Abstract
To constrain the values of the model parameters for the cosmological models involving the time-decaying $\Lambda$ term, we have computed sets of theoretical predictions for the N-m relation of galaxies as well as the CMB angular power spectrum: three types of variation, viz., ${\Lambda}{\propto} T^{-1},\;a^{-m}$, and $H^n$ are thereby assumed following Overduin & Cooperstock (1998), although we concentrate here on the discussion of the results obtained from the first type. Our results for the N-m relation indicate that the observed excess of the galaxy counts N in the faint region beyond the blue apparent magnitude 24 can be reasonably well accounted for with the value of ${\iota}$ in the range between 0.2 and 1. Furthermore, a comparison of our computational results of the CMB spectra with the observational data shows that the models with a mild degree of the $\Lambda$ term decay, viz., with the value of ${\iota}{\le}$0.4, are favorable. In this case, the age of our universe turns out to be larger than or equal to 14 Gyr, the lower limit inferred from some Uranium datings.