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The main observations that appear to require dark matter and/or dark energy can be explained within this model. Namely,
* The [[Galaxy rotation curve|flat rotation curves of galaxies]].<ref name="Deur09">{{cite journal |arxiv=0901.4005|title=Implications of Graviton-Graviton Interaction to Dark Matter|year=2009|last1=Deur|first1=Alexandre|journal=Phys. Lett. B|volume=676 |issue=1–3|pages=21–24|doi=10.1016/j.physletb.2009.04.060 |bibcode=2009PhLB..676...21D |s2cid=118596512 }}</ref><ref name="Deur21a">{{cite journal |arxiv=2004.05905|doi=10.1140/epjc/s10052-021-08965-5|title=Relativistic corrections to the rotation curves of disk galaxies|year=2021|last1=Deur|first1=Alexandre|journal=Eur. Phys. J. C|volume=81 |issue=3|page=213|bibcode=2021EPJC...81..213D |s2cid=215745418 }}</ref><ref name="Deur16a" >{{cite journal |title=Self-interacting scalar fields at high-temperature |author=Deur, A. |journal=Eur. Phys. J. C |volume=77 |issue=6 |year=2017 |pages=412 |doi=10.1140/epjc/s10052-017-4971-x |arxiv=1611.05515|bibcode=2017EPJC...77..412D |s2cid=254106132 }}</ref> These results, however, have been challenged.<ref>{{cite arXiv |eprint=2303.11094 |title=Does gravitational confinement sustain flat galactic rotation curves without dark matter? |year=2023 |last1=Barker |first1=W. E. V. |last2=Hobson |first2=M. P. |last3=Lasenby |first3=A. N.|class=gr-qc }}</ref><ref>{{cite arXiv |eprint=2306.00992 |title=Comment on "Does gravitational confinement sustain flat galactic rotation curves without dark matter?" |year=2023 |last1=Deur |first1=A.|class=gr-qc }}</ref>
* The [[Cosmic Microwave Background]] [[anisotropies]].<ref name="Deur22a">{{cite journal |title=Effect of the field self-interaction of General Relativity on the cosmic microwave background anisotropies |author=Deur, A. |journal=Class. Quant. Grav. |volume=39 |issue=13 |year=2022 |pages=135003 |doi=10.1088/1361-6382/ac7029 |arxiv=2203.02350|bibcode=2022CQGra..39m5003D |s2cid=247244759 }}</ref>
* The [[Accelerating expansion of the universe#Supernova observation|fainter luminosities of distant supernovae]] and their consequence on the [[accelerating expansion of the universe]].<ref name="Deur19a" />
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