Spatial Periodicity of Galaxy Number Counts, CMB Anisotropy, and SNIa
  Hubble Diagram Based on the Universe Accompanied by a Non-Minimally Coupled
  Scalar Field
  We have succeeded in establishing a cosmological model with a non-minimally
coupled scalar field $\phi$ that can account not only for the spatial
periodicity or the {\it picket-fence structure} exhibited by the galaxy $N$-$z$
relation of the 2dF survey but also for the spatial power spectrum of the
cosmic microwave background radiation (CMB) temperature anisotropy observed by
the WMAP satellite. The Hubble diagram of our model also compares well with the
observation of Type Ia supernovae. The scalar field of our model universe
starts from an extremely small value at around the nucleosynthesis epoch,
remains in that state for sufficiently long periods, allowing sufficient time
for the CMB temperature anisotropy to form, and then starts to grow in
magnitude at the redshift $z$ of $\sim 1$, followed by a damping oscillation
which is required to reproduce the observed picket-fence structure of the
$N$-$z$ relation. To realize such behavior of the scalar field, we have found
it necessary to introduce a new form of potential $V(\phi)\propto
\phi^2\exp(-q\phi^2)$, with $q$ being a constant. Through this parameter $q$,
we can control the epoch at which the scalar field starts growing.
