  We study the cosmological properties of a metastable de Sitter vacuum
obtained recently in the framework of type IIB flux compactifications in the
presence of three D7-brane stacks, based on perturbative quantum corrections at
both world-sheet and string loop level that are dominant at large volume and
weak coupling. In the simplest case, the model has one effective parameter
controlling the shape of the potential of the inflaton which is identified with
the volume modulus. The model provides a phenomenological successful
small-field inflation for a value of the parameter that makes the minimum very
shallow and near the maximum. The horizon exit is close to the inflection point
while most of the required e-folds of the Universe expansion are generated near
the minimum, with a prediction for the ratio of tensor-to-scalar primordial
fluctuations $r \sim 4 \times 10^{-4}$. Despite its shallowness, the minimum
turns out to be practically stable. We show that it can decay only through the
Hawking-Moss instanton leading to an extremely long decay rate. Obviously, in
order to end inflation and obtain a realistic model, new low-energy physics is
needed around the minimum, at intermediate energy scales of order $10^{12}$
GeV. An attractive possibility is by introducing a "waterfall"' field within
the framework of hybrid inflation.
