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 $\Lambda (t)$ models, the present value of the vacuum energy density is quantified by a positive $\beta$ parameter smaller than unity. In the case of milliarcsecond compact radio-sources, we find that the allowed intervals for $\beta$ and the matter density parameter ${\Omega }_m$ are heavily dependent on the value of the mean projected linear size $l$. For $l\simeq 20h^{-1}-30h^{-1}$ 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 $\beta$, the best fit for these angular size data corresponds to a decaying $\Lambda (t)$ 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 $\Lambda (t)$ cosmologies.

6 pages, 3 figures, revised version to appear in Phys. Rev. D

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