Quantifying the CMB Degeneracy Between the Matter Density and Hubble Constant in Current Experiments

Understand

We revisit the degeneracy between the Hubble constant, $H_0$, and matter density, $\Omega_m$, for current cosmic microwave background (CMB) observations within the standard $\Lambda CDM$ model.

• We show that Planck, Wilkinson Microwave Anisotropy Probe (WMAP), South Pole Telescope (SPT), and Atacama Cosmology Telescope Polarimeter (ACTPol) temperature power spectra produce different values of the exponent $x$ from minimizing the variance of the product $\Omega_mH_0^x$.
• The distribution of $x$ from the different data sets does not follow the Markov Chain Monte Carlo (MCMC) best-fit values for $H_0$ or $\Omega_m$.
• Particularly striking is the difference between Planck multipoles $\ell\leq800$ ($x=2.81$), and WMAP ($x = 2.94$), despite very similar best-fit cosmologies.