HDRP lightning broken

I am trying to update my project to the HDRP, but I am facing some issues. The lightning seems to act completely unnatural:


Those are the results I get using a directional light. It seems that the surfaces that are not in direct view of the directional light get no light at all. I tried to increase the intensity of the light, but that only affected the surfaces that are already lit.

Any idea how to make things look good? I really like a lot of the HDRP features, so it would be nice to get it to work properly

 

Try increasing your shadow resolution, adjusting your bias scale, and indirect multiplier. Also, you may want to use the post processing stack. In your Lighting tab, increase the bounces. Also a reflection probe would help soften the shadows and bounce light back to the indirect surfaces covered by shadows.