The viability of two different classes of \Lambda ( t ) CDM cosmologies is tested by using the APM 08279+5255 , an old quasar at redshift z = 3.91 .
In the first class of models , the cosmological term scales as \Lambda ( t ) \sim R ^ { - n } .
The particular case n = 0 describes the standard \Lambda CDM model whereas n = 2 stands for the Chen and Wu model .
For an estimated age of 2 Gyr , it is found that the power index has a lower limit n > 0.21 , whereas for 3 Gyr the limit is n > 0.6 .
Since n can not be so large as \sim 0.81 , the \Lambda CDM and Chen and Wu models are also ruled out by this analysis .
The second class of models is the one recently proposed by Wang and Meng which describes several \Lambda ( t ) CDM cosmologies discussed in the literature .
By assuming that the true age is 2 Gyr it is found that the \epsilon parameter satisfies the lower bound \epsilon > 0.11 , while for 3 Gyr , a lower limit of \epsilon > 0.52 is obtained .
Such limits are slightly modified when the baryonic component is included .