Evidences for an Old Universe
Rates at which galaxies at different distances are receding from the Milky Way (7-20 Ga for bounded universe, 10-20 Ga for unbounded)
Study of globular clusters in our galaxy (14-18 Ga)
Beginning of nucleosynthesis, based on study of long-lived nuclides (8.6-15.7 Ga)
Best estimate = 15 +- 1.5 Ga
Notes:
According to Dalrymple (p. 393), "there are three astrophysical methods by which the age of the Galaxy or the age of the visible universe may be estimated":
1. "From the rates at which galaxies at different distances are receding from the Milky Way Galaxy, the time at which the expansion or inflation of the universe began can be calculated... Hubble constant values in the range 50-100 km/s/Mpc give a corresponding Hubble time of 10-20 Ga for an unbounded universe that will expand forever and 7-20 Ga for a bounded universe that is decelerating and will eventually begin to contract."
2. "Their very low metal contents indicate that the oldest stars in the Galaxy are those in globular clusters, which reside in the spherical ‘halo' that surrounds the galactic disk. The ages of stars in a globular cluster can be estimated by comparing their turnoff point from the main sequence on the Hertzsprung-Russell diagram to theoretical isochrones calculated for stars of various masses and compositions. Results from well-studied globular clusters indicate that the Galaxy formed about 14-18 Ga".
3. "The mean age of the r-process elements can be calculated from the abundances, production ratios, and decay constants of long-lived nuclides. Results for two long-lived chronometer pairs suggest a model-independent younger limit for the beginning of nucleosynthesis and the age of the Galaxy of 8.6 Ga, and a model-dependent older limit of 15.7 Ga."
Requiring that these results be consistent, further analysis considering the most reasonable values for the density of nuclear matter and the amount of helium relative to hydrogen created during the Big Bang yields an age for the universe of 15 +- 1.5 Ga.