- “weak gravitational lensing” with the visible light instrument (which has higher resolution than the IR one) to measure very precisely the shapes of galaxies, to enable a statistical study of distortions in their shapes, caused by weak lensing due to dark matter (and regular matter which they can observe “directly”)
- “galaxy clustering” with the near IR instrument to calculate distances to the galaxies (via their redshift) which they can use to map out 3D distribution of galaxies and compare to simulations for example (there is a nice figure on this page: https://www.euclid-ec.org/euclid-core-science showing a few surveys and simulations)
There is more information on their blog here as well: https://www.euclid-ec.org/blog
The images here are simply first light images (i doubt the horsehead nebula or globular clusters are part of the core science of Euclid); more images and spectra will be taken in the coming years to do the actual core science (which will require a lot more data)
How is the data being presented here helping us investigate dark matter/energy, which is not in the data?