Constraints on Supersymmetric Grand Unified Theories from Cosmology

TL;DR

The work probes how cosmic strings formed at the end of SUSY GUT hybrid inflation imprint on the CMB and uses WMAP data to constrain the model parameters. It shows that F-term inflation is viable only for very small superpotential couplings $\kappa$ (e.g., $\kappa \lesssim 7\times 10^{-7}$ for certain representations) unless the curvaton mechanism is invoked, which relaxes the bound to $\kappa \lesssim 8\times 10^{-3}$. In D-term inflation, the inflaton value is of order the Planck scale, requiring a SUGRA treatment; the strings contribution to the CMB varies with the gauge and Yukawa couplings, yielding robust bounds $g \lesssim 2\times 10^{-2}$, $\lambda \lesssim 3\times 10^{-5}$, and $\sqrt{\xi} \lesssim 2\times 10^{15}$ GeV. Collectively, the results constrain both F-term and D-term SUSY GUT inflation scenarios, highlight the role of the curvaton in alleviating fine-tuning, and emphasize the necessity of SUGRA for D-term models to be cosmologically viable.

Abstract

Within the context of SUSY GUTs, cosmic strings are generically formed at the end of hybrid inflation. However, the WMAP CMB measurements strongly constrain the possible cosmic strings contribution to the angular power spectrum of anisotropies. We investigate the parameter space of SUSY hybrid (F- and D- term) inflation, to get the conditions under which theoretical predictions are in agreement with data. The predictions of F-term inflation are in agreement with data, only if the superpotential coupling $κ$ is small. In particular, for SUSY SO(10), the upper bound is $κ\lsim 7\times 10^{-7}$. This fine tuning problem can be lifted if we employ the curvaton mechanism, in which case $κ\lsim 8\times 10^{-3}$; higher values are not allowed by the gravitino constraint. The constraint on $κ$ is equivalent to a constraint on the SSB mass scale $M$, namely $M \lsim 2\times 10^{15}$ GeV. The study of D-term inflation shows that the inflaton field is of the order of the Planck scale; one should therefore consider SUGRA. We find that the cosmic strings contribution to the CMB anisotropies is not constant, but it is strongly dependent on the gauge coupling $g$ and on the superpotential coupling $λ$. We obtain $g\lsim 2\times 10^{-2}$ and $λ\lsim 3\times 10^{-5}$. SUGRA corrections induce also a lower limit for $λ$. Equivalently, the Fayet-Iliopoulos term $ξ$ must satisfy $\sqrtξ\lsim 2\times 10^{15}$ GeV. This constraint holds for all allowed values of $g$.

Figures (7)

• Figure 1: Evolution of the inflationary scale $M$ in units of $10^{15}$ GeV as a function of the dimensionless coupling $\kappa$. The three curves correspond to $\mathcal{N}=\mathbf{27}$ (curve with broken line), $\mathcal{N}=\mathbf{126}$ (full line) and $\mathcal{N}=\mathbf{351}$ (curve with lines and dots).
• Figure 2: Evolution of the cosmic strings contribution to the quadrupole anisotropy as a function of the coupling of the superpotential, $\kappa$. The three curves correspond to $\mathcal{N}=\mathbf{27}$ (curve with broken line), $\mathcal{N}= \mathbf{126}$ (full line) and $\mathcal{N}=\mathbf{351}$ (curve with lines and dots).
• Figure 3: Constraints on the single parameter $\kappa$ of the model. The gravitino constraint implies $\kappa\leq 8\times 10^{-3}$. The allowed cosmic strings contribution to the CMB angular power spectrum implies $\kappa \hbox{$<$$\sim$} 7\times 10^{-7}$, for $\mathcal{N}=\mathbf{126}$.
• Figure 4: The cosmic strings (dark gray), curvaton (light gray) and inflaton (gray) contributions to the CMB temperature anisotropies as a function of the the initial value of the curvaton field ${\cal\psi}_{\rm init}$, and the superpotential coupling $\kappa$, for ${\cal N}=\mathbf{126}$.
• Figure 5: On the left, evolution of the mass scale $\sqrt\xi$ as a function of the coupling $\lambda$. On the right, evolution of the cosmic strings contribution to the quadrupole anisotropy as a function of the coupling of the superpotential, $\lambda$. These plots are derived in the framework of SUSY.