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

Abstract

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 $Λ(t)$ 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 $Ω_m$ are heavily dependent on the value of the mean projected linear size $l$. For $l \simeq 20h^{-1} - 30h^{-1}$ pc, the best fit occurs for $β\sim 0.58$, $Ω_{\rm{m}} \sim 0.58$, and $β\sim 0.76$, $Ω_{\rm{m}} \sim 0.28$, respectively. This analysis shows that if one minimizes $χ^{2}$ for the free parameters $l$, $Ω_{\rm{m}}$ and $β$, the best fit for these angular size data corresponds to a decaying $Λ(t)$ with $Ω_{\rm{m}} = 0.54$ $β=0.6$ 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 $Λ(t)$ cosmologies.