Constraints on Brane Inflation and Cosmic Strings

TL;DR

This work analyzes brane-inflation scenarios with a single brane–antibrane pair in the slow-roll regime while allowing a cosmic-string component in the CMB. It derives analytic relations between fundamental model parameters ($V_0$, $\gamma$, $\beta$) and observables ($n_s$, $r$, $P_{\cal R}$, $G\mu$), and performs MCMC fits to WMAP3 data to constrain these quantities, including the string contribution. Key findings show that including strings tightens bounds to $n_s<1.02$, $G\mu\lesssim 2.5\times10^{-7}$, and $\phi_e/M_P<0.56$ (with $\log_{10}(\gamma/(10^{16}\mathrm{GeV})^4) < 5.3$ and $\log_{10}(V_0/(10^{16}\mathrm{GeV})^4) < -2.3$ in the general case), and Planck-like data could push $G\mu$ down to $\sim6.5\times10^{-8}$ and tighten $\beta$ to $\lesssim0.004$. Consequently, the tensor-to-scalar ratio $r$ is generically tiny in these models (e.g., $r/M<2\times10^{-5}$ for $M=1$), unless one invokes fast-roll/DBI dynamics, which decouple $r$ from $G\mu$ and predict distinct non-Gaussian signatures. Overall, the results connect string-scale parameters to CMB observables and highlight Planck-era prospects for testing brane-inflation scenarios via both temperature/polarization spectra and potential cosmic-string–driven B-modes.

Abstract

By considering simple, but representative, models of brane inflation from a single brane-antibrane pair in the slow roll regime, we provide constraints on the parameters of the theory imposed by measurements of the CMB anisotropies by WMAP including a cosmic string component. We find that inclusion of the string component is critical in constraining parameters. In the most general model studied, which includes an inflaton mass term, as well as the brane-antibrane attraction, values n_s < 1.02 are compatible with the data at 95 % confidence level. We are also able to constrain the volume of internal manifold (modulo factors dependent on the warp factor) and the value of the inflaton field to be less than 0.66M_P at horizon exit. We also investigate models with a mass term. These observational considerations suggest that such models have r < 2*10^-5, which can only be circumvented in the fast roll regime, or by increasing the number of antibranes. Such a value of r would not be detectable in CMB polarization experiment likely in the near future, but the B-mode signal from the cosmic strings could be detectable. We present forecasts of what a similar analysis using PLANCK data would yield and find that it should be possible to rule out Gμ> 6.5*10^-8 using just the TT, TE and EE power spectra.

Figures (3)

• Figure 1: Selected 2D likelihood surfaces for the general potential (\ref{['masspot']}) without (left set of four panels) and with (right set of four panels) including the cosmic string component. For each set of four: (top left) $n_{\rm s}$-$\log_{10}\beta$; (top-right) $n_s-\log_{10}G\mu$; (bottom-right) $\log_{10}(\gamma/(10^{16}{\rm GeV})^4)-\beta$; (bottom-left) $\log_{10}\gamma-\log_{10}(G\mu)$. In all cases the lines correspond to the $68\%$ and $95\%$ joint likelihood limits and the coloured dots correspond to the derived values of $\phi_{\rm e}$ for each member of the chain. It should be clear from these plots that there is an upper limit on $\beta$ and a narrow range of $n_{\rm s}$ is allowed for a specific value of $\beta$. Without including the string contribution, the value of $G\mu$ plotted is that which would be computed using (\ref{['stringtension']}) - there is essentially no meaningful constraint on $\gamma$ and models with $G\mu$ greater than present limits have been allowed in the analysis. With the inclusion of strings, the limit on $G\mu$ imposed by the data has no trivial effects on the allowed parameter ranges, as discussed in the text.
• Figure 2: Results for standard 6 parameter fit with the addition of cosmic strings. The contours show $68\%$ and $95\%$ confidence intervals for WMAP (light contours) and PLANCK (dark contours). Notice that the degeneracies between $n_{\rm s}$, $\Omega_{\rm b}h^2$ and $G\mu$ which is very obvious for WMAP is broken by the high resolution PLANCK data, allowing each of the parameters to be measured individually.
• Figure 3: Same as Fig. \ref{['figure:bi_current']} for simulated PLANCK data. Note that the scales are the same as for the current constraints, illustrating substantial improvement likely from PLANCK.