The main scrolling commands in Vim are:
I just found this plugin called "accelerated-smooth-scroll" ("Vim plugin for accelerated smooth scroll (mapping to , ") which can be for example used through Vundle by putting this line in your .vimrc:
Plugin 'yonchu/accelerated-smooth-scroll'
Then by restarting Vim and running the :PluginInstall command, then again restart Vim and use the (Ctrl+D) and (Ctrl+O) commands normally.
Sadly, this plugin also moves the cursor instead of what I wanted: to just scroll the screen like the and commands.