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 autopower spectrum, utilizing the distribution of quasars 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 analyze 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 Lambda CDM model with three standard neutrino species, we can translate this into a constraint of Omega mh2 = 0.139-F0.036-0.046. We can break the Omega m-H0 degeneracy with low-redshift distance measurements from type-Ia supernova (SN) data from Pantheon-F, we obtain a sound-horizon free estimate of the Hubble-Lema & icirc;tre parameter of H0 = 65.2-F4.9-6.2 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-F7.2-3.5 km/s/Mpc, in line with DESI-only full-shape results where the sound-horizon scale is marginalized 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.