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Cosmology with cosmic chronometers

The "cosmic chronometers" approach provides an independent technique to constrain the expansion history of the Universe H(z) from the differential evolution of massive and passive ETGs.

People involved at the Department and main collaborators: M. Moresco (UniBo), A. Cimatti (UniBo), L. Pozzetti (INAF-OABO), R. Jimenez (ICREA, Barcelona), L. Verde (ICREA, Barcelona).

The determination of the expansion rate of the Universe, traced by the Hubble parameter H(z), is one of the most crucial cosmological measurements as it directly depends on the energy components of the Universe (and in particular the "dark energy" in case of an accelerated expansion). In order to unveil the nature of the energy components of the Universe, it is therefore fundamental to constrain H(z) very precisely.
Several observational probes, from standard "candles" (e.g. Type Ia Supernovae) to standard "rulers" (e.g. Baryonic Acoustic Oscillations) can be used to derive H(z), but none of them has achieved high accuracy results over a significant fraction of the Universe lifetime.
An independent approach is provided by the "cosmic chronometers", because it gives a measurement of the expansion rate without relying on the nature of the metric between the chronometer and us, which is not the case for methods which depend on integrated quantities along the line of sight.
The cosmic chronometers formalism is straightforward: H(z)=-1/(1+z)dz/dt.   Based on the above equation, it is possible to estimate the expansion rate of the Universe at different epochs using the age differences of old elliptical galaxies that are passively evolving (Jimenez & Loeb, 2002, AJ, 573, 37), since they can be used as standard chronometers whose differential age evolution as a function of cosmic time directly probes the Hubble parameter.
Motivated by this possibility, we started a project aimed at exploring the feasibility and reliability of this approach using spectroscopic data of passive early-type galaxies (ETGs) over the widest possible redshift range.
As a first test, we applied this method to low-redshift ETGs selected from the SDSS (Moresco et al., 2011, JCAP, 03, 045) and obtained an independent estimate of the Hubble constant H0=72.6+/-2.9(stat)+/-2.3(syst) km Mpc-1s-1 (68% confidence), consistent with other results.Then, we applied this method to a large spectroscopic sample of ETGs (SDSS-MGS, SDSS-LRG, zCOSMOS, K20, GDDS, UDS, …) at 0.15<z<1.4 and obtained independent and 5-12% accuracy measurements of H(z) during the last 8 billion years.
This provided a direct and robust evidence of the accelerated expansion of the Universe, confirming also the well-established standard ΛCDM model, and showed other cosmological applications including the properties of neutrinos. More details can be found in Moresco et al. (2012a), Moresco et al. (2012b) and Jimenez et al. (2012, JCAP, 03, 014).
The "cosmic chronometer" method has been applied also using a different approach, based on the age estimate from spectral fitting and evaluating the differential age evolution from the upper envelope of the age-redshift relation (Jimenez et al. 2003, ApJ, 593, 622; Simon et al. 2005, PhRvD, 71, 123001; Stern et al. 2010, JCAP, 2, 8). For further details, see . Despite the different approaches, the results obtained are fully consistent, and the H(z) measurements (based on BC03 models) can be used combined, as done in Moresco et al. (2012b).

We also provided two new H(z) measurements at z~2 from the analysis of near-infrared spectroscopy of the few very massive and passive galaxies observed at z>1.4 available in literature, taking into account in the final error budget all possible sources of systematic uncertainties (star formation history, stellar metallicity, model dependencies).

Recently, we exploited the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 to provide 5 new constraints on the Hubble parameter H(z) in the redshift range 0.3<z<0.5, with an accuracy of ~11-16% incorporating both statistical and systematic errors. 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+/-0.1, and to significantly disfavor the null hypothesis of no transition between decelerated and accelerated expansion at 99.9% confidence level.

This web page aims at becoming the reference place where results and data relative to the cosmic chronometer projects will be made available to the community.

As of 11/01/2016, we make publicly available the following files :

  • H(z) measurements based on BC03 stellar population synthesis models up to z~1.1 (Moresco et al. 2012a)
  • H(z) measurements based on MaStro stellar population synthesis models up to z~1.1 (Moresco et al 2012a)
  • H(z) measurements from high-z massive and passive galaxies up to z~2 (Moresco 2015)
  • H(z) measurements at z~0.45 from BOSS analysis based on BC03 stellar population synthesis models (Moresco et al. 2016)
  • H(z) measurements at z~0.45 from BOSS analysis based on MaStro stellar population synthesis models (Moresco et al. 2016)
  • full compilation of H(z) measurements based on BC03 stellar population synthesis models (comprising measurements from Simon et al. 2005, Stern et al. 2010, Moresco et al. 2012a, Moresco 2015, Moresco et al. 2016)

In the attached files they can be downloaded separately; in each file it can be found the data quoted in Table 4 of Moresco et al. (2012a), in Table 1 of Moresco (2015), and in Table 3 of Moresco et al. (2016). In the last file it can be found also a full compilation of H(z) dataset, comprising H(z) measurements obtained with the cosmic chronometers approach from Simon et al. (2005, PhRvD, 71, 123001), Stern et al. (2010, JCAP, 2, 8), Moresco et al. (2012, JCAP, 08, 006), Moresco (2015, MNRAS Letter, 450, 16), Moresco et al. (2016). 
While the dependence on stellar population synthesis model is unimportant for most cosmological analyses (as shown in Moresco et al. 2012b), and the full compilation can be safely used, if you want to be conservative the files obtained with different stellar population synthesis models are also provided.


When using these datasets, please cite the corresponding papers:

  • Moresco, M., Cimatti, A., Jimenez, R., Pozzetti, L. et al, 2012, JCAP, 08, 006 (arXiv:1201.3609 , Moresco et al. 2012a)
  • Moresco, M., Verde, L., Pozzetti, L., Jimenez, R., Cimatti, A., 2012, JCAP, 07, 053 (arXiv:1201.6658, Moresco et al. 2012b)
  • Moresco, M., 2015, MNRAS Letter, 450, 16 (arXiv:1503.01116)
  • Moresco, M., Pozzetti, L., Cimatti, A., Jimenez, R., Maraston, C., Verde, L., Thomas, D., Citro, A., Tojeiro, R., Wilkinson, D., 2016, submitted to JCAP (arXiv:1601.01701)

Last update 11/01/2016



Andrea Cimatti


Dipartimento di Fisica e Astronomia

Via Piero Gobetti 93/2

Bologna (BO)

tel: +39 051 20 9 5817

Michele Ennio Maria Moresco

tel: +39 051 20 95762