### [1010.0831] Constraining the expansion rate of the Universe

Posted:

**October 29 2010**The comparison of the luminosity (or angular diameter) distance [tex]D(z)[/tex] and the Hubble parameter [tex]H(z)[/tex] as a function of redshift is an important observational test. The FRW metric implies a unique relationship between [tex]D(z)[/tex] and [tex]H(z)[/tex]. Given one of them (plus the spatial curvature at any one time), the other is fully determined. It follows that it is possible to test the 4D FRW metric directly by measuring these quantities independently. If they do not satisfy the FRW relationship, the universe is not described by the 4D FRW metric, independent of the existence of dark energy or modified gravity. This test was suggested by Clarkson et al in 0712.3457.

Distances can be obtained in a fairly model-independent manner from supernovae and the CMB, determining [tex]H(z)[/tex] is more difficult. One possibility, suggested in arXiv:astro-ph/0106145 by Jimenez and Loeb and implemented in arXiv:astro-ph/0412269, 0907.3149, and 0807.0039, is to find the age of the universe as a function of redshift from galaxies. This gives [tex]t(z)[/tex], i.e. [tex]z(t)[/tex], i.e. [tex]a(t)[/tex], from which one gets [tex]H(z)[/tex]. In fact, since one only wants [tex]H(z)[/tex], the absolute age is not needed, only the change in age matters.

In the present paper, the authors introduce a new observable which they argue to be cleanly correlated with the galaxy age, namely the amplitude of a break in the absorption spectrum at 4000 Å due to ionized metals in stars. They find that this correlates linearly with galaxy age (at fixed metallicity). The authors then use data from an impressive number of 13 987 galaxies from 0.15<z<0.3 to put constraints on cosmological parameters.

The break-age correlation, produces too small ages for the galaxies, in the range 4-6 Gyr, as opposed to an expected age of about 10 Gyr. The authors write that this shouldn't matter, since only the evolution of the ages matters. Being completely ignorant of the field, I wonder whether one can trust the model in the quantity of interest if predicts another quantity wrong, even if one happens not to be interested in that quantity. Also, the spread of the ages is large, as the oldest galaxies have ages of 8-10 Gyr, so I again wonder about the reliability of the differential age. Though I guess one can get good statistics because there are so many objects.

The parameter estimation is pretty standard and includes strong priors, and I didn't find the results particularly interesting. (Curiously, the authors apparently consider assuming a flat [tex]\Lambda[/tex]CDM model with [tex]\Omega_\Lambda[/tex] in the 1[tex]\sigma[/tex] WMAP7 range a weak prior!)

As I am interested in the possibility that the late-time observations could be explained in terms of deviations from the FRW metric due to structure formation, I find the conceptually new possibility of testing the FRW metric more interesting that parameter constraints, but these will probably be possible with any interesting level precision only with future data. (It was mentioned in 0902.2006 that the data at that time was too noisy; in 0909.1479 the test was applied to an LTB model.)

Distances can be obtained in a fairly model-independent manner from supernovae and the CMB, determining [tex]H(z)[/tex] is more difficult. One possibility, suggested in arXiv:astro-ph/0106145 by Jimenez and Loeb and implemented in arXiv:astro-ph/0412269, 0907.3149, and 0807.0039, is to find the age of the universe as a function of redshift from galaxies. This gives [tex]t(z)[/tex], i.e. [tex]z(t)[/tex], i.e. [tex]a(t)[/tex], from which one gets [tex]H(z)[/tex]. In fact, since one only wants [tex]H(z)[/tex], the absolute age is not needed, only the change in age matters.

In the present paper, the authors introduce a new observable which they argue to be cleanly correlated with the galaxy age, namely the amplitude of a break in the absorption spectrum at 4000 Å due to ionized metals in stars. They find that this correlates linearly with galaxy age (at fixed metallicity). The authors then use data from an impressive number of 13 987 galaxies from 0.15<z<0.3 to put constraints on cosmological parameters.

The break-age correlation, produces too small ages for the galaxies, in the range 4-6 Gyr, as opposed to an expected age of about 10 Gyr. The authors write that this shouldn't matter, since only the evolution of the ages matters. Being completely ignorant of the field, I wonder whether one can trust the model in the quantity of interest if predicts another quantity wrong, even if one happens not to be interested in that quantity. Also, the spread of the ages is large, as the oldest galaxies have ages of 8-10 Gyr, so I again wonder about the reliability of the differential age. Though I guess one can get good statistics because there are so many objects.

The parameter estimation is pretty standard and includes strong priors, and I didn't find the results particularly interesting. (Curiously, the authors apparently consider assuming a flat [tex]\Lambda[/tex]CDM model with [tex]\Omega_\Lambda[/tex] in the 1[tex]\sigma[/tex] WMAP7 range a weak prior!)

As I am interested in the possibility that the late-time observations could be explained in terms of deviations from the FRW metric due to structure formation, I find the conceptually new possibility of testing the FRW metric more interesting that parameter constraints, but these will probably be possible with any interesting level precision only with future data. (It was mentioned in 0902.2006 that the data at that time was too noisy; in 0909.1479 the test was applied to an LTB model.)