Cosmic equation of state from combined angular diameter distances: Does the tension with luminosity distances exist?

Abstract

Using relatively complete observational data concerning four angular diameter distance (ADD) measurements and combined $\mathrm{SN}+\mathrm{GRB}$ observations representing current luminosity distance (LD) data, this paper investigates the compatibility of these two cosmological distances considering three classes of dark energy equation of state (EoS) reconstruction. In particular, we use strongly gravitationally lensed systems from various large systematic gravitational lens surveys and galaxy clusters, which yield the Hubble constant independent ratio between two angular diameter distances ${D}_{ls}/{D}_{s}$ data. Our results demonstrate that, with more general categories of standard ruler data, ADD and LD data are compatible at $1\ensuremath{\sigma}$ level. Second, we note that consistency between ADD and LD data is maintained irrespective of the EoS parametrizations: there is a good match between the universally explored Chevalier-Polarski-Linder model and other formulations of cosmic equation of state. Especially for the truncated generalized equation of state (GEoS) model with $\ensuremath{\beta}=\ensuremath{-}2$, the conclusions obtained with ADD and LD are almost the same. Finally, statistical analysis of generalized dark energy equation of state performed on four classes of ADD data provides stringent constraints on the EoS parameters ${w}_{0}$, ${w}_{\ensuremath{\beta}}$, and $\ensuremath{\beta}$, which suggest that dark energy was a subdominant component at early times. Moreover, the GEoS parametrization with $\ensuremath{\beta}\ensuremath{\simeq}1$ seems to be a more favorable two-parameter model to characterize the cosmic equation of state, because the combined angular diameter distance data ($\mathrm{SGL}+\mathrm{CBF}+\mathrm{BAO}+\mathrm{WMAP}9$) provide the best-fit value $\ensuremath{\beta}=0.75{1}_{\ensuremath{-}0.480}^{+0.465}$.