Observation of Discrete Oscillations in a Model-independent Plot of
  Cosmological Scale Factor vs. Lookback Time and a Scalar Field Model
  We have observed damped longitudinal cosmological-scale oscillations in a
unique model-independent plot of scale factor against cosmological time for
Type Ia supernovae data. We found several first-derivative relative
maxima/minima spanning the range of reported transition-redshifts. These
extrema comprise 2 full cycles with a period of approximately 0.15 Hubble times
(H0=68 km/s/Mpc). This period corresponds to a fundamental frequency of
approximately 7 cycles over the Hubble time. Transition-z values quoted in the
literature generally fall near these minima and may explain the reported wide
spread up to the predicted LCDM value of approximately z = 0.77. We also
observe second and third harmonics of the fundamental. The scale factor data is
analyzed several different ways including smoothing, Fourier transform and
autocorrelation. We propose a cosmological scalar field harmonic oscillator
model for the observation. On this time scale, for a quantum scalar field, the
scalar field mass is extraordinarily small at 3x10-32 eV. Our scalar field
density parameter precisely replaces the LCDM dark matter density parameter in
the Friedmann equations, resulting in essentially identical data fits, and its
present value matches the Planck value. Thus the wave is fundamentally a dark
matter wave. We therefore posit that this scalar field manifests itself as the
dark matter.
