On the use of scaling relations for the Tolman test
  The use of relations between structural parameters of early type galaxies to perform the Tolman test is reconsidered. Scaling relations such as the FP or the Kormendy relation, require the transformation from angular to metric sizes, to compare the relation at different z values. This transformation depends on the assumed world model: galaxies of a given angular size, at a given z, are larger (in kpc) in a non-expanding universe than in an expanding one. Furthermore, the luminosities of galaxies are expected to evolve with z in an expanding model. These effects are shown to conspire to reduce the difference between the predicted SB change with redshift in the expanding and non expanding cases. We find that the predictions for the visible photometric bands of the expanding models with passive luminosity evolution are very similar to those of the static model till z about 1, and therefore, the test cannot distinguish between the two world models. Recent good quality data are consistent with the predictions from both models. In the K-band, where the expected (model) luminosity evolutionary corrections are smaller, the differences between the xpanding and static models amount to about 0.4 (0.8) magnitudes at z = 0.4 (1). It is shown that, due to that small difference between the predictions in the covered z-range, and to the paucity and uncertainties of the relevant SB photometry, the existing K-band data is not adequate to distinguish between the different world metrics, and cannot be yet used to discard the static case. It is pointed out that the scaling relations could still be used to rule out the non-evolving case if it could be shown that the coefficients change with the redshift. 
Mariano Moles (1,2), Ana Campos (1,2), Per Kjaergaard (3), Giovanni   Fasano (4), Daniela Bettoni (4) ((1) IMAFF, CSIC (Madr...