Cosmological properties of a class ofΛdecaying 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 $0<~m<\mathrm{}3)$. The models are equivalent to standard cosmology with matter and radiation plus an exotic fluid with the equation of state $p_x=(m/3\mathrm{}-1){\rho }_x.$ We study the effect of the decaying $\Lambda$ term on the cosmic microwave background anisotropy and by using a seminumeric method we compute the angular power spectrum (up to $l=20)$ for different values of $m$ and ${\Omega }_{m0\mathrm{}}$. 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 ${\Omega }_{m0\mathrm{}}$ 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 ${\Omega }_{m0\mathrm{}}$, while those from lensing statistics are more important for $m\gtrsim 1$. Models with ${\Omega }_{m0\mathrm{}}\gtrsim 0.2$ and $m\gtrsim 1.6$ are in good agreement with the data.