## Weak lensing statistics as a probe of and power spectrum
^{1} Service de Physique Théorique, C.E. de Saclay,
F-91191 Gif-sur-Yvette Cedex, France^{2} Observatoire Midi-Pyrénées, 14 Av. Edouard
Belin, F-31400 Toulouse, France^{3} Institut d'Astrophysique de Paris,
Boulevard Arago, F-75014 Paris, France^{4} Observatoire de Paris, (DEMIRM), 61 Av. de
l'Observatoire, F-75014 Paris, France
The possibility of detecting weak lensing effects from deep wide
field imaging surveys has opened new means of probing the large-scale
structure of the Universe and measuring cosmological parameters. In
this paper we present a systematic study of the expected dependence of
the low order moments of the filtered More precisely we show that the variance of the convergence varies approximately as , whereas the skewness varies as , where is the projected power spectrum and the redshift of the sources. Thus, used jointly they can provide both and . However, the dependence on the redshift of the sources is large and could be a major concern for a practical implementation. We have estimated the errors expected for these parameters in a realistic scenario and sketched what would be the observational requirements for doing such measurements. A more detailed study of an observational strategy is left for a second paper.
## Contents- 1. Introduction
- 2. The physical model for the galaxy and mass distributions
- 3. The Weak-Lensing equations
- 4. The variance of the smoothed convergence
- 5. Higher-order moments
- 5.1. Second order perturbation theory for the local convergence
- 5.2. The expression of the local skewness
- 5.3. Numerical results for a realistic case
- 5.4. Dependence on the redshift
- 5.5. Dependence on the cosmological parameters
- 5.6. Discussion, simplified model
- 5.7. Systematics due to other quadratic couplings
- 6. Error evaluations due to the cosmic variance
- 7. Discussion and conclusions
- Acknowledgements
- Appendix A
- Appendix B: evaluation of the cosmic errors
- References
© European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |