Observing the Geometry of Warped Compactification via Cosmic Inflation

TL;DR

Using Dirac-Born-Infeld inflation as an example, it is demonstrated that the detailed geometry of warped compactification can leave an imprint on the cosmic microwave background.

Abstract

Using DBI inflation as an example, we demonstrate that the detailed geometry of warped compactification can leave an imprint on the cosmic microwave background (CMB). We compute CMB observables for DBI inflation in a generic class of warped throats and find that the results (such as the sign of the tilt of the scalar perturbations and its running) depend sensitively on the precise shape of the warp factor. In particular, we analyze the warped deformed conifold and find that the results can differ from those of other warped geometries, even when these geometries approximate well the exact metric of the warped deformed conifold.

Figures (3)

• Figure 1: a.) The warp factor for the AdS (blue dashed) and exact KS throat (black solid) are plotted as a function of the canonical scalar field scaled by its value at the edge where the throat is glued to the bulk space. We have chosen our parameters to be $h_{tip}=10^{-2}$, $M_p = 100 m_s$ for these plots. b.) The absolute value of the spectral index for the two throats (blue solid for AdS and thick black solid for KS). We take the absolute value of $n_s -1$ in order to show simultaneously the results for AdS and KS throat in one plot. The cusp in the AdS spectral curve corresponds to the tilt changing from negative at larger $\phi$ to positive for smaller $\phi$. This also happens where the warp factors begin to differ. c.) The absolute value of the running of the scalar spectral index is shown for the AdS (blue) and KS (thick black) throats. The cusps in the AdS curve correspond to the running changing from negative to positive to negative again, as can easily be seen in the plot of the spectral index, see b.).
• Figure 2: The absolute value of the spectral index for the AdS (thin blue line) and KS (thick black line) throats is shown as a function of the number of e-folds for $h_{tip} = 10^{-2}$ and $M_p = 100 m_s$. The spectral index for AdS changes sign from negative to positive at the kinked point, so we see that the region where spectral index for the two throats is different falls within the last 60 e-folds of inflation.
• Figure 3: a.) The absolute value of the scalar spectral index is shown for the AdS (thin blue line) and exact KS (thick black line) throats as a function of the redshift factor at the tip $h_{tip}$ at 55 e-folds back from the end of inflation defined in the text. We have fixed $M_p = 100 m_s$. b.) The running of the spectral index also evaluated at 55 e-folds back for the AdS and KS throats.