A-term inflation and the MSSM

Abstract

The parameter space for A-term inflation is explored with $W=λ_p φ^p/(p M_P^{p-3})$. With p=6 and λ_p~1, the observed spectrum and spectral tilt can be obtained with soft mass of order 10^2 GeV but not with a much higher mass. The case p=3 requires λ_p~10^{-9} to 10^{-12}. The ratio m/A requires fine-tuning, which may be justified on environmental grounds. An extension of the MSSM to include non-renormalizable terms and/or Dirac neutrino masses might support either A-term inflation or modular inflation.

Figures (3)

• Figure 1: The graphic shows lines of constant $n$ (solid line), $\phi_0$ (dashed line) and $\delta^2/m^2$ (thick solid line) for the cases $p=6$ (left hand panel), $p=4$ (central panel) and $p=3$ (right hand panel), as obtained from Eqs. (\ref{['phi0']}), (\ref{['delta^2']}) and (\ref{['phi0^2']}), in the $m$-$\lambda_p$ plane ($\phi_0$ and $m$ are expressed in GeV). Also shown the region where the spectral index is within the observational limits, along with lines $n=1.5$ and $n=0.92$ (corresponding to $\delta^2/m^2=0$) added for reference. The amount of fine-tuning $\delta^2/m^2$ ranges between $\sim10^{-22}$ and $\sim10^{-12}$.
• Figure 2: The graphic shows lines of constant $n$, $\phi_0$ and $\delta^2/m^2$ in the $m$-$\lambda_p$ plane. The left hand panel corresponds to ${\cal P}_{\zeta}^{1/2}$ ten times smaller than the observed value and the right hand panel to ${\cal P}_{\zeta}^{1/2}$ ten times bigger. When ${\cal P}_{\zeta}^{1/2}$ is reduced below its observed value, $V^{\prime}$ must increase in order to reproduce the observed spectrum. This, in turn, results in an increase in $\delta^2/m^2$. On the contrary, when ${\cal P}_{\zeta}^{1/2}$ increases $\delta^2/m^2$ decreases. Given that $(\delta^2/m^2)/(\phi_0/M_P)^4$ does not depend on the particular value ${\cal P}_{\zeta}^{1/2}$ the relative position of the lines of constant $\delta^2$ and $\phi_0$ remains unchanged, as can be seen by comparing the left hand and right hand panels.
• Figure 3: Spectral index $n$ for $p=3,4$ and $p=6$ taking $N=50$. The curves $p=3$ and $p=4$ are indistinguishable.