  Both inflationary and quintessence cosmologies require scalar fields which
roll very slowly over cosmological time scales, and so typically demand
extremely flat potentials. Sufficiently flat potentials are notoriously
difficult to obtain from realistic theories of microscopic physics, and this
poses a naturalness problem for both types of cosmologies. We propose a
brane-world-based microscopic mechanism for generating scalar potentials which
can naturally be flat enough for both types of cosmological applications. The
scalars of interest are higher-dimensional bulk pseudo-Goldstone bosons whose
scale of symmetry breaking is exponentially suppressed in the
higher-dimensional theory by the separation between various branes. The light
scalars appear in the effective 4D theory as pseudo-Goldstone bosons. Since
naturalness problems are more severe for quintessence models, motivated by our
construction we explore in more detail the possibilities for using
pseudo-Goldstone bosons to build quintessence models. Depending on how the
cosmological constant problem is solved, these models typically imply the
universe is now entering a matter-dominated oscillatory phase for which the
equation of state parameter w = p/rho oscillates between w = 1 and w = -1.
