Cosmological properties of a class of $\Lambda$ decaying cosmologies

We investigate some properties of flat cosmological models with a $\Lambda$ term that decreases with time as $\Lambda \propto a^{-m}$ (a is the scale factor and m is a parameter $0\leq m < 3$). The models are equivalent to standard cosmology with matter and radiation plus an exotic fluid with the equation of state $p_x = (m/3 -1)\rho_x$. We study the effect of the decaying $\Lambda$ term on the cosmic microwave background (CMB) anisotropy and by using a seminumeric method we compute the angular power spectrum (up to l=20) for different values of m and $\Omega_{m0}$. We also investigate the constraints imposed on the models by the magnitude-redshift test in which high-redshift type Ia supernovae (SNe Ia) are used as standard candles. We obtain the 95.4%, 90%, and 68% confidence levels on the parameters m and $\Omega_{m0}$ and compare them with those arising from lensing statistics. Our analysis reveals that the SNe Ia constraints are stronger for low values of m and $\Omega_{m0}$, while those from lensing statistics are more important for $m > \sim 1$. Models with $\Omega_{m0} > \sim 0.2$ and $m > \sim 1.6$ are in good agreement with the data.