Approximating Density Probability Distribution Functions Across Cosmologies

Abstract

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: $n_s$, the spectral slope, and ${\sigma }_L$, the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, $s_L=\sqrt{⟨(d{v}_{\mathrm{pec}}^L/dr{)}^2⟩}/H$. We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.

arXiv comment9 pages, 10 figures, submitted to ApJ, comments welcome

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• Measuring the Density Fields around Bright Quasars at $z\sim 6$ with XQR-30 Spectra