Model-Independent Measurement of the Matter-Radiation Equality Scale in DESI 2024

TL;DR

This work reports the first model-independent detection of the matter-radiation equality turnover in a galaxy auto-power spectrum using DESI Year 1 data from QSO and LRG samples, validated with data-blinding to avoid bias. It introduces a five-parameter, template-based turnover model around a fiducial scale and fits it via a Gaussian likelihood, incorporating window functions and a deprojection framework to control systematics. The turnover measurements yield a near-unity dilation parameter $\alpha_{TO}$ for both tracers and enable a sound-horizon-free constraint on $\Omega_m h^2$; combining turnover with BAO and SN data provides competitive H0 estimates and tests for evolving dark energy. The results establish the turnover as a robust, complementary standard ruler for low-redshift cosmology and point toward substantial gains with the full DESI data set and inclusion of additional tracers.

Abstract

The peak of the matter power spectrum, known as the turnover (TO) scale, is determined by the horizon size at the time of matter-radiation equality. This scale can serve as a standard ruler, independent of other features in the matter power spectrum, such as baryon acoustic oscillations (BAO). Here, we present the first detection of the turnover in the galaxy auto-power spectrum, utilising the distribution of quasars (QSO) and luminous red galaxies (LRG) measured by the Dark Energy Spectroscopic Instrument (DESI) during its first year of survey operations in a model-independent manner. To avoid confirmation bias, we first analyse the data using data blinding methods designed for the DESI baryon acoustic oscillation, redshift space distortion and scale-dependent bias signals. We measure the angle-averaged dilation distance $D_V(z = 1.651) = (38.1\pm 2.5)r_H$ from the quasars and $D_{V}(z = 0.733) = (21.8\pm 1.0)r_H$ from the LRG sample in units of the horizon $r_H$ at the matter-radiation-equality epoch. Combining these two constraints and assuming a flat $Λ$CDM model with three standard neutrino species, we can translate this into a constraint of $Ω_{m}h^2 = 0.139^{+0.036}_{-0.046}$. We can break the $Ω_m$-$H_0$ degeneracy with low-redshift distance measurements from type-Ia supernova (SN) data from Pantheon+, we obtain a sound-horizon free estimate of the Hubble-Lemaître parameter of $H_0=65.2^{+4.9}_{-6.2}$ km/s/Mpc, consistent with sound-horizon dependent DESI measurements. On the other hand, combining the DESI BAO and TO, we find a truly DESI-only measurement of $H_0=74.0^{+7.2}_{-3.5}$ km/s/Mpc, in line with DESI-only full-shape results where the sound-horizon scale is marginalised out. This discrepancy in $H_0$ can be reconciled in a $w_0w_a$CDM cosmology, where the combination of DESI BAO and TO data yields $H_0 = 66.5\pm 7.2\;\mathrm{km/s/Mpc}$.

Figures (13)

• Figure 1: The evolution of the mass density of different components as a function of redshift, assuming a single massive neutrino species with mass 0.06 eV (golden line), and two other massless species (combined with the photons in the red dashed line). The equality redshift $z_\mathrm{eq}$ is given by the point where the blue (total relativistic energy density) and green (total non-relativistic energy density) lines coincide. For comparison, we also show the combined neutrino energy density in a cosmology where all neutrinos are massless as a red dot-dashed line. We can observe, that at the matter-radiation-equality epoch, the massive neutrino effectively behaves like a massless neutrino.
• Figure 2: Constraints on turnover parameters from the mean of DESI Y1 LRG and QSO EZmock power spectra obtained with different values of $k_\mathrm{max}$. The filled contours correspond to the fiducial $k_\mathrm{max} = 0.2\, h/\mathrm{Mpc}$ used throughout this article.
• Figure 3: DESI Y1 LRG and QSO power spectra. Pale data points and errorbars show the blinded data, whereas opaque ones the data after unblinding. The solid curves represent the best fit (cf. Section \ref{['sec:results']}). The apparent mismatch between data and best fit at small scales are the effect of the mode deprojection of the modelling uncertainty at these scales far from the power spectrum peak (cf. equation \ref{['eq:moddeproj']}).
• Figure 4: Top:$\alpha_\mathrm{TO}$-$m$ contours obtained from the same Abacus LRG mock without any blinding applied (red), and with a blinding corresponding to $f_\mathrm{NL}^\mathrm{blind} = \pm 20$ applied. Bottom: The dependence of the best-fitting values of $m$ and $\alpha_\mathrm{TO}$ and their uncertainties as a function of $f_\mathrm{NL}^\mathrm{blind}$.
• Figure 5: Products of the normalised redshift distributions of the LRG and QSO samples.