Constraints on Supersymmetric Models of Hybrid Inflation

TL;DR

This work analyzes how a sub-dominant cosmic-string contribution can reconcile SUSY hybrid inflation models with CMB data. By combining F-term and D-term inflation with a modeled string spectrum and performing MCMC fits to WMAP3 and high-resolution data, the authors derive precision constraints on model parameters: $\log\kappa$, $M$, and $m_{\rm FI}$, along with the string tension $G\mu$. They find that including strings allows $n_s$ to reach around 0.98–1.02 and imposes $G\mu \lesssim 3\times10^{-7}$ (2$\sigma$), with a corresponding $B$-mode signal near $0.3\mu$K rms at $\ell\approx1000$ comparable to lensing-induced B-modes. The results suggest that, if SUSY hybrid inflation is realized in nature, the associated GUT-scale parameters could be directly inferred from cosmological data, though uncertainties in string dynamics and foregrounds remain important.

Abstract

We point out that the inclusion of a string component contributing around 5% to the CMB power spectrum amplitude on large scales can increase the preferred value of the spectral index n_s of density fluctuations measured by CMB experiments. While this finding applies to any cosmological scenario involving strings, we consider in particular models of supersymmetric hybrid inflation, which predict n_s >= 0.98, in tension with the CMB data when strings are not included. Using MCMC analysis we constrain the parameter space allowed for F- and D-term inflation. For the F-term model, using minimal supergravity corrections, we find that \logκ= -2.34\pm 0.38 and M= (0.518\pm 0.059) * 10^16 GeV. The inclusion of non-minimal supergravity corrections can modify these values somewhat. In the corresponding analysis for D-term inflation, we find \logκ= -4.24\pm 0.19 and m_FI= (0.245\pm 0.031) * 10^16 GeV. Under the assumption that these models are correct, these results represent precision measurements of important parameters of a Grand Unified Theory. We consider the possible uncertainties in our measurements and additional constraints on the scenario from the stochastic background of gravitational waves produced by the strings. The best-fitting model predicts a B-mode polarization signal \approx 0.3 μK rms peaking at l \approx 1000. This is of comparable amplitude to the expected signal due to gravitational lensing of the adiabatic E-mode signal on these scales.

Figures (16)

• Figure 1: The computed values of $n_{s}$ (top-left), $\log P_{\cal R}$ (top-right) $\log G\mu$ (bottom-left) and $N_e$ (bottom-right) as a function of $F$-term model parameters $\kappa$ and $M$ for $T_{\rm R}=10^{9}{\rm GeV}$ and g=0.7.
• Figure 2: The computed values of $n_{s}$ (left) and $\log P_{\cal R}$ (right) including the curvature $V_{R}$, and tadpole corrections, $V_{TP}$, to the $F$-term model for $a_S=1{\rm TeV}$, $T_{\rm R}=10^{9}{\rm GeV}$ and $g=0.7$.
• Figure 3: The computed values of $n_{s}$ (left) and $m_{\rm FI}$ for a fixed $P_{\cal R}$, given by (\ref{['power']}). The solid line has the SUGRA parameter $g=10^{-4}$, the dotted line $g=10^{-3}$ and the short-dashed line $g=10^{-2}$. Below $g=10^{-2}$ the observable properties are only very weakly dependent on $g$ for the range of $\kappa$ considered. The long-dashed line shows $g=0.05$, and for small values of $\kappa$ the induced values of $m_{\rm FI}$ and $g$ are increased.
• Figure 4: The computed values of $n_{s}$ (top-left), $\log P_{\cal R}$ (top-right), $\log G\mu$ (bottom-left) and $N_e$ (bottom-right) as a function of $D$-term model parameters $\kappa$ and $M_{\rm FI}$ for $g=10^{-3}$, $T_{\rm R}=10^{9}{\rm GeV}$ and $s=S$.
• Figure 5: Spectrum of anisotropies predicted by the cosmic string model used in this analysis normalized to COBE. The solid line is the temperature anisotropy, the dotted line is the $E$-mode polarization and the dashed line if the $B$-mode polarization. In the right panel we show the ratio of the temperature spectra for $\beta_{r}=1$ (solid), $\beta_{r}=1.3$ (dot), $\beta_{r}=1.6$ (short dash), $\beta_{r}=2.2$ (long dash), $\beta_{r}=2.5$ (dot-short dash), $\beta_{r}=2.8$ (dot-long dash) compared to $\beta_{r}=1.9$.