Galaxy N-z Relation and CMB Spectrum Based on Cosmological Model with   Scalar Field Having Modified Potential Form
  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 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 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. 
Koichi Hirano, Kiyoshi Kawabata, Zen Komiya, Hiroshi Bunya
astro-ph.CO gr-qc hep-ph hep-th