The minimal power spectrum: Higher order contributions
J. N. Fry · The Astrophysical Journal · 1994
It has been an accepted belief for some time that gravity induces a minimal tail P(k) approximately k4 in the power spectrum as k approaches 0 for distributions with no initial power on large scales. In a recent numerical experiment with initial power confined to a restricted range in k, Shandarin and Melott (1990) found a k approaches 0 tail that at early stages of evolution behaves as k4 and grows with time as a4(t), where a(t) is the cosmological expansion factor, and at late times depends on scale as k3 and grows with time as a2(t). I compute analytically several contributions to the power spectrum of higher order than those included in earlier work, and I apply the results to the particular case of initial power restricted to a finite range of k. As expected, in the perturbative regime P(k) approximately a4k4 from the first correction to linear perturbation theory is the dominant term as k approaches 0. Numerical investigations show that the higher order contributions go as k4 also. However, perturbation theory alone cannot tell whether the P approximately a2k3 result is 'nonperturbative' or a numerical artifact.