On the asymptotic behaviour of cosmic density-fluctuation power spectra of cold dark matter

Abstract

We study the small-scale asymptotic behaviour of the cold dark matter density fluctuation power spectrum in the Zel'dovich approximation, without introducing an ultraviolet cut-off. Assuming an initially correlated Gaussian random field and spectral index $0<n_s<1$, we derive the small-scale asymptotic behaviour of the initial momentum-momentum correlations. This result is then used to derive the asymptotics of the power spectrum in the Zel'dovich approximation. Our main result is an asymptotic series, dominated by a $k^{-3}$ tail at large wave-numbers, containing higher-order terms that differ by integer powers of $k^{n_s-1}$ and logarithms of $k$. Furthermore, we show that dark matter power spectra with an ultraviolet cut-off develop an intermediate range of scales where the power spectrum is accurately described by the asymptotics of dark matter without a cut-off. These results reveal information about the mathematical structure that underlies the perturbative terms in kinetic field theory and thus the non-linear power spectrum. We also discuss the sensitivity of the small-scale asymptotics to the spectral index $n_s$.

15 pages, 1 table, 6 figures; published in Monthly Notices of the Royal Astronomical Society (MNRAS)

References in corpus (7)

• Universal structure of dark matter haloes over a mass range of 20 orders of magnitude
• The core-cusp problem: a matter of perspective
• The Probability Distribution of Astrophysical Gravitational-Wave Background Fluctuations
• Asymptotic expansions for the Large Scale Structure
• Kinetic Field Theory for Cosmic Structure Formation
• On the asymptotic behaviour of cosmic density-fluctuation power spectra
• Multiple-Scales Approach to The Averaging Problem in Cosmology

Cited by in corpus (2)

• Kinetic Field Theory for Cosmic Structure Formation
• Kinetic Field Theory: Perturbation theory beyond first order