In the Wikipedia article "Loop Quantum Gravity" one can read
ESA's INTEGRAL satellite measured polarization of photons of different wavelengths and was able to place a limit in the granularity of space that is less than $10^{-48}$ m or 13 orders of magnitude below the Planck scale.
What is the present status of this experiment? Does it mean that LQG is falsified?
This looks like a typical case where a scientist publishes a paper that makes certain specific and limited claims, but public relations people at their organization then put out a press release making popularized and overly sensationalized and overly broad claims.
The actual paper seems to be this: Laurent, https://arxiv.org/abs/1106.1068 . They write down a certain perturbation to be added to the electromagnetic field's Lagrangian that violates Lorentz invariance, and then put limits on the size of that term based on observations. Untangling the tensor notation, I think the term they hypothesize is something roughly of the form $\partial(\textbf{E}\cdot\textbf{B})/\partial t$. This violates parity, and also violates Lorentz invariance because the $t$ coordinate is that of a certain preferred frame of reference. The result of this is that the speed of light differs slightly depending on whether the photon's chirality is right- or left-handed. They don't see any such effect.
As far as I can tell, no LQG theorist ever made any prediction that there should be a violation of all these symmetries at the Planck scale. Laurent, who is an observationalist, simply writes down the lowest-order term they can come up with that preserves gauge invariance and rotational symmetry.
Over the last 10-15 years, there has been a history of people hypothesizing that LQG could be used to make testable predictions about the dispersion of the vacuum. However, the people actually working on LQG, like Rovelli, never made any such predictions. More info here:
Does the discreteness of spacetime in canonical approaches imply good bye to STR?
http://physicsforums.com/showpost.php?p=2650816&postcount=28
Does it mean that LQG is falsified?
Placing a limit on something,- strictly speaking is not falsification, however like-hood of finding space granularity is decreased very much, to the point that maybe searches of space granularity will not make sense at all. IMHO, nobody has proved that some value can't be less than Plank scale dictates. In contrary, it is known that some parameters can be less that Plank level states. For example , electron is $\approx 10^{22}$ times lighter than a Plank mass. Also your mentioned limits are placed only on certain versions of Loop Quantum Gravity. It's because everything depends on how we interpret/understand "granularity of space". What it means, really ? Nobody knows. Should we look for a small-compact dosage of space ? Then maybe this limit suits here. But what if we understand space quantification badly ? Maybe space unit is some sort of scattered thin fractal ? Or something else completely. Then this placed limit is not suitable very much in these cases. Of course one can argue that this will not be LQG theory. Maybe, or maybe it will be some modification of it. In any case, falsification means that experiment finds evidences which disproves theory completely, such as Michelson & Morley experiment disproved "ether existence which drags light in it". This is not the case here.
