DR

The paper formulates a geometric supergravity framework for inflation inspired by anti-D3 brane uplifts, encoding the dynamics in a Kähler function $\mathcal{G}$ that includes a nilpotent multiplet $S$ with $S^2=0$. By deriving $\mathbf{V} = e^{\mathcal{G}}(\mathcal{G}^{\alpha\overline\beta} \mathcal{G}_\alpha \mathcal{G}_{\overline\beta} - 3)$ and connecting it to a moduli-dependent $\mathcal{G}_{S\overline S}$ (often set by the gravitino mass via $|m_{3/2}|^2$ and $\mathbf{V}$), the authors show how a given inflationary potential can be realized within a controlled geometry. They develop a suite of explicit models—Polynomial, T-models, E-models, and disk mergers (two-disk, cascade, and seven-disk)—where the curvature invariants, especially the nonvanishing bisectional curvature $R^{bisec}$, govern stability and mass spectra, ensuring no tachyons during inflation and at the minimum. The framework yields flexible control over the Hubble scale, cosmological constant, and SUSY breaking, while maintaining consistency with Planck data via attractor-like potentials and multi-stage inflation. Overall, the work provides a compact, geometrically grounded path from string-theoretic uplifting to phenomenologically viable inflation, with clear prescriptions to diagnose stability through curvature and to realize diverse inflationary plateaus and cascades.

Abstract

Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The Kähler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and gravitino mass. We illustrate it by providing generalized versions of polynomial chaotic inflation, T- and E-models of $α$-attractor type, disk merger. We also describe a multi-stage cosmological attractor regime, which we call cascade inflation.

Figures (6)

• Figure 1: The potential $V(\phi) = {m^{2}\phi^{2}\over 2}\,\bigl(1-a\phi +a^{2}b\,\phi^{2}\bigr)$ for $a = 0.12$ and $b = 0.30$ (upper curve), $b = 0.29$ (middle), and $b = 0.28$ (lower curve). The potential is shown in units of $m^{2}$, with $\phi$ in Planck units. For $b = 0.29$ (the middle curve), at the moment corresponding to $N= 58$ e-folding from the end of inflation one has $n_{s}= 0.965$ and $r = 0.012$, perfectly matching the Planck data.
• Figure 2: Basic T-model with $\alpha = 1$. The height of the potential here and in other figures is in units $m^{2}$ and the values of the fields are in Planck mass units.
• Figure 3: Basic E-model with $\alpha = 1/3$.
• Figure 4: Merger of two disks with $\alpha =1/3$ creates the inflaton potential with $\alpha = 2/3$. Here we considered an example with $M = 6\, m$.
• Figure 5: Merger of two disks with $\alpha =1/3$ creates the inflaton T-model potential with $\alpha = 2/3$. In this figure we show the potential with $M = 10\, m$.