Background photon temperature T¯ : A new cosmological Parameter?

Abstract

The background photon temperature¯T is one of the fundamental cosmological parameters, and it is often set equal to the precise measurement Tobs of the comic microwave background (CMB) temperature by the COBE Far Infrared Absolute Spectrometer (FIRAS). However, even in future CMB experiments,¯T will remain unknown due to the unknown monopole contribution Θ0 at our position to the observed (angle-averaged) temperature Tobs. Using the Fisher formalism, we find that the standard analysis with¯TTobs underestimates the error bars on cosmological parameters by 1%2% of the present errors, and the best-fit parameters obtained in the analysis are biased by 1% of their standard deviation. These systematic errors are negligible for the Planck data analysis, providing a justification to the standard practice. However, with¯TTobs, these systematic errors will always be present and irreducible, and future cosmological surveys might misinterpret the measurements.

Monopole fluctuation of the CMB and its gauge invariance

“…Note that the exact value of our reference ηo (or its theoretical prediction) depends on our choice of cosmological parameters, but it is independent of our choice of coordinate system to describe the observed universe. Furthermore, it was noted [18,21] that the background CMB temperature T (η o ), not T (η o ), is really the CMB temperature today in a homogeneous universe, corresponding to the cosmological parameter ω γ , or the radiation density parameter. For later convenience we define…”

“…Equations ( 25) and ( 27) make it clear that the observed mean temperature T Ω , for instance, from the COBE Far Infrared Absolute Spectrometer (FIRAS) [26] differs from the background CMB temperature T , or the ensemble average, as it includes the monopole fluctuation Θ0 at our position. It was pointed out [18,27] that the ensemble average is equivalent to the Euclidean average, including not only the angle average over the sky, but also the spatial average over different observer positions. Consequently, the mean temperature T Ω today (or the angle average) depends on the spatial position of the observation due to the monopole fluctuation, and its value alone cannot determine the cosmological parameter ω γ (or T ).…”

“…The standard Boltzmann codes such as CAMB [16] and CLASS [17] provide the multipole coefficients a lm and their angular power spectra C l := |a lm | 2 with l ≥ 2, and the comparison to observations determines the best-fit cosmological parameters. However, in the standard data analysis of CMB measurements, the background CMB temperature is set equal to the observed mean temperature T ≡ T Ω by hand, and this formally incorrect procedure results in two problems [18]: 1) The background dynamics in our model predictions differs from the background evolution in our Universe, unless the monopole Θ0 at our position happens to be zero by accident. 2) By using the observed mean T Ω as the background temperature T , the angular multipole coefficients obtained from the observations correspond to…”

“…The gauge-dependence of the standard expression originates from the ambiguity in defining the hypersurface for the background CMB temperature today: being a function of time, the background temperature in the standard background-perturbation split of the observed photon temperature depends on the coordinate system chosen to describe the time coordinate of the observer. However, it was shown [18] that the background CMB temperature today is in fact well defined and there exists no further gauge ambiguity.…”

“…We argue that the background CMB temperature today in eq. ( 7) is unambiguously defined in a given model and its cosmological parameters, and in fact it is one of the fundamental cosmological parameters [18]. Once a choice of the cosmological parameters is made, the monopole fluctuation can be inferred from the angle-average of the observed CMB temperature.…”