Turnover detection using the power spectrum and bispectrum

TL;DR

This work investigates the turnover in the matter power spectrum as a robust standard ruler set by matter–radiation equality, independent of redshift and galaxy bias. The authors forecast turnover detection and precision for Euclid-like and MegaMapper-like spectroscopic surveys using the monopole power spectrum and the equilateral bispectrum, modeling the turnover with a four-parameter asymmetric parabola around $k_0$. They find that PS-only forecasts yield turnover detections at roughly $6\sigma$ (Euclid-like) and $13.5\sigma$ (MegaMapper-like), with $k_0$ precisions of a few percent, while including the bispectrum raises the significance to about $6.4\sigma$ and $14.6\sigma$ and improves $k_0$ precision by ~10–17%. The turnover is a powerful, redshift-stacking probe, with implications for constraining $\Omega_{m0} h^2$ and $H_0$ independently of BAO, though future work should address wide-angle and relativistic corrections in high-redshift surveys.

Abstract

The turnover at the peak of the Fourier matter power spectrum encodes a fundamental signature of matter-radiation equality in the early Universe. This delivers a potential standard ruler, independent of baryon acoustic oscillations and therefore able to break parameter degeneracies and improve precision. Furthermore, the turnover scale is independent of redshift and clustering bias, allowing for stacking of the signals from redshift bins. In practice, the very large scale of the turnover means that sample variance and systematics are serious impediments to its detection. Detections of the turnover and measurements of its scale have been made in the WiggleZ, eBOSS, Quaia, and DESI surveys. Upcoming surveys should improve the detection significance and reduce errors on the turnover scale. We use MCMC forecasts for turnover detection in a spectroscopic Euclid-like survey and a futuristic MegaMapper-like survey. In addition to the power spectrum, we include the signal from the bispectrum in equilateral configurations. These surveys are forecast to detect the turnover at $\sim\! 6σ$ (Euclid-like) and $\sim\! 15σ$ (MegaMapper-like), with precision on the turnover scale of $\sim\! 4\%$ and $\sim\! 2\%$. The inclusion of the bispectrum delivers a modest improvement of $\sim\! 10-17\%$ in the constraints on the turnover scale.

Figures (7)

• Figure 1: Growth factor ( left) and growth rate ( right).
• Figure 2: Matter power spectrum ( left), galaxy monopole power spectrum ( right).
• Figure 3: Monopole of redshift-space power spectrum with 1$\sigma$ errors for Euclid-like survey at redshift $z=1$ ( left) and $z=1.5$ ( right) computed with CLASS (solid black) and compared to the asymmetric parabola best-fit model in \ref{['eq:asymmetric_parabola']} (dashed green and $1\sigma$ shading).
• Figure 4: Triangle plot of parameter constraints from the power spectrum monopole of a Euclid-like survey (all redshift and $k$ bins combined).
• Figure 5: As in \ref{['fig:Ps0_triangle']}, for a MegaMapper-like survey.