We investigate the dynamics of the generalized \Lambda CDM model , which the \Lambda term is running with the cosmological time .
The \Lambda ( t ) term emerges from the covariant theory of the scalar field \phi with the self-interacting potential V ( \phi ) .
On the example of the model \Lambda ( t ) = \Lambda _ { \text { bare } } + \frac { \alpha ^ { 2 } } { t ^ { 2 } } we show the existence of a mechanism of the modification of the scaling law for energy density of dark matter : \rho _ { \text { dm } } \propto a ^ { -3 + \lambda ( t ) } .
We discuss the evolution of \Lambda ( t ) term and pointed out that during the cosmic evolution there is a long phase in which this term is approximately constant .
This effect justifies Alcaniz and Lima ’ s approach to \Lambda ( H ) cosmologies .
We also present the statistical analysis of both the \Lambda ( t ) CDM model with dark energy and decaying dark matter and the \Lambda CDM standard cosmological model .
We divide the observational data into two groups : low z data ( SNIa , BAO , H ( z ) and AP test ) and high z data ( Planck , WP and lensing ) .
While for the former we find the best fit value of the parameter \lambda is positive ( \lambda = 0.0338 , energy transfer is from the dark energy to dark matter sector ) , for the latter we find that \lambda is -0.0199 which is an evidence that the energy transfer is from decaying dark matter .
This disagreement correlates with estimated values of H _ { 0 } ( 67.77 km/ ( s Mpc ) and 65.62 km/ ( s Mpc ) respectively ) .
The decaying dark matter causes to lowering a mass of dark matter particles which are lighter than CDM particles and remain relativistic .
The rate of the process of decaying matter is estimated .
We show that in the models of decaying dark matter , the cosmological constant problem disappears naturally .
The model with decaying dark matter possesses one parameter more but in light of the AIC it is better than the \Lambda CDM standard cosmological model .