Constraining the expansion rate of the Universe using low-redshift ellipticals as cosmic chronometers

Abstract: We present a new methodology to determine the expansion history of the Universe analyzing the spectral properties of early type galaxies (ETG). We found that for these galaxies the 4000\AA break is a spectral feature that correlates with the relative ages of ETGs. In this paper we describe the method, explore its robustness using theoretical synthetic stellar population models, and apply it using a SDSS sample of $\sim$14 000 ETGs. Our motivation to look for a new technique has been to minimise the dependence of the cosmic chronometer method on systematic errors. In particular, as a test of our method, we derive the value of the Hubble constant $H_0 = 72.6 \pm 2.8$ (stat) $\pm2.3$ (syst) (68% confidence), which is not only fully compatible with the value derived from the Hubble key project, but also with a comparable error budget. Using the SDSS, we also derive, assuming w=constant, a value for the dark energy equation of state parameter $w = -1 \pm 0.2$ (stat) $\pm0.3$ (syst). Given the fact that the SDSS ETG sample only reaches $z \sim 0.3$, this result shows the potential of the method. In future papers we will present results using the high-redshift universe, to yield a determination of H(z) up to $z \sim 1$.