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On the asymptotic behaviour of cosmic density-fluctuation power spectra

by Sara Konrad, Matthias Bartelmann

Submission summary

As Contributors: Matthias Bartelmann · Sara Konrad
Arxiv Link: (pdf)
Date submitted: 2021-10-15 09:39
Submitted by: Konrad, Sara
Submitted to: SciPost Physics
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
Approach: Theoretical


We study the small-scale asymptotic behaviour of the cosmic density-fluctuation power spectrum in the Zel'dovich approximation. For doing so, we extend Laplace's method in arbitrary dimensions and use it to prove that this power spectrum necessarily develops an asymptotic tail proportional to $k^{-3}$ , irrespective of the cosmological model and the power spectrum of the initial matter distribution. The exponent $-3$ is set only by the number of spatial dimensions. We derive the complete asymptotic series of the power spectrum and compare the leading- and next-to-leading-order terms to derive characteristic scales for the onset of non-linear structure formation, independent of the cosmological model and the type of dark matter. Combined with earlier results on the mean-field approximation for including particle interactions, this asymptotic behaviour is likely to remain valid beyond the Zel'dovich approximation. Due to their insensitivity to cosmological assumptions, our results are generally applicable to particle distributions with positions and momenta drawn from a Gaussian random field. We discuss an analytically solvable toy model to further illustrate the formation of the $k^{-3}$ asymptotic tail.

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Submission 2110.07427v1 on 15 October 2021

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