The strongest lower limits for t0 come from studies of the stellar populations of globular clusters (GCs). In the mid-1990s the best estimates of the ages of the oldest GCs from main sequence turnoff magnitudes were tGC 15 - 16 Gyr [15, 124, 23]. A frequently quoted lower limit on the age of GCs was 12 Gyr , which was then an even more conservative lower limit on t0 = tGC + tGC, where tGC> ~ 0.5 Gyr is the time from the Big Bang until GC formation. The main uncertainty in the GC age estimates came from the uncertain distance to the GCs: a 0.25 magnitude error in the distance modulus translates to a 22% error in the derived cluster age .
In spring of 1997, analyses of data from the Hipparcos astrometric satellite indicated that the distances to GCs assumed in obtaining the ages just discussed were systematically underestimated [101, 51]. It follows that their stars at the main sequence turnoff are brighter and therefore younger. Stellar evolution calculation improvements also lowered the GC age estimates. In light of the new Hipparcos data, Chaboyer et al.  have done a revised Monte Carlo analysis of the effects of varying various uncertain parameters, and obtained tGC = 11.5±1.3 Gyr (1), with a 95% C.L. lower limit of 9.5 Gyr. The latest detailed analysis  gives tGC = 11.5±2.6 Gyr from main sequence fitting using parallaxes of local subdwarfs, the method used in [101, 51]. These authors get somewhat smaller GC distances when all the available data is used, with a resulting tGC = 12.9±2.9 Gyr (95% C.L.). However, if main sequence fitting is the more reliable method, the younger age may be more appropriate.
Stellar age estimates are of course based on stellar evolution calculations, which have also improved significantly. But the solar neutrino problem reminds us that we are not really sure that we understand how even our nearest star operates; and the sun plays an important role in calibrating stellar evolution, since it is the only star whose age we know independently (from radioactive dating of early solar system material). An important check on stellar ages can come from observations of white dwarfs in globular and open clusters .
What if the GC age estimates are wrong for some unknown reason? The only other non-cosmological estimates of the age of the universe come from nuclear cosmochronometry - radioactive decay and chemical evolution of the Galaxy - and white dwarf cooling. Cosmochronometry age estimates are sensitive to a number of uncertain issues such as the formation history of the disk and its stars, and possible actinide destruction in stars [79, 82]. However, an independent cosmochronometry age estimate of 15.6±4.6 Gyr has been obtained based on data from two low-metallicity stars, using the measured radioactive depletion of thorium (whose half-life is 14.2 Gyr) compared to stable heavy r-process elements [27, 28]. This method could become very important if it were possible to obtain accurate measurements of r-process element abundances for a number of very low metallicity stars giving consistent age estimates, and especially if the large errors could be reduced.
Independent age estimates come from the cooling of white dwarfs in the neighborhood of the sun. The key observation is that there is a lower limit to the luminosity, and therefore also the temperature, of nearby white dwarfs; although dimmer ones could have been seen, none have been found (cf. however ). The only plausible explanation is that the white dwarfs have not had sufficient time to cool to lower temperatures, which initially led to an estimate of 9.3±2 Gyr for the age of the Galactic disk . Since there was evidence, based on the pre-Hipparcos GC distances, that the stellar disk of our Galaxy is about 2 Gyr younger than the oldest GCs (e.g., [121, 108]), this in turn gave an estimate of the age of the universe of t0 11±2 Gyr. Other analyses [132, 56] conclude that sensitivity to disk star formation history, and to effects on the white dwarf cooling rates due to C/O separation at crystallization and possible presence of trace elements such as 22Ne, allow a rather wide range of ages for the disk of about 10±4 Gyr. One determination of the white dwarf luminosity function, using white dwarfs in proper motion binaries, leads to a somewhat lower minimum luminosity and therefore a somewhat higher estimate of the age of the disk of ~ 10.5+2.5-1.5 Gyr . More recent observations  and analyses  lead to an estimated age of the galactic disk of 8±1.5 Gyr.
We conclude that t0 13 Gyr, with ~ 10 Gyr a likely lower limit. Note that t0 > 13 Gyr implies that h 0.50 for matter density m = 1, and that h 0.73 even for m as small as 0.3 in flat cosmologies (i.e., with m + = 1).