  Following \cite{Lin:2009yt}, we explore the parameter space of the case when
the supersymmetry (SUSY) breaking scale is lower, for example, in gauge
mediated SUSY breaking model. During inflation, the form of the potential is
$V_0$ plus MSSM (MSSM stands for Minimal Supersymmetric Standard Model) (or A
term (It is called A-term inflation when the inflaton field is any direction
(gauge or singlet) that generates an A-term.)) inflation. We show that the
model works for a wide range of the potential $V_0$ with the soft SUSY breaking
mass $m\sim O(1)$ TeV. The implication to MSSM (or A-term) inflation is that
the flat directions which is lifted by the non-renormalizable terms described
by the superpotential $W=\lambda_p \phi^{p-1}/M^{p-3}_P$ with $p=4$ and $p=5$
are also suitable to be an inflaton field for $\lambda_p=O(1)$ provided there
is an additional false vacuum term $V_0$ with appropriate magnitude. The flat
directions corresponds to $p=6$ also works for $0 \lae V_0/M_P^4 \lae
10^{-40}$.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena;High Energy Physics - Theory