Using a relatively complete observational data concerning four angular diameter distance ( ADD ) measurements and combined SN+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 \sigma level .
Secondly , we note that consistency between ADD and LD data is maintained irrespective of the EoS parameterizations : there is a good match between the universally explored CPL model and other formulations of cosmic equation of state .
Especially for the truncated GEoS model with \beta = -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 _ { \beta } and \beta , which suggest that dark energy was a subdominant component at early times .
Moreover , the GEoS parametrization with \beta \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 ( SGL+CBF+BAO+WMAP9 ) provide the best-fit value \beta = 0.751 ^ { +0.465 } _ { -0.480 } .