  This paper is about the use of a novel, exact functional quantization method
as applied to two commonly studied actions in theoretical physics. The
functional method in question has its roots in the exact renormalisation group
flow techniques pioneered by Wilson, but with the flow parameter not limited to
the familiar momentum cutoff. Finding a configuration satisfying an expression
for the exact effective action which does not vary with this parameter provides
the basis for finding solutions to the physical actions we study. Firstly, the
method is applied to an expression for the bare action of the pseudo-scalar
axion used to explain the strong CP problem in QCD. When quantized, we find
that the effective potential of the axion, when interactions are not
considered, is necessarily flattened by spinodal instability effects. We regard
this flattening asrepresenting the very early stage in the development of the
axion potential, when the Peccei-Quinn U(1) symmetry is spontaneously broken
resulting in a double-well potential. Using commonly quoted values for the
parameters of such a potential, we devise an expression for the energy density
of the emerging axion potential and this is compared to dark energy. We then
apply the functional method to the bosonic string with time varying graviton,
dilaton and antisymmetric tensor (resulting in the string-axion) background
fields. We achieve a demonstration of conformal invariance in a
non-perturbative manner in the beta functions, contrasting with conventional
string cosmology where cancellation of a perturbative expansion is performed.
We then offer some hints as to possible cosmological implications of our
configuration in terms of optical anisotropy.
