CMB distance priors revisited: effects of dark energy dynamics, spatial curvature, primordial power spectrum, and neutrino parameters

Abstract: As a physical and sufficient compression of the full CMB data, the CMB distance priors, or shift parameters, have been widely used and provide a convenient way to include CMB data when obtaining cosmological constraints. In this paper, we revisit this data vector and examine its stability under different cosmological models. We find that the CMB distance priors are an accurate substitute for the full CMB data when probing dark energy dynamics. This is true when the primordial power spectrum model is directly generalized from the power spectrum of the model used in the derivation of the distance priors from the CMB data. We discover a difference when a non-flat model with the untilted primordial inflation power spectrum is used to measure the distance priors. This power spectrum is a radical change from the more conventional tilted primordial power spectrum and violates fundamental assumptions for the reliability of the CMB shift parameters. We also investigate the performance of CMB distance priors when the sum of neutrino masses $\sum m_{\nu}$ and the effective number of relativistic species $N_{\text{eff}}$ are allowed to vary. Our findings are consistent with earlier results: the neutrino parameters can change the measurement of the sound horizon from CMB data, and thus the CMB distance priors. We find that when the neutrino model is allowed to vary, the cold dark matter density $\omega_{c}$ and $N_{\text{eff}}$ need to be included in the set of parameters that summarize CMB data, in order to reproduce the constraints from the full CMB data. We present an updated and expanded set of CMB distance priors which can reproduce constraints from the full CMB data within $1\sigma$, and are applicable to models with massive neutrinos, as well as non-standard cosmologies.