> I'd also appreciate a link to the explanation of "What in GR we would consider perturbations of dS and IR corrections."
Here's a quick overview of perturbation theory then an example of how one might apply it in GR.
https://www.wikiwand.com/en/Perturbation_theory
http://theory.physics.helsinki.fi/~inf/Lectures/Lecture2.pdf
IR is "infrared", low-energy physics, as opposed to UV, "ultraviolet", high-energy physics. In this context, UV means strong gravity where quantum effects are expected to be important. Galaxy-galaxy gravitational lensing (which is the subject of the Brouwer et al. paper that's the subject of the newscientist article linked at the top) is purely a weak gravity problem[1], so is in the IR limit of General Relativity. If you want different results from standard General Relativity you can add corrections by hand in a variety of ways; in the galaxy-galaxy lensing case they would be in the infrared.
[1] strong gravity is hidden behind the event horizons of the black holes of the galaxies and, arguendo, if we could see the strong gravity near the black hole centres, it would not be relevant by virtue of being drowned out by all the stars, gas, dust and other matter.
ETA: This is nice and terse, too: https://www.wikiwand.com/en/Non-exact_solutions_in_general_r...