Álvarez, EnriqueGonzález Martín, SergioPérez Martín, Carmelo2023-06-182023-06-182016-06-301. E. Álvarez, S. González-Martín, M. Herrero-Valea, and C. P. Martín, Unimodular gravity redux,Phys. Rev. D 92, 061502 (2015). 2. A. Einstein, Do gravitational fields play an essential part in the structure of the elementary particles of matter?, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 1919, 433 (1919). 3. D. McDuff, On the group of volume-preserving diffeomorphisms of Rn, Trans. Am. Math. Soc.261, 103 (1980). 4. J. J. van der Bij, H. van Dam, and Y. J. Ng, The exchange of massless spin two particles,Physica A (Amsterdam) 116A, 307 (1982). 5. E. Álvarez, S. González-Martín, M. Herrero-Valea, and C. P. Martín, Quantum corrections to unimodular gravity, J. High Energy Phys. 08 (2015) 078. 6. A. L. Besse, Einstein Manifolds (Springer, New York, 2007). 7. C. N. Kozameh, E. T. Newman, and K. P. Tod, Conformal Einstein spaces, Gen. Relativ. Gravit.17, 343 (1985). 8. F. G. Friedlander, The Wave Equation on a Curved Space-Time (Cambridge, Cambridge University Press, 2010).0556-282110.1103/PhysRevD.93.123018https://hdl.handle.net/20.500.14352/24584© 2016 American Physical Society. The origin of this work lies in a question by Gerardus ’t Hooft at the Shapes of Gravity meeting held in Nijmegen in 2016. It has been partially supported by the European Union FP7 ITN INVISIBLES (Marie Curie Actions, PITN- GA-2011- 289442) and (HPRN-CT-200-00148); COST action MP1405 (Quantum Structure of Spacetime), COST action MP1210 (The String Theory Universe) as well as by FPA2012-31880 (MICINN, Spain), FPA2014-54154-P (MICINN, Spain), and S2009ESP-1473 (CA Madrid). This project has received funding from the European Union’ s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 690575. This project has also received funding from the European Union’ s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 674896. The authors acknowledge the support of the Spanish MINECO Centro de Excelencia Severo Ochoa program under Grant No. SEV-2012-0249.The symmetries of unimodular gravity are clarified somewhat.engjournal articlehttp://dx.doi.org/10.1103/PhysRevD.93.123018http://journals.aps.org/open access53AstronomyAstrophysicsPhysicsParticlesFieldsFísica (Física)22 Física