Cosmological constraints from angular homogeneity scale measurements

Abstract

In this paper, we obtain new measurements of the angular homogeneity scale ($θ_H$) from the BOSS DR12 and eBOSS DR16 catalogs of Luminous Red Galaxies of the Sloan Digital Sky Survey. Considering the flat $Λ$CDM model, we use the $θ_H(z)$ data to constrain the matter density parameter ($Ω_{m0}$) and the Hubble constant ($H_{0}$). We find $H_0 = 65^{+10}_{-7}$ km s$^{-1}$ Mpc$^{-1}$ and $Ω_{m0}>0.296$. By combining the $θ_H$ measurements with current Baryon Acoustic Oscillations (BAO) and Type Ia Supernova (SN) data, we obtain $H_{0}= 66.8 \pm 5.0$ km s$^{-1}$ Mpc$^{-1}$ and $Ω_{m0} = 0.292^{+0.013}_{-0.015}$ ($θ_H$ + BAO) and $H_{0}=66.8 \pm 5.4 $ km s$^{-1}$ Mpc$^{-1}$ and $Ω_{m0}=0.331 \pm 0.018$ ($θ_H$ + SN). We show that $θ_H$ measurements help break the BAO and SN degeneracies concerning $H_0$, as they do not depend on the sound horizon scale at the drag epoch or the SN absolute magnitude value obtained from the distance ladder method. Hence, despite those constraints are less stringent compared to other probes, $θ_H$ data may provide an independent cosmological probe of $H_0$ in light of the Hubble tension. For completeness, we also forecast the constraining power of future $θ_H$ data via Monte Carlo simulations. Considering a relative error of the order of 1$\%$, we obtain competitive constraints on $Ω_{m0}$ and $H_0$ ($\approx 5\%$ error) from the joint analysis with current SN and BAO measurements.