  We study the cosmology of a string derived supersymmetric flipped $SU(5)$
model in the context of free-fermionic heterotic constructions that allow full
calculability of the effective supergravity in perturbation theory around the
fermionic vacuum where all string moduli have fixed values. The model has 3
generations of chiral families and a Higgs sector leading to particle
phenomenology consistent with low energy data, that has been extensively
studied in the past. Here, we show that it can also accommodate a novel
successful cosmology, based on the no-scale effective supergravity derived from
string theory as well as an appropriate induced superpotential suppressed by
five powers of the string scale. It utilises two gauge singlet chiral
superfields present in the low energy spectrum: the inflaton $y$, identified as
the superpartner of a state mixed with R-handed neutrinos, and the goldstino
$z$ with a superpotential of the form $W_I=M_I z(y-\lambda y^2)$ (in
supergravity units) where $\lambda$ is a dimensionless ${\cal O}\left(1\right)$
parameter and $M_I$ the mass scale of inflation generated at 5th order by the
breaking of an anomalous $U(1)_A$ gauge symmetry, characteristic of heterotic
string chiral vacua. The resulting scalar potential leads to Starobinsky type
inflation. Our results can be easily generalised to a large class of models
with similar properties.
