  We calculate deviations in cosmological observables as a function of
parameters in a class of connection-based models of quantum gravity. In this
theory non-trivial modifications to the background cosmology can occur due to a
distortion of the wave function of the Universe at the transition from matter
to dark energy domination (which acts as a "reflection" in connection space).
We are able to exclude some regions of parameter space and show with projected
constraints that future experiments like DESI will be able to further constrain
these models. An interesting feature of this theory is that there exists a
region of parameter space that could naturally alleviate the $S_8$ tension.
