Plasma Suppression of Large Scale Structure Formation in the Universe

We point out that during the reionization epoch of the cosmic history, the plasma collective effect among the ordinary matter would suppress the large scale structure formation. The imperfect Debye shielding at finite temperature would induce a residual long-range electrostatic potential which, working together with the baryon thermal pressure, would counter the gravitational collapse. As a result the effective Jean's length, $\tilde{\lambda}_J$, is increased by a factor, $\tilde{\lambda}_J/\lambda_J=\sqrt{8/5}$, relative to the conventional one. For scales smaller than the effective Jean's scale the plasma would oscillate at the ion-acoustic frequency. The modes that would be influenced by this effect depend on the starting time and the initial temperature of reionization, but roughly lie in the range $0.5 h{\rm Mpc}^{-1}< k$, which corresponds to the region of the Lyman-$\alpha$ forest from the inter-galactic medium. We predict that in the linear regime of density-contrast growth, the plasma suppression of the matter power spectrum would approach $1-(\Omega_{dm}/\Omega_m)^2\sim 1-(5/6)^2\sim 30$.