Inflation at the Tip

TL;DR

This work explores inflation driven by a D3-brane localized at the tip of a warped deformed conifold, with the inflaton potential sourced entirely by F-term moduli stabilization corrections in a KKLT-like setup and without anti-D3-branes. It shows that slow-roll hilltop inflation is achievable with careful tuning of the uplift and stabilization parameters, while pure DBI inflation at the tip struggles to produce the required number of e-foldings. The authors argue for a viable scenario in which slow-roll and DBI phases alternate, enabled by more generic D7 embedding functions, and they discuss mechanisms to tame the inflaton mass via uplifting. The study also clarifies the challenges of realizing natural inflation in this stringy context and highlights the role of uplifting scalings (e.g., V_up ∝ U^{-b}) in radial stability and model viability. Overall, the work maps out conditions under which angular D3-brane inflation at the tip can be phenomenologically relevant, and it suggests concrete directions for constructing consistent, testable string-theoretic inflation models.

Abstract

We study the motion of a (space filling) D3-brane at the tip of a warped deformed conifold, looking for inflationary trajectories. In our setup no anti D3-brane is present and the inflaton potential is induced by threshold corrections to the superpotential. First we study the slow roll regime and find that, allowing for fine tuning, hilltop inflation compatible with CMB data can take place. Then we consider the DBI regime and formulate a necessary condition for a phenomenologically viable inflationary stage. En passant, we propose a mechanism to cancel the large inflaton mass in the standard radial D3-anti D3-brane inflation.

Figures (7)

• Figure 2: The drawing describes the geometrical meaning of the parameters $\mu$, i.e. the distance of the stack of D7-branes to the tip, and $\varepsilon$, i.e. the size of the tip.
• Figure 3: WMAP3 data and the predictions of natural inflation are shown in the $n_s-r$ plane. The figure is taken from Savage:2006tr.
• Figure 4: On the left: a cartoon of the hilltop inflation model. On the right: we show explicitly how the fine tune works. The potential \ref{['nat inf']} is plotted for $C/\Lambda=\{0.5,\,0.4,\,0.3,\,0.2,\,0.1,\,0\}$. The thick line corresponds to $C=\Lambda/2$, i.e. a perfect cancellation of the mass term in \ref{['mass']}. The lowest (blue) line corresponds to $C=0$, i.e. the natural inflation potential \ref{['nat infl pot']}.
• Figure 5: On the left: $\gamma$ is plotted for the Natural Inflation potential; it grows monotonically from 1 to $(2f\Lambda/3)^{1/2}M_{Pl} /d$. On the right: the plot shows that the DBI condition \ref{['cond1']} and \ref{['cond2']} for the Natural Inflation potential \ref{['nat infl pot']} with $d\ll M_{Pl}$ are satisfied everywhere except for the two extremal regions, $\phi\simeq0$ and $\phi\simeq d\pi$.
• Figure 6: The scalar spectral index $n_s$ and $\gamma$ are plotted for three different values $d=0.12,\,0.08,\,0.04$. For $d<0.04$ the requirements $n_s=0.958\pm0.016$ and $\gamma<22$ cannot be satisfied at the same time.