  We investigate the ability of current CMB data to reliably constrain the form
of the primordial power spectrum generated during inflation. We attempt to
identify more exotic power spectra that yield equally good fits to the data as
simple power-law spectra. In order to test a wide variety of spectral shapes,
we combine the flow formalism, which is a method of stochastic model
generation, with a numerical integration of the mode equations of quantum
fluctuations. This allows us to handle inflation models that yield spectra that
are not well described by the standard spectral parameterization. Using the
latest WMAP data-set, we find a high degree of variation in possible spectral
shapes. In particular, we find strongly running spectra arising from
fast-rolling inflaton fields providing equally good fits to the data as
power-law spectra arising from slowly-rolling fields. Current data poorly
constrains the spectrum on scales (k < 0.01 h{\rm Mpc}^{-1}), where the error
due to cosmic variance is large. Among the statistically degenerate models, we
identify spectra with strong running on these larger scales, but with reduced
running at smaller scales. These models predict values for the tensor-to-scalar
ratio, (r), that lie outside the 2-(\sigma) confidence interval obtained from
SDSS+WMAP data for spectra that are parametrized as power-laws or spectra with
constant running. By considering more generalized power spectra, we therefore
open up regions of parameter space excluded for simpler models.
