The existence of a background of ultra-strongly interactinggravitons is a key postulate of the author's low-energy gravitymodel. Side effects of the model due to photons interacting withthis background may be important for cosmology, and theirobservation would be essential to support the model. The mostimportant such effect is the quantum redshift mechanism, which mayconstitute an alternative to the generally accepted mechanismassociated with the expansion of the universe. The model shouldhave a weakening of the light flux due to a change in the numberof photons, which replaces the influence of dark energy. Scatteredphotons may form a new background that can be detected by deepspace missions. Some important predictions of the model are testedusing observational data sets of SNe Ia, compact quasars andLyman-alpha emitters. The article shows that the linear function$H(z) $ of the model satisfactorily describes the results ofmeasurements of the Hubble parameter. Using a trial function forthe weakening parameter, the possibility of a differentinterpretation of the Hubble tension is illustrated. Theincreasing angular diameter distance of this model is fitted to aset of 120 measurements of the angular sizes of compact quasarswith redshifts of $0.46 -- 2.76$ with independent calibration oftheir linear sizes. Attention is drawn to the possibility of afalse interpretation of changes in the measured sizes ofLyman-alpha emitters observed by JWST in the redshift range of $3-- 7$ as evolutionary effects in the $Lambda$CDM model, sincethese changes can be due to the increasing angular diameterdistance of this model.