A 6% measurement of the Hubble parameter at $z\sim0.45$: direct evidence of the epoch of cosmic re-acceleration

Abstract

Deriving the expansion history of the Universe is a major goal of modern cosmology. To date, the most accurate measurements have been obtained with Type Ia Supernovae and Baryon Acoustic Oscillations, providing evidence for the existence of a transition epoch at which the expansion rate changes from decelerated to accelerated. However, these results have been obtained within the framework of specific cosmological models that must be implicitly or explicitly assumed in the measurement. It is therefore crucial to obtain measurements of the accelerated expansion of the Universe independently of assumptions on cosmological models. Here we exploit the unprecedented statistics provided by the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 to provide new constraints on the Hubble parameter $H(z)$ using the em cosmic chronometers approach. We extract a sample of more than 130000 of the most massive and passively evolving galaxies, obtaining five new cosmology-independent $H(z)$ measurements in the redshift range $0.3<z<0.5$, with an accuracy of $\sim$11-16\% incorporating both statistical and systematic errors. Once combined, these measurements yield a 6\% accuracy constraint of $H(z=0.4293)=91.8\pm5.3$ km/s/Mpc. The new data are crucial to provide the first cosmology-independent determination of the transition redshift at high statistical significance, measuring $z_{t}=0.4\pm0.1$, and to significantly disfavor the null hypothesis of no transition between decelerated and accelerated expansion at 99.9\% confidence level. This analysis highlights the wide potential of the cosmic chronometers approach: it permits to derive constraints on the expansion history of the Universe with results competitive with standard probes, and most importantly, being the estimates independent of the cosmological model, it can constrain cosmologies beyond -and including- the $Λ$CDM model.

Figures (10)

• Figure 1: Stellar mass (left panel) and redshift (right panel) distributions, colored by the various velocity dispersion subsamples.
• Figure 2: Median stacked spectra as a function of redshift bins and $\rm\sigma$ bins (the upper and lower panels of each plot respectively). The spectra in the upper panels of each plot are extracted at fixed $\rm\sigma$ (grey lines, ${\rm 250<\sigma<300}$), while the spectra in the lower panels are extracted at fixed redshift (colored lines, $z\sim0.4$). The upper plots show the median spectra. All spectra have been normalized near to the vertical dashed lines; therefore the differences in the upper panels flatten at higher wavelengths, but the steepening of the slope of the continuum with increasing mass and decreasing redshift is evident. This trend may be interpreted in the framework of the "mass-downsizing" scenario, with more massive galaxies being redder and older than less massive ones. The lower plots are zoom-in around three specific absorption features, i.e. $D_{n}4000$, H$\beta$, and Fe5015, highlighted in yellow; it is also shown, highlighted in green, the region corresponding to [OIII]$\lambda$5007 line.
• Figure 3: Stellar metallicity estimated from full spectral fitting with STARLIGHT, VESPA and FIREFLY (respectively left, center and right panels), and adopting M11 and BC03 models (respectively upper and lower panels). The grey shaded region represents the mean value, averaged between all models and codes, as discussed in the text.
• Figure 4: Calibration of the $D_{n}4000$-age relations. Upper plots: $D_{n}4000$-age relation for different EPS models, metallicities and SFH. Left and right panels show M11 and BC03 models, respectively, where the green lines show the relations for solar metallicity, blue for sub-solar and orange for over-solar; lines from solid to dashed represent SFH with progressively higher $\tau$, from 0.05 to 0.3 Gyr. Lower panel show the linear best fit to each metallicity, in the two $D_{n}4000$ ranges discussed in the text. Lower plots: fitted $A(SFH,Z/Z_{\odot})$-metallicity relation for different EPS models. The orange shaded area represent the best fit to the data, shown as black points. The green shaded area represent the total error on $A(SFH,Z/Z_{\odot})$, given the uncertainty on the measured metallicity, while the blue area show the contribution to the error due to SFH.
• Figure 5: Upper panel: median $D_{n}4000$--z relations obtained for the various velocity dispersion subsamples. The dashed lines show the theoretical $D_{n}4000$--z relations estimated from M11 models (with solar metallicity) for four differed redshifts of formation, respectively 1, 1.5, 2, 2.5 from bottom to top. Lower panel: $H(z)$ measurements obtained with BC03 and M11 models, compared with literature data available in this redshift range Simon2005Stern2010Moresco2012a. For illustrative purpose, the estimates obtained with BC03 models have been slightly offset in redshift.