We study large-scale inhomogeneous perturbations and instabilities of interacting dark energy ( IDE ) models .
Past analysis of large-scale perturbative instabilities , has shown that we can only test IDE models with observational data when its parameter ranges are either w _ { x } \geq - 1 and \xi \geq 0 , or w _ { x } \leq - 1 ~ { } and ~ { } \xi \leq 0 , where w _ { x } is the dark energy equation of state ( EoS ) , and \xi is a coupling parameter governing the strength and direction of the energy transfer .
We show that by adding a factor ( 1 + w _ { x } ) to the background energy transfer , the whole parameter space can be tested against all the data and thus , the instabilities in such interaction models can be removed .
We test three classes of interaction model using the latest astronomical data from different sources .
Precise constraints are found .
Our analysis shows that a very small but non-zero deviation from pure \Lambda -cosmology is suggested by the observational data while the no-interaction scenario can be recovered at the 68.3 % confidence-level .
In particular , for three IDE models , identified as IDE 1 , IDE 2 , and IDE 3 , the 68.3 % CL constraints on the interaction coupling strengths are , \xi = 0.0360 _ { -0.0360 } ^ { +0.0091 } ( IDE 1 ) , \xi = 0.0433 _ { -0.0433 } ^ { +0.0062 } ( IDE 2 ) , \xi = 0.1064 _ { -0.1064 } ^ { +0.0437 } ( IDE 3 ) .
In addition , we find that the dark energy EoS tends towards the phantom region taking the 68.3 % CL constraints , w _ { x } = -1.0230 _ { -0.0257 } ^ { +0.0329 } ( IDE 1 ) , w _ { x } = -1.0247 _ { -0.0302 } ^ { +0.0289 } ( IDE 2 ) , and w _ { x } = -1.0275 _ { -0.0318 } ^ { +0.0228 } ( IDE 3 ) .
However , the possibility of w _ { x } > -1 is also not rejected by the astronomical data used here .
Moreover , we find in all IDE models that , as the value of Hubble constant decreases , the behavior of the dark energy EoS shifts from phantom to quintessence type with its EoS very close to that a simple cosmological constant at the present time .