Deflationary cosmology: Constraints from angular size and ages of globular clusters

Observational constraints to a large class of decaying vacuum cosmologies are derived using the angular size data of compact radio sources and the latest age estimates of globular clusters. For this class of deflationary $\Lambda \mathrm{}\left(t\right)\mathrm{}$ models, the present value of the vacuum energy density is quantified by a positive β parameter smaller than unity. In the case of milliarcsecond compact radio-sources, we find that the allowed intervals for β and the matter density parameter ${\Omega }_m$ are heavily dependent on the value of the mean projected linear size l. For $l\simeq {20h}^{-1}-{30h}^{-1}\hspace{0.5em}\mathrm{pc},$ the best fit occurs for $\beta \sim 0.58,$ ${\Omega }_{\mathrm{m}}\sim 0.58,$ and $\beta \sim 0.76,$ ${\Omega }_{\mathrm{m}}\sim 0.28,$ respectively. This analysis shows that if one minimizes ${\chi }^2$ for the free parameters l, ${\Omega }_{\mathrm{m}}$ and β, the best fit for these angular size data corresponds to a decaying $\Lambda \mathrm{}\left(t\right)\mathrm{}$ with ${\Omega }_{\mathrm{m}}=0.54,$ $\beta =0.6,$ and ${l=22.64h}^{-1}$ pc. Constraints from age estimates of globular clusters and old high redshift galaxies are not so restrictive, thereby suggesting that there is no age crisis for this kind of $\Lambda \mathrm{}\left(t\right)\mathrm{}$ cosmologies.