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Abstract In standard cosmology, the cosmic homogeneity scale is the transition scale above which the patterns arising from non-uniformities – such as groups and clusters of galaxies, voids, and filaments – become indistinguishable from a random distribution of sources. Recently, different groups have investigated the feasibility of using such a scale as a cosmological test and arrived at different conclusions. In this paper, we complement and extend these studies by exploring the evolution of the spatial ( $$R_{\textrm{H}}$$ R H ) and angular ( $$\theta _{\textrm{H}}$$ θ H ) homogeneity scales with redshift, assuming a spatially flat, $$\varLambda $$ Λ -Cold Dark Matter universe and linear cosmological perturbation theory. We confirm previous results concerning the non-monotonicity of $$R_{\textrm{H}}$$ R H with the matter density parameter $$\varOmega _{\textrm{m0}}$$ Ω m0 but also show that it exhibits a monotonical behavior with the Hubble constant $$H_{0}$$ H 0 within a large redshift interval. More importantly, we find that, for $$z \gtrsim 0.6$$ z ≳ 0.6 , $$\theta _{\textrm{H}}$$ θ H presents a monotonical behavior with $$\varOmega _{\textrm{m0}}$$ Ω m0 , as well as for $$H_0$$ H 0 the entire redshift interval analyzed. We find also that the angular homogeneity scale is sensitive to $$H_{0}$$ H 0 , especially at higher redshifts. Using the currently available $$\theta _{\textrm{H}}$$ θ H measurements, we illustrate the constraints on the $$\varOmega _{\textrm{m0}}$$ Ω m0 – $$H_{0}$$ H 0 plane through a MCMC analysis and show the feasibility of using the angular homogeneity scale as a new, model-independent way to constrain cosmological parameters.

Abstract The measurement of present-day temperature of the Cosmic Microwave Background (CMB), $$T_0 = 2.72548 \pm 0.00057$$ T 0 = 2.72548 ± 0.00057 K (1 $$\sigma $$ σ ), made by the Far-InfraRed Absolute Spectrophotometer (FIRAS) as recalibrated by the Wilkinson Microwave Anisotropy Probe (WMAP), is one of the most precise measurements ever made in Cosmology. On the other hand, estimates of the Hubble Constant, $$H_0$$ H 0 , obtained from measurements of the CMB temperature fluctuations assuming the standard $$\varLambda $$ Λ CDM model exhibit a large ( $$4.1\sigma $$ 4.1 σ ) tension when compared with low-redshift, model-independent observations. Recently, some authors argued that a slightly change in $$T_0$$ T 0 could alleviate or solve the $$H_0$$ H 0 -tension problem. Here, we investigate evidence for a hotter or colder universe by performing an independent analysis from currently available temperature-redshift T(z) measurements. Our analysis (parametric and non-parametric) shows a good agreement with the FIRAS measurement and a discrepancy of $$\ge 1.9\sigma $$ ≥ 1.9 σ from the $$T_0$$ T 0 values required to solve the $$H_0$$ H 0 tension. This result reinforces the idea that a solution of the $$H_0$$ H 0 -tension problem in fact requires either a better understanding of the systematic errors on the $$H_0$$ H 0 measurements or new physics.

Abstract We address the $$\simeq 4.4\sigma $$ ≃4.4σ tension between local and the CMB measurements of the Hubble Constant using simulated Type Ia Supernova (SN) data-sets. We probe its directional dependence by means of a hemispherical comparison through the entire celestial sphere as an estimator of the $$H_0$$ H0 cosmic variance. We perform Monte Carlo simulations assuming isotropic and non-uniform distributions of data points, the latter coinciding with the real data. This allows us to incorporate observational features, such as the sample incompleteness, in our estimation. We obtain that this tension can be alleviated to $$3.4\sigma $$ 3.4σ for isotropic realizations, and $$2.7\sigma $$ 2.7σ for non-uniform ones. We also find that the $$H_0$$ H0 variance is largely reduced if the data-sets are augmented to 4 and 10 times the current size. Future surveys will be able to tell whether the Hubble Constant tension happens due to unaccounted cosmic variance, or whether it is an actual indication of physics beyond the standard cosmological model.