Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2

TL;DR

The paper advances the cosmic chronometer program by delivering two new $H(z)$ measurements up to $z \sim 2$ using very massive, passive galaxies and the D4000 spectral indicator. It employs the relation $H(z) = -\frac{1}{1+z} A(SFH, Z/Z_{\odot}) \frac{dz}{dD4000_n}$, calibrating $A(SFH, Z/Z_{\odot})$ with stellar population synthesis models and accounting for metallicity and SFH systematics. The authors demonstrate a modest yet non-negligible improvement (~5%) in constraints on $\Omega_M$ and $w_0$ when adding the new data to D4000-based measurements, and they forecast substantial gains for a Euclid-like survey, underscoring the high potential of cosmic chronometers to map the expansion history at $1.5 < z < 2$. Overall, the study highlights the method’s robustness as a single-probe approach at high redshift and its strong synergy with upcoming large surveys.

Abstract

One of the most compelling tasks of modern cosmology is to constrain the expansion history of the Universe, since this measurement can give insights on the nature of dark energy and help to estimate cosmological parameters. In this letter are presented two new measurements of the Hubble parameter H(z) obtained with the cosmic chronometer method up to $z\sim2$. Taking advantage of near-infrared spectroscopy of the few very massive and passive galaxies observed at $z>1.4$ available in literature, the differential evolution of this population is estimated and calibrated with different stellar population synthesis models to constrain H(z), including in the final error budget all possible sources of systematic uncertainties (star formation history, stellar metallicity, model dependencies). This analysis is able to extend significantly the redshift range coverage with respect to present-day constraints, crossing for the first time the limit at $z\sim1.75$. The new H(z) data are used to estimate the gain in accuracy on cosmological parameters with respect to previous measurements in two cosmological models, finding a small but detectable improvement ($\sim$5 %) in particular on $Ω_{M}$ and $w_{0}$. Finally, a simulation of a Euclid-like survey has been performed to forecast the expected improvement with future data. The provided constraints have been obtained just with the cosmic chronometers approach, without any additional data, and the results show the high potentiality of this method to constrain the expansion history of the Universe at these redshifts.

Figures (4)

• Figure 1: Redshift (left plot) and stellar mass (right plot) histograms for the high-z passive galaxies analyzed. The red dotted lines show how the sample has been divided into three redshift bins.
• Figure 2: Upper plot: D4000$_{n}$-z relation for the galaxies considered in this analysis (black points), their weighted average (red points) and the median relation obtained at lower redshifts in moresco2012a in the same mass regime. Intermediate plot: Hubble parameter measurements obtained (red points), compared with literature data. Filled points have been obtained with D4000-based cosmic chronometers, while the open points from the relative age based method. The theoretical relation is not a best-fit to the data, but the $H(z)$ obtained assuming a Planck fiducial cosmology planck. The best fits to the data for a open $\Lambda$CDM cosmology and for a flat wCDM cosmology are shown respectively with a dotted and dashed line. Lower plot: Simulated H(z) data from a Euclid-like survey. The inner errorbar represent the statistical error, while the outer errorbar the total error.
• Figure 3: Marginalized contour plots for an open $\Lambda$CDM cosmology (four upper panels) and in a flat wCDM cosmology (four lower panels). In each cosmology are shown 1-$\sigma$, 2-$\sigma$, and 3-$\sigma$ confidence levels (light, medium and dark gray respectively) considering only the D4000 data or all the data, as highlighted in the captions. Solid lines show the constraints obtained including the new $H(z)$ data, while dashed lines show the constraints without them; the relative gain in accuracy obtainable with these new data can be inferred by comparing the two lines.
• Figure 4: One-dimensional marginalized $\chi^{2}$ for cosmological parameters in an open $\Lambda$CDM cosmology (upper panels) and in a flat wCDM cosmology (lower panels). In each case it is shown for comparison the constraints obtained with D4000 data (with and without the new $H(z)$ measurements, grey and red dashed lines), with all the data (with and without the new $H(z)$ measurements, black and red solid lines), and also with the simulated data added (blue dashed lines).