The relative age of galaxies at different redshifts can be used to infer the Hubble parameter and put constraints on cosmological models .
We select luminous red galaxies ( LRGs ) from the SDSS DR7 and then cross-match it with the MPA/JHU catalogue of galaxies to obtain a large sample of quiescent LRGs at redshift z \sim 0.03 - 0.39 .
The total 23,883 quiescent LRGs are divided 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 \lesssim 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 } km~ { } s ^ { -1 } ~ { } Mpc ^ { -1 } or H _ { 0 } = 74 ^ { +5 } _ { -4 } km~ { } s ^ { -1 } ~ { } Mpc ^ { -1 } 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 .