The age problem in the ΛCDM model

The age problem in the ΛCDM model is re-examined. We define the elapsed time T of an object as its age plus the age of the Universe when it was born. Therefore in any cosmology T must be smaller than the age of the Universe. For the old quasar APM 08279+5255 at z= 3.91, previous studies have determined that the best-fitting value of T, 1σ lower limit and lowest limit to T are 2.3, 2.0 and 1.7 Gyr, respectively. Constrained from SNIa+R+A+d, SNIa+R+A+d+H(z) and WMAP5+2dF+SNLS+HST+BBN, the ΛCDM model can only accommodate T(z= 3.91) = 1.7 Gyr at 1σ deviation. Constrained from WMAP5 results only, the ΛCDM model can only accommodate T(z= 3.91) = 1.7 Gyr at 2σ deviation. In all these cases, we found that the ΛCDM model accommodates the total age (14 Gyr for z= 0) of the Universe estimated from old globular clusters, but cannot accommodate statistically the 1σ lower limit to the best-fitting age of APM 08279+5255 at z= 3.91. These results imply that the ΛCDM model may suffer from an age problem.