The role of $T_0$ in CMB anisotropy measurements

The quantity $T_0$, the cosmic microwave background (CMB) monopole, is an often neglected seventh parameter of the standard cosmological model. As well as its variation affecting the physics of the CMB, the measurement of $T_0$ is also used to calibrate the anisotropies, via the orbital dipole. We point out that it is easy to misestimate the effect of $T_0$ because the CMB anisotropies are conventionally provided in temperature units. In fact the anisotropies are most naturally described as dimensionless and we argue for restoring the convention of working with $Delta T/T$ rather than $Delta T$. As a free cosmological parameter, $T_0$ most naturally only impacts the CMB power spectra through late-time effects. Thus if we ignore the COBE-FIRAS measurement, current CMB data only weakly constrain $T_0$. Even ideal future CMB data can at best provide a percent-level constraint on $T_0$, although adding large-scale structure data will lead to further improvement. The FIRAS measurement is so precise that its uncertainty negligibly effects most, but not all, cosmological parameter inferences for current CMB experiments. However, if we eventually want to extract all available information from CMB power spectra measured to multipoles $ellsimeq5000$, then we will need a better determination of $T_0$ than is currently available.