Is there evidence for a hotter Universe

The measurement of present-day temperature of the Cosmic Microwave Background (CMB), $$T_0 = 2.72548 \pm 0.00057$$  K (1 $$\sigma $$ ), 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, $$H_0$$ , obtained from measurements of the CMB temperature fluctuations assuming the standard $$\varLambda $$ CDM model exhibit a large ( $$4.1\sigma $$ ) tension when compared with low-redshift, model-independent observations. Recently, some authors argued that a slightly change in $$T_0$$ could alleviate or solve the $$H_0$$ -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 $$\ge 1.9\sigma $$ from the $$T_0$$ values required to solve the $$H_0$$ tension. This result reinforces the idea that a solution of the $$H_0$$ -tension problem in fact requires either a better understanding of the systematic errors on the $$H_0$$ measurements or new physics.