Comparing Brane Inflation to WMAP

TL;DR

Brane inflation in Type IIB string theory, with a D3-brane moving down a warped throat and governed by a DBI action, is tested against WMAP3, SDSS LRG, and SNLS data. The study derives background and perturbation predictions across slow-roll and relativistic regimes, including throat-warping effects and the bulk-volume bound that tightly limits the field range and observable signatures. A comprehensive Monte Carlo analysis shows that, under the bound, slow-roll-like DBI models with small tensor-to-scalar ratio best fit the data, while large tensor modes or strong non-Gaussianity are strongly constrained; relaxing the bound or adopting multi-throat constructions could reopen viable regions. Overall, the work connects cosmological observations to the compactification geometry of extra dimensions and highlights potential stringy signatures to pursue with current and future experiments.

Abstract

We compare the simplest realistic brane inflationary model to recent cosmological data, including WMAP 3-year cosmic microwave background (CMB) results, Sloan Digital Sky Survey luminous red galaxies (SDSS LRG) power spectrum data and Supernovae Legacy Survey (SNLS) Type 1a supernovae distance measures. Here, the inflaton is simply the position of a $D3$-brane which is moving towards a $\bar{D}3$-brane sitting at the bottom of a throat (a warped, deformed conifold) in the flux compactified bulk in Type IIB string theory. The analysis includes both the usual slow-roll scenario and the Dirac-Born-Infeld scenario of slow but relativistic rolling. Requiring that the throat is inside the bulk greatly restricts the allowed parameter space. We discuss possible scenarios in which large tensor mode and/or non-Gaussianity may emerge. Here, the properties of a large tensor mode deviate from that in the usual slow-roll scenario, providing a possible stringy signature. Overall, within the brane inflationary scenario, the cosmological data is providing information about the properties of the compactification of the extra dimensions.

Figures (15)

• Figure 1: A cartoon of the throat in the compact extra dimensions. There may in general be warped throats of a variety of sizes attached to the bulk space. $R$ sets the scale of the throat, while $h_A$ is the warping at the bottom. The $D$3-brane moves down the throat, attracted by a $\bar{D}$3-brane (or a stack of them) sitting at the bottom. The inflation, $\phi$, is related to the brane position, $r$.
• Figure 2: Comparison of the various warp factor expressions. The solid (red) line is the full warped deformed conifold expression. The long dashed (green) line is the AdS warp factor. The dot-dashed (dark blue) is the log-corrected expression, and the short-dashed (light blue) is the mass-gap. For this plot $N_A=10^6$, $M=4000$. The vertical black line indicates $\tau_E$, where the tachyon develops and inflation ends.
• Figure 3: As in Figure \ref{['largeM']} showing warp factors for (top panels) $N_A=10^6$, $M=800$ and (bottom panels) $N_A=10^2$, $M=10$. The right hand panels show a zoomed in region. The vertical black line indicates $\tau_E$, where the tachyon develops and inflation ends.
• Figure 4: Comparison of $n_s$ in different warped geometries.
• Figure 5: Taxonomy of the inflationary parameter space for the AdS warp geometry showing DBI inflationary models from a Monte Carlo simulation which satisfy the WMAP+SDSS+SN1a normalization constraint (\ref{['As_exp2']}) at 95% c.l.. The figure shows the wide variety of inflationary behavior arising from DBI inflation, including relativistic models ($1.1<\gamma<10$,filled yellow triangles and $\gamma>10$ full red squares), large tensor modes (open green triangles), and blue and red-tilted slow-roll spectra (black and blue crosses, respectively). The taxonomy is presented in terms of relationships between the predicted spectrum observables ($n_{s}$, $r$, $dn_{s}/dlnk$) and key model parameters ($m^{2}$, $h_{A}$, $N_{A}$, $\gamma$,and $\phi_{pivot}$). Note that the bottom right figure shows models in comparison to the bulk volume bound imposed by Baumann:2006cd. If the bound is imposed only slow-roll (low tensor, small running, non-relativistic models) with $\phi_{pivot}-\phi_{A}<\sqrt{4/N_{A}}$ are allowed. See the main text for further discussion.