The validity of distance duality relation , \eta = D _ { L } ( z ) ( 1 + z ) ^ { -2 } / D _ { A } ( z ) = 1 , an exact result required by the Etherington reciprocity theorem , where D _ { A } ( z ) and D _ { L } ( z ) are the angular and luminosity distances , plays an essential part in cosmological observations and model constraints .
In this paper , we investigate some consequences of such a relation by assuming \eta a constant or a function of the redshift .
In order to constrain the parameters concerning \eta , we consider two groups of cluster gas mass fraction data including 52 X-ray luminous galaxy clusters observed by Chandra in the redshift range 0.3 \sim 1.273 and temperature range T _ { gas } > 4 keV , under the assumptions of two different temperature profiles [ 1 ] .
We find that the constant temperature profile is in relatively good agreement with no violation of the distance duality relation for both parameterizations of \eta , while the one with temperature gradient ( the Vikhlinin et al .
temperature profile ) seems to be incompatible even at 99 % CL .