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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 $m_ϕ=3.2\times 10^{-31}h$ ${\rm eV}$ 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: $Ω_{m,0}=0.28\pm 0.03$ (95% C.L.), $Ω_{ϕ,0} < 0.035$ (95% C.L.), $ξ> -158$ (95% C.L.) (in the range $ξ\le 0$). The best fit values of the energy density parameter of the scalar field and the coupling constant are $Ω_{ϕ,0}= 0.01$ and $ξ= -25$, respectively. The value of $Ω_{ϕ,0}$ 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 $Ω_{ϕ,0}$ and $ξ$ 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.