Prospects of inflation in delicate D-brane cosmology

TL;DR

This paper analyzes inflation from a mobile D3-brane in a warped conifold with moduli stabilization corrections to the nonperturbative superpotential. It demonstrates that the two-field dynamics of $\phi$ and $\chi$ demand a rotated field $\psi$ for a proper single-field description, yielding a larger number of e-foldings than the naive $\phi$-only approach. The scalar perturbations are controlled by $\eta_{\psi\psi}$, and the tensor-to-scalar ratio is small; however simultaneously satisfying the COBE normalization and the observed spectral index is challenging. Overall, the work underscores the need to treat multi-field effects in string-inspired inflation and suggests that fine-tuning or multi-throat setups may be required for viability.

Abstract

We study D-brane inflation in a warped conifold background that includes brane-position dependent corrections for the nonperturbative superpotential. Instead of stabilizing the volume modulus chi at instantaneous minima of the potential and studying the inflation dynamics with an effective single field (radial distance between a brane and an anti-brane) phi, we investigate the multi-field inflation scenario involving these two fields. The two-field dynamics with the potential V(phi,chi) in this model is significantly different from the effective single-field description in terms of the field phi when the field chi is integrated out. The latter picture underestimates the total number of e-foldings even by one order of magnitude. We show that a correct single-field description is provided by a field psi obtained from a rotation in the two-field space along the background trajectory. This model can give a large number of e-foldings required to solve flatness and horizon problems at the expense of fine-tunings of model parameters. We also estimate the spectra of density perturbations and show that the slow-roll parameter eta_{psi psi}=M_{pl}^2 V_{,psi psi}/V in terms of the rotated field psi determines the spectral index of scalar metric perturbations. We find that it is generally difficult to satisfy, simultaneously, both constraints of the spectral index and the COBE normalization, while the tensor to scalar ratio is sufficiently small to match with observations.

Figures (8)

• Figure 1: The trajectory of the scalar fields in the $(\phi,\sigma)$ plane for the model parameters $n=8$, $A_0=1$, $\omega_0\equiv b\sigma_0=10.1$, $\omega_F=9.9951$, $W_0=3.496 \times 10^{-4}$, $D_0=1.215 \times 10^{-8}$ and $\phi_{\mu}=0.25$. The curves (a) and (b) correspond to the trajectories derived by solving the background equations numerically for the initial conditions $\phi_i/\phi_\mu=0.8$ and $\phi_i/\phi_\mu=0.5$, respectively. The initial values of the field $\chi$ are chosen to satisfy the relation (\ref{['chire']}) with $\sigma_0=\omega_0/b=12.8597$. We also plot the approximate trajectory (\ref{['chire']}).
• Figure 2: The potential $V(\phi,\chi)$ for the model parameters $n=8$, $A_0=1$, $\omega_0\equiv b\sigma_0=10.1$, $\omega_F=9.9951$, $W_0=3.496 \times 10^{-4}$, $D_0=1.215 \times 10^{-8}$ and $\phi_{\mu}=0.25$. The solid curves correspond to the one derived by solving the background equations numerically for the initial conditions $\phi_i/\phi_\mu=0.8$ and $\dot{\phi}_i/\phi_\mu=-1.0\times 10^{-10}m$, where $m=10^{-7}M_{\rm pl}$ is a mass to normalize time $t$. Note that the initial conditions for the field $\chi$ are chosen to satisfy the relation (\ref{['chire']}), i.e., $\chi_i/M_{\rm pl}=3.1385$. The upper panel shows the potential in terms of the function of $\phi/\phi_\mu$ for several fixed values of $\bar{\chi} \equiv \chi/M_{\rm pl}$ (plotted as dotted curves). The lower panel shows the potential in terms of the function of $\chi/M_{\rm pl}$ for several fixed values of $\bar{\phi} \equiv \phi/\phi_{\mu}$.
• Figure 3: The solid curve represents the potential obtained by numerically solving the background equations in two-field system for the same model parameters and initial conditions as in Fig. \ref{['fig2']}. The dotted curve corresponds to the potential (\ref{['Vstar']}) under the single $\phi$ field approximation.
• Figure 4: The evolution of the number of e-foldings in terms of the function of $\phi/\phi_\mu$ for the two-field system (solid curve) and for the system under the single $\phi$ field approximation (dotted curve). The model parameters and initial conditions are the same as in Fig. \ref{['fig2']}.
• Figure 5: The evolution of the slow-roll parameters $\eta_{\psi \psi}$ and $\eta_{\phi \phi}$ in terms of the function of $\phi/\phi_\mu$. The model parameters and initial conditions are chosen as in the case of Fig. \ref{['fig2']}. The period of inflation is determined by the condition $|\eta_{\psi \psi}|<1$.