  We construct an inflationary model in 6D supergravity that is based on
explicit time-dependent solutions to the full higher-dimensional field
equations, back-reacting to the presence of a 4D inflaton rolling on a
space-filling codimension-2 source brane. Fluxes in the bulk stabilize all
moduli except the `breathing' modulus (that is generically present in
higher-dimensional supergravities). Back-reaction to the inflaton roll causes
the 4D Einstein-frame on-brane geometry to expand, a(t) ~ t^p, as well as
exciting the breathing mode and causing the two off-brane dimensions to expand,
r(t) ~ t^q. The model evades the general no-go theorems precluding 4D de Sitter
solutions, since adjustments to the brane-localized inflaton potential allow
the power p to be dialed to be arbitrarily large, with the 4D geometry becoming
de Sitter in the limit p -> infinity (in which case q = 0). Slow-roll solutions
give accelerated expansion with p large but finite, and q = 1/2. Because the
extra dimensions expand during inflation, the present-day 6D gravity scale can
be much smaller than it was when primordial fluctuations were generated -
potentially allowing TeV gravity now to be consistent with the much higher
gravity scale required at horizon-exit for observable primordial gravity waves.
Because p >> q, the 4 on-brane dimensions expand more quickly than the 2
off-brane ones, providing a framework for understanding why the observed four
dimensions are presently so much larger than the internal two. If uplifted to a
10D framework with 4 dimensions stabilized, the 6D evolution described here
could describe how two of the six extra dimensions evolve to become much larger
than the others, as a consequence of the enormous expansion of the 4 large
dimensions we can see.
