Does loop quantum gravity explain the dark matter effect without dark matter? Does loop quantum gravity explain the dark matter effect (the rotational curves of the galaxies, the increased velocitoes of galaxies within galaxy clusters) without using dark matter?
As far as I understand LQG is about a granular nature of spacetime on the Planck scale. Therefore, it has nothing to do with dark matter at the first sight.
However, some hopes might go in the direction of quantum gravity in general to explain the effect if one day everything is calculated through correctly.
 A: The trouble is explaining away dark matter, which is what you're really talking about, is only worth doing if dark matter being real is empirically worse.
Galaxies exist because the gravity in randomly extra-dense regions of space allowed such structure to form. Dark matter explains rotation curves etc.${}^\ast$ in terms of galaxies having however much baryonic and dark matter that region of space randomly had. Observations show either

*

*the relative amounts of each vary by galaxy and some galaxies have little if any dark matter, or

*if dark matter doesn't exist galaxies nonetheless behave as if (i) is correct.

Any proposed alternative to dark matter must explain all observational details in terms of 2. LQG doesn't do that. Indeed, nothing has yet done this well enough for 1 to be less plausible.
${}^\ast$ There are other reasons not to expect non-dark-matter explanations to succeed, such as the discernible baryonic/dark distinction in the Bullet Cluster.
A: If you look back at my answer to your earlier question Arvin Ash said the following here   “How do particles traverse this quantized space? When mass and energy are added to the spin foam the shape of the volumes of the spin network is distorted. This distorts space and time… This distortion of space and time is what we perceive as gravity.”
So based on his statement, gravity is caused by the distortion of space and time in LQG. So "dark matter" is not required for gravity, just this distortion which can be achieved with energy.  "Dark Matter" should really be called "Dark Gravity".
