  Fluxbrane inflation is a stringy version of D-term inflation in which two
fluxed D7-branes move towards each other until their (relative) gauge flux
annihilates. Compared to brane-antibrane inflation, the leading-order
inflationary potential of this scenario is much flatter. In the present paper
we first discuss a new explicit moduli stabilisation procedure combining the F-
and D-term scalar potentials: It is based on fluxed D7-branes in a geometry
with three large four-cycles of hierarchically different volumes. Subsequently,
we combine this moduli stabilisation with the fluxbrane inflation idea,
demonstrating in particular that CMB data (including cosmic string constraints)
can be explained within our setup of hierarchical large volume CY
compactifications. We also indicate how the eta-problem is expected to
re-emerge through higher-order corrections and how it might be overcome by
further refinements of our model. Finally, we explain why recently raised
concerns about constant FI terms do not affect the consistent, string-derived
variant of D-term inflation discussed in this paper.
