The Age-Redshift Relation For Luminous Red Galaxies Obtained From the
  Full Spectrum Fitting and Its Cosmological Implications
  The relative age of galaxies at different redshifts can be used to infer the
Hubble parameter and put constraints on cosmological models. We select 23,883
quiescent luminous red galaxies (LRGs) from the SDSS DR7 and divide them into
four sub-samples according to their velocity dispersions and each sub-sample is
further divided into 12 redshift bins. The spectra of the LRGs in each redshift
and velocity bin are co-added in order to obtain a combined spectrum with
relatively high $S/N$. Adopting the GalexEV/SteLib model, we estimate the mean
ages of the LRGs from these combined spectra by the full-spectrum fitting
method. We check the reliability of the estimated age by using Monte-Carlo
simulations and find that the estimates are robust and reliable. Assuming that
the LRGs in each sub-sample and each redshift bin were on average formed at the
same time, the Hubble parameter at the present time $H_0$ is estimated from the
age--redshift relation obtained for each sub-sample, which is compatible with
the $H_0$ value measured by other methods. We demonstrate that a systematic
bias (up to $\sim 20%$) may be introduced to the $H_0$ estimation because of
recent star formation in the LRGs due to the later major mergers at $z\la 0.4$,
but this bias may be negligible for those sub-samples with large velocity
dispersions. Using the age--redshift relations obtained from the sub-sample
with the largest velocity dispersion or the two sub-samples with high velocity
dispersions, we find $H_0= 65^{+7}_{-3}\kmsmpc$ or $H_0= 74^{+5}_{-4}\kmsmpc$
by assuming a spatially flat $\Lambda$CDM cosmology. With upcoming surveys,
such as the Baryon Oscillation Spectroscopic Survey (BOSS), even larger samples
of quiescent massive LRGs may be obtained, and thus the Hubble parameter can be
measured with high accuracy through the age--redshift relation.
