## 6. Cosmological constraintsFig. 1 provides a first comparison of our signal with some cosmological models. In order to rule out models we need to estimate first the sample variance in the variance of the shear. Although it has not been yet exactly derived analytically (because calculations in the non-linear regime are difficult), ray-tracing simulations can give an accurate estimate of it. We used the ray-tracing simulations of Jain et al. 1999 for this purpose. Table 2 shows the two simulations we used. The CDM model with is not an independent simulation, but was constructed from the CDM model with simply by dividing by 0.6. This should empirically mimic a model with both and equal to one. The redshift of the sources is equal to 1, which is not appropriate for our data. However, for the depth of the survey, we believe that it represents fairly well the mean redshift of the galaxies, which is the dominant factor in determining the second moment. Fig. 10 shows the amplitude and the scale dependence of the variance of the shear for the three cosmological models, compared to our signal. It is remarkable that models (1) and (3) can be marginally rejected (We did not plot the error bars due to the intrinsic ellipticity for clarity: they can be obtained from Fig. 8).
Our measurements are in agreement with the cluster normalized model (2). Also plotted is the theoretical prediction of a CDM model, with , , and a redshift of the sources . It shows that the low- model is also in good agreement with the data, which means that weak gravitational lensing provides cosmological constraints similar to the cluster abundance results (Eke et al. 1996, Blanchard et al. 1999): the second moment of the shear measures a combination of and (see Eq. 8). A measure of the third moment of the convergence would break the - degeneracy, but this requires more data (see Bernardeau et al. 1997, Van Waerbeke et al. 1999, Jain et al. 1999). It should also be noted that for the simulations, we have considered cold dark matter models with shape parameter ; higher values of increase the theoretical predictions on scales of interest, e.g. the , model would be ruled out even more strongly. We conclude that our analysis is consistent with the current favored cosmological models, although we cannot yet reject other models with high significance. Since we have only analyzed 2 square degrees of the survey, with forthcoming larger surveys we should be able to set strong constraints on the cosmological models as discussed below. Due to the imprecise knowledge of the redshift distribution in our data, the interpretation might still be subject to modifications. The final state of our survey in 4 colors will however permit the measurement of this distribution by estimating photometric redshifts for the source galaxies.
© European Southern Observatory (ESO) 2000 Online publication: June 26, 2000 |