# $\bar T$: A New Cosmological Parameter?

## TL;DR

This paper discusses the fundamental cosmological parameter $ar T$, highlighting that its unknown monopole contribution can bias parameter estimation in future CMB experiments, despite current precise measurements.

## Contribution

It introduces the issue of fixing $ar T$ to the observed temperature and shows how this causes systematic errors that are irreducible and can bias cosmological inferences.

## Key findings

- Systematic errors from fixing $ar T$ are smaller than Planck errors.
- Future surveys may misinterpret measurements due to irreducible biases.
- Fixing $ar T$ biases parameter estimates proportionally to $ heta_0$.

## Abstract

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 $\Theta_0$ at our position to the observed (angle-averaged) temperature $\langle T\rangle^{\rm obs}$. 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 $\Theta_0$. 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.