There are feasible observational tests being proposed, a physicist at Stockholm (S. Hossenfelder) has organized a couple of conferences/workshops on *Experimental Search for Quantum Gravity*. Here is a writeup on the one in Stockholm in 2010:
http://arxiv.org/abs/1010.3420
Hossenfelder and co-workers recently proposed a new trace of Loop qg to look for in cosmic ray spectrum. From Loop-type BH. Google "hossenfelder emission spectra" and get
http://arxiv.org/abs/1202.0412
Loop leads to a simple explanation of what makes up dark matter, which if correct, would result in a signature in high energy radiation such as cosmic ray. This is new (2012) and not in the 2010 workshop report I mentioned.
Some other papers propose a LQG "footprint" to look for in the microwave background (left over light from early universe where LQG predicts a particular start to expansion).
Google "grain barrau footprint loop" and get
http://arxiv.org/abs/0902.0145
Cosmological footprints of loop quantum gravity
J. Grain, A. Barrau
(Submitted on 2 Feb 2009 (v1), last revised 4 Mar 2009 (this version, v2))
The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated holonomy correction should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.
Comments: Accepted by Phys. Rev. Lett., 7 pages, 2 figures
Most tests would require a new generation astrophysical instruments, or data that has not yet been reported from the Planck spacecraft , but this one by Wen Zhao uses already collected data:
Google "zhao constraints early universe models" and get
http://arxiv.org/abs/1007.2396
Wen Zhao is already working with available CMB data from the WMAP spacecraft to limit the range of parameters for Loop and other models of early universe. He participated in Hossenfelder's 2010 workshop and the work is included in the report I mentioned.
More papers related to observational testing of LQG, these are all 2009 or later. The link is slow, Spires system will be replaced soon, but efficient. Some 49 papers including some I mentioned.
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29
Here's a less efficient search by the new tool which will replace Spires, but still pretty good:
http://inspirehep.net/search?ln=en&...earch=Search&sf=&so=d&rm=citation&rg=100&sc=0
Finds 48 papers from the period 2008-2011, mostly the same papers.