Prospects of inflation in delicate D-brane cosmology

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 $\ensuremath{\chi}$ at instantaneous minima of the potential and studying the inflation dynamics with an effective single field (radial distance between a brane and an antibrane) $\ensuremath{\phi}$, we investigate the multifield inflation scenario involving these two fields. The two-field dynamics with the potential $V(\ensuremath{\phi},\ensuremath{\chi})$ in this model is significantly different from the effective single-field description in terms of the field $\ensuremath{\phi}$ when the field $\ensuremath{\chi}$ is integrated out. The latter picture underestimates the total number of e-foldings even by 1 order of magnitude. We show that a correct single-field description is provided by a field $\ensuremath{\psi}$ 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 ${\ensuremath{\eta}}_{\ensuremath{\psi}\ensuremath{\psi}}={M}_{\mathrm{pl}}^{2}{V}_{,\ensuremath{\psi}\ensuremath{\psi}}/V$ in terms of the rotated field $\ensuremath{\psi}$ 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 cosmic background explorer normalization, while the tensor to scalar ratio is sufficiently small to match with observations.