Constraining Cosmological Parameters Based on Relative Galaxy Ages
Raul Jimenez, Abraham Loeb
TL;DR
This paper introduces a differential-age method to constrain cosmological parameters by measuring the derivative of redshift with cosmic time, $\\frac{dz}{dt}$, through the relative ages of two samples of passively-evolving galaxies at nearby redshifts. By focusing on $\\frac{dz}{dt}$ and its second derivative $\\frac{d^2 z}{dt^2}$, the authors show enhanced sensitivity to the dark-energy equation of state $w_Q(z)$—especially at $z \sim 1$–$2$ where $\\frac{d^2 z}{dt^2}$ constrains $w_Q$ more directly than the luminosity-distance observable. They provide a practical assessment using simulated spectra, demonstrating that high signal-to-noise UV spectroscopy of red, metal-rich ellipticals can yield relative ages with uncertainties on the order of $0.05$–$0.1$ Gyr, and that roughly 70 galaxy pairs are needed for 2σ discrimination between constant and evolving $w_Q(z)$. The method offers a viable, ground-based complement to SN surveys for probing dark energy and can also constrain $H_0$ from local $z$-pairs, potentially achieving percent-level precision with forthcoming large surveys, while remaining independent of the Cepheid distance scale.
Abstract
We propose to use relative galaxy ages as a means of constraining cosmological parameters. By measuring the age difference between two ensembles of old galaxies at somewhat different redshifts, one could determine the derivative of redshift with respect to cosmic time, dz/dt. At high redshifts, z=1-2, this measurement would constrain the equation-of-state of the dark energy, while at low redshifts, z< 0.2, it would determine the Hubble constant, H_0. The selected galaxies need to be passively-evolving on a time much longer than their age difference.