  We introduce a duality relation between two distinct branes, a cosmological
brane with macroscopic matter and a holographic brane with microscopic gauge
fields. Using brane-world cosmology with a single brane in a 5-dimensional AdS5
background, we find an explicit time-dependent holographic correspondence
between the bulk metric surrounding the cosmological brane and the N=4 gauge
field theory living on the boundary of the Z2-symmetric mirror bulk, identified
with the holographic brane. We then relate the cosmic acceleration on the
cosmological brane to the conformal anomaly of the gauge theory on the
holographic brane. This leads to a dual microscopic interpretation of the
number of e-foldings of the cosmological eras on the cosmological brane.
