Observational tests for oscillating expansion rate of the Universe
  We investigate the observational constraints on the oscillating scalar field
model using data from type Ia supernovae, cosmic microwave background
anisotropies, and baryon acoustic oscillations. According to a Fourier
analysis, the galaxy number count $N$ from redshift $z$ data indicates that
galaxies have preferred periodic redshift spacings. We fix the mass of the
scalar field as $m_\phi=3.2\times 10^{-31}h$ ${\rm eV}$ such that the scalar
field model can account for the redshift spacings, and we constrain the other
basic parameters by comparing the model with accurate observational data. We
obtain the following constraints: $\Omega_{m,0}=0.28\pm 0.03$ (95% C.L.),
$\Omega_{\phi,0} < 0.035$ (95% C.L.), $\xi > -158$ (95% C.L.) (in the range
$\xi \le 0$). The best fit values of the energy density parameter of the scalar
field and the coupling constant are $\Omega_{\phi,0}= 0.01$ and $\xi= -25$,
respectively. The value of $\Omega_{\phi,0}$ is close to but not equal to $0$.
Hence, in the scalar field model, the amplitude of the galaxy number count
cannot be large. However, because the best fit values of $\Omega_{\phi,0}$ and
$\xi$ are not $0$, the scalar field model has the possibility of accounting for
the periodic structure in the $N$--$z$ relation of galaxies. The variation of
the effective gravitational constant in the scalar field model is not
inconsistent with the bound from observation.
