Transfer of power in non-linear gravitational clustering

Abstract

We investigate the transfer of power between different scales and the coupling of modes during the non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales, and use numerical simulations to study the evolution of this power spectrum. Non-linear effects generate power at other scales, with most power flowing from larger to smaller scales. The 'cascade' of power leads to equipartition of energy at smaller scales, implying a power spectrum with index n≈-1. We find that such a spectrum is produced in the range 1<δ<200 for density contrast delta. This result continues to hold even when small-scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index n_c≈-1 in this range. For n<n_c, power in this range grows faster than linear rate, while if n>n_c, it grows at a slower rate - thereby changing the index closer to n_c. At scales larger than the narrow range of scales with initial power, a k⁴ tail is produced. We demonstrate that non-linear small scales do not affect the growth of perturbations at larger scales.