Towards an Explicit Model of D-brane Inflation

TL;DR

This work constructs and analyzes an explicit warped D-brane inflation scenario with stabilized moduli, showing that D7-brane backreaction can modify the inflaton potential but does not uniformly flatten it via a quadratic term. Inflation is achieved only in a narrow region of microphysical parameter space, particularly for a simple Kuperstein embedding where slow-roll occurs near an approximate inflection point after accounting for the adiabatic volume modulus, VEV shift. The study reveals strong geometric constraints linking microscopic parameters, throat/bulk volumes, and the field range, which greatly restricts the available parameter space and complicates cosmological predictions. Overall, the paper demonstrates that explicit top-down string constructions can realize warped D-brane inflation, but inflation is non-generic and tightly constrained by the compactification geometry and moduli stabilization effects.

Abstract

We present a detailed analysis of an explicit model of warped D-brane inflation, incorporating the effects of moduli stabilization. We consider the potential for D3-brane motion in a warped conifold background that includes fluxes and holomorphically-embedded D7-branes involved in moduli stabilization. Although the D7-branes significantly modify the inflaton potential, they do not correct the quadratic term in the potential, and hence do not cause a uniform change in the slow-roll parameter eta. Nevertheless, we present a simple example based on the Kuperstein embedding of D7-branes, z_1=constant, in which the potential can be fine-tuned to be sufficiently flat for inflation. To derive this result, it is essential to incorporate the fact that the compactification volume changes slightly as the D3-brane moves. We stress that the compactification geometry dictates certain relationships among the parameters in the inflaton Lagrangian, and these microscopic constraints impose severe restrictions on the space of possible models. We note that the shape of the final inflaton potential differs from projections given in earlier studies: in configurations where inflation occurs, it does so near an inflection point. Finally, we comment on the difficulty of making precise cosmological predictions in this scenario. This is the companion paper to arXiv:0705.3837.

Figures (6)

• Figure 1: Cartoon of an embedded stack of D7-branes wrapping a four-cycle $\Sigma_4$, and a mobile D3-brane, in a warped throat region of a compact Calabi-Yau. The D3-brane feels a force from the D7-branes and from an anti-D3-brane at the tip of the throat.
• Figure 2: Inflaton potential $\mathbb{V}(\phi)$. Compactification data:$n=8$, $\omega_F = 10$, $N = 32$, $Q_\mu = 1.2$, $B_6=1.5$, $B_4= 9$, $s=1.1$, which implies $\phi_\mu = 0.25$, $W_0 = -3.432 \times 10^{-4}$, $D+D_{\rm other}=1.2 \times 10^{-8}$, $\omega_0 \approx 10.1$.
• Figure 3: The inflaton potential $\mathbb{V}(\phi)$ as a function of $s$. The transition from metastability to monotonicity is shown; old inflation and new inflation are continuously connected.
• Figure 4: $\eta(\phi)$ as a function of the number of $e$-folds of inflation, $N_e$. In the green band, $|\eta| < 2\pi N_{\rm tot}^{-1}$.
• Figure 5: Spectral index $n_s$, evaluated on CMB scales, as a function of the total number of $e$-folds of inflation, $N_{\rm tot}$. The light band gives the WMAP3 2$\sigma$ limit on $n_s$ (for $r \equiv 0$) Observations.