The cosmic microwave background (CMB) temperature, $T$, surely the most precisely measured cosmological parameter, has been inferred from local measurements of the black body spectrum to an exquisite precision of 1 part in $\sim 4700$. On the other hand, current precision allows inference of other basic cosmological parameters at the $\sim 1\%$ level from CMB power spectra, galaxy correlation and lensing, luminosity distance measurements of supernovae, as well as other cosmological probes. A basic consistency check of the standard cosmological model is an independent inference of $T$ at recombination. In this work, we first use the recent Planck data, supplemented by either the first year data release of the dark energy survey, baryon acoustic oscillations (BAO) data, and the Pantheon SNIa (supernovae type Ia) catalog, to extract $T$ at the $\sim 1\%$ precision level. We then explore correlations between $T$, the Hubble parameter, $H_0$, and the global spatial curvature parameter, ${\mathrm{\Omega }}_k$. Our parameter estimation indicates that imposing the local constraint from the SH0ES experiment on $H_0$ results in significant statistical preference for departure at recombination from the locally inferred $T$. However, only moderate evidence is found in this analysis for tension between local and cosmological estimates of $T$, if the local constraint on $H_0$ is relaxed. All other data set combinations that include the CMB with either BAO, SNIa, or both, disfavor the addition of a new free temperature parameter even in the presence of the local constraint on $H_0$. Analysis limited to the Planck data set suggests the temperature at recombination was higher than expected at recombination at the $\gtrsim 95\%$ confidence level if space is globally flat. An intriguing interpretation of our results is that fixing the temperature to its locally inferred value would result in a preference for spatially closed Universe, if $T(z)$ is assumed to evolve adiabatically and the analysis is based only on the Planck data set.

• Received 7 September 2020
• Accepted 29 September 2020

DOI:https://doi.org/10.1103/PhysRevD.102.083532