The evolution of two-point correlation function of galaxies with a twin-peak initial power spectrum

The evolution equation of two-point correlation function $\xi$ of galaxies can analytically describe the large scale structure of the galaxy distribution, and the solution depends also upon the initial condition. The primeval spectrum of the baryon acoustic oscillations (BAO) contains multi peaks that survived the Silk damping, and, as a relevant portion, two peaks of the primeval BAO spectrum fall into the range of current galaxy surveys. Incorporating this portion, we use a twin-peak initial power spectrum of the galaxies, and obtain the evolution solution from a redshift $z=8$ to $z=0$ in the Gaussian approximation. The outcome $\xi(r)$ at $z=0.6$ still exhibits the 100 Mpc periodic bumps as observed by the WiggleZ survey, a feature largely determined by the Jeans length $\lambda_J$ in the equation. In particular, due to the superposition of the twin peaks in the initial condition, $\xi(r)$ shows a shallow trough at $\sim 70 h^{-1}$Mpc and a deep trough at $\sim 140 h^{-1}$Mpc, agreeing with the observational data, much better than our previous work that used a simple one-peak initial spectrum.