Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements

TL;DR

This work introduces a differential-age cosmic chronometer approach to reconstruct the expansion history H(z) using the ages of the oldest, passively evolving red-envelope galaxies in clusters, combining Keck LRIS spectroscopy with public SDSS, SPICES, and VVDS data. By fitting single stellar populations and extracting the differential ages across redshift, the authors derive H(z) at key redshifts (notably around z≈0.5 and z≈0.8) and then constrain cosmological parameters by joint analysis with CMB data, including models with arbitrary curvature and a time-varying dark-energy equation of state $w(z)=w_0+w_a(1-a)$. They further constrain the number of relativistic species $N_{ m rel}$ and the total neutrino mass $m_ u$, and perform a Chebyshev-polynomial reconstruction of the dark-energy potential $V(z)$, finding consistency with a cosmological constant. The study demonstrates that direct H(z) measurements from cosmic chronometers offer a complementary, resource-efficient pathway to probing dark energy and cosmic geometry, while highlighting the critical role of blue-wavelength coverage and robust stellar-population modeling. The results motivate continued expansion of the data set and refinement of models to solidify the differential-age technique as a competitive dark-energy probe alongside SN, BAO, and weak lensing.

Abstract

We present new determinations of the cosmic expansion history from red-envelope galaxies. We have obtained for this purpose high-quality spectra with the Keck-LRIS spectrograph of red-envelope galaxies in 24 galaxy clusters in the redshift range 0.2 < z < 1.0. We complement these Keck spectra with high-quality, publicly available archival spectra from the SPICES and VVDS surveys. We improve over our previous expansion history measurements in Simon et al. (2005) by providing two new determinations of the expansion history: H(z) = 97 +- 62 km/sec/Mpc at z = 0.5 and H(z) = 90 +- 40 km/sec/Mpc at z = 0.8. We discuss the uncertainty in the expansion history determination that arises from uncertainties in the synthetic stellar-population models. We then use these new measurements in concert with cosmic-microwave-background (CMB) measurements to constrain cosmological parameters, with a special emphasis on dark-energy parameters and constraints to the curvature. In particular, we demonstrate the usefulness of direct H(z) measurements by constraining the dark- energy equation of state parameterized by w0 and wa and allowing for arbitrary curvature. Further, we also constrain, using only CMB and H(z) data, the number of relativistic degrees of freedom to be 4 +- 0.5 and their total mass to be < 0.2 eV, both at 1-sigma.

Figures (17)

• Figure 1: For sufficiently high $S/N$ data over sufficient wavelength range, the age-metallicity degeneracy is lifted. Input mock spectra are from the library by CB08 to which we have added random noise with $S/N = 10$ per resolution element of 3 Å. The thin solid line is the input age. When we fit the same CB08 spectra to these mock spectra with both the age and metallicity as free parameters, we find a very good recovery of the age, with a random dispersion smaller than a few percent. The age-metallciity degeneracy is removed from spectra with blue-light coverage ($2500 - 7500$ Å) and modest $S/N$.
• Figure 2: Age recovery for two different stellar-population models, CB08 and BC03, which rely on different input stellar physics (see text). The (rest frame) wavelength range of the fitted spectrum is $2500$ to $7500$ Å. Note the good age recovery despite different input physics, especially at higher metallicities where the absorption lines are stronger and help lift the age-metallicity degeneracy.
• Figure 3: Same as Fig. \ref{['fig:fig2']} but for a (rest frame) wavelength range of $4500$ to $7500$ Å. Note that it becomes increasingly diffcult to recover the age when blue light in the spectrum is not measured.
• Figure 4: Relative flux of theoretical single stellar populations (SSPs) in the wavelength range $2500$ to $7500$ Å for four different ages: $3, 5, 7, 9$ Gyr, from top to bottom as a ratio of the 2 Gyr spectrum. The plot illustrates how differential ages are measured and the essential role of blue wavelength coverage for this experiment.
• Figure 5: Example of spectra from our observing program. Observed Keck spectra of red galaxies in the cluster MACS J2129.4$-$0741 at $z=0.570$.