N-z Relation and CMB Anisotropies in the Universe with an Oscillating Scalar Field Having a Null Field State

We investigate whether or nor it is possible to find a scalar field model or models that are capable of explaining simultaneously the observed $N$-$z$ relation given by the 2dF Galaxy Redshift Survey, which still seems to exhibit a spatial periodicity of the galaxy distribution(the ‘picket-fence structure’), and the CMB spectrum obtained by the WMAP experiments. It is found that both the observed size of the spatial periodicity and the amplitude of the 2dF $N$-$z$ relation can be fairly well fitted by the theoretical computations based on the scalar field models with $-20\le \xi \le -10$, and $140\le m_{\rm s} \le 160$,where$\xi$isthegravitationalcouplingparameter,and$m_{\rm s}$ the normalized mass of the scalar field, respectively. To reproduce the CMB spectrum of the WMAP, we find that it is very crucial to have a null state of the scalar field in the early epochs of evolution of the universe.