On the asymptotic behaviour of cosmic density-fluctuation power spectra of cold dark matter
Feb 16, 202215 pages
Published in:
- Mon.Not.Roy.Astron.Soc. 515 (2022) 4, 5823-5835
- Published: Aug 18, 2022
e-Print:
- 2202.08059 [astro-ph.CO]
View in:
Citations per year
Abstract: (Oxford University Press)
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 kns−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.Note:
- 15 pages, 1 table, 6 figures; published in Monthly Notices of the Royal Astronomical Society (MNRAS)
- cosmology: dark matter
- cosmology: large-scale structure of Universe
- cosmology: theory
References(27)
Figures(6)