$\bar{T}$: A New Cosmological Parameter?

The background photon temperature $\bar{T}$ is one of the fundamental cosmological parameters. Despite its significance, $\bar{T}$ has never been allowed to vary in the data analysis, owing to the precise measurement of the comic microwave background (CMB) temperature by COBE FIRAS. However, even in future CMB experiments, $\bar{T}$ will remain unknown due to the unknown monopole contribution ${\mathrm{\Theta }}_0$ at our position to the observed (angle-averaged) temperature $⟨T{⟩}^{\mathrm{o}\mathrm{b}\mathrm{s}}$. By fixing $\bar T\equiv\langle T\rangle^{\rm obs}$, the standard analysis underestimates the error bars on cosmological parameters, and the best-fit parameters obtained in the analysis are biased in proportion to the unknown amplitude of ${\mathrm{\Theta }}_0$. Using the Fisher formalism, we find that these systematic errors are smaller than the error bars from the $Planck$ satellite. However, with $\bar T\equiv\langle T\rangle^{\rm obs}$, these systematic errors will always be present and irreducible, and future cosmological surveys might misinterpret the measurements.