Distant Galaxies Confirm Dark Energy's Existence and Universe's Flatness
scientificamerican.com
scientificamerican.com
They assume that galaxies are oriented randomly (from our viewpoint). In actual observations this does not appear to be the case. They then compensate for it to make all orientations as you would expect (random); The force that caused this distortion can then be calculated and it indicates the existence of dark energy.
I'm actually not entirely sure dark energy has any effect on spacetime itself, this is merely speculation which hopefully somebody could answer in better detail.