Model-independent measurement of the matter-radiation equality scale in DESI 2024

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 DV(z = 1.651) = (38.1± 2.5)rH from the quasars and DV(z = 0.733) = (21.8± 1.0)rH from the LRG sample in units of the horizon rH at the matter-radiation-equality epoch. Combining these two constraints and assuming a flat ΛCDM model with three standard neutrino species, we can translate this into a constraint of Ωₘh² = 0.139+0.036-0.046. We can break the Ωₘ-H₀ degeneracy with low-redshift distance measurements from type-Ia supernova (SN) data from Pantheon+, we obtain a sound-horizon free estimate of the Hubble-Lema\^itre parameter of H₀=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 H₀=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 H₀ can be reconciled in a w₀wₐCDM cosmology, where the combination of DESI BAO and TO data yields H₀ = 66.5± 7.2\;km/s/Mpc.