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Quadratic gravity

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Quadratic gravity (QG) is an extension of general relativity obtained by adding all local quadratic-in-curvature terms to the Einstein–Hilbert Lagrangian.[1] Doing this makes the theory renormalizable.[1] This is a one of a number of f(R) gravity theories.[2]: 63  It has been suggested that consistency with quantum chromodynamics requires these additional quadratic terms.[3]

The theory was originally developed by Kellogg Stelle in 1977,[4] but had difficulty being accepted as a viable theory because of its introduction of a massive spin-2 ghost particle with negative norm.[5][1] Aside from the massive ghost, the theory also predicts the existence of the graviton and an additional scalar boson.[5] This scalar particle appears also in Alexei Starobinsky's work of 1980 on the early universe, where he retained only the lowest quadratic term. In Starobinsky inflation, the scalar particle is responsible for cosmic inflation.[5][1]

QG, besides being renormalizable, has also been shown to feature an ultraviolet fixed point.[6] Unitarity, essential to a theory quantum gravity, has been established under certain conditions.[7]

John Donoghue believes quadratic gravity could become a viable theory of quantum gravity.[5] He has reinterpreted its ghost particles as time-reversed unstable particles.[8][7]

Work has been directed towards using the Event Horizon Telescope to test for the possibility of QG being a valid theory.[9]

References

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  1. ^ a b c d Salvio, Alberto (2018). "Quadratic Gravity". Frontiers in Physics. 6 (77) 77. arXiv:1804.09944. Bibcode:2018FrP.....6...77S. doi:10.3389/fphy.2018.00077.
  2. ^ Clifton, Timothy; Ferreira, Pedro G.; Padilla, Antonio; Skordis, Constantinos (1 March 2012). "Modified gravity and cosmology". Physics Reports. Modified Gravity and Cosmology. 513 (1): 1–189. doi:10.1016/j.physrep.2012.01.001. ISSN 0370-1573.
  3. ^ Salvio, Alberto (2021). "Dimensional Transmutation in Gravity and Cosmology". Int. J. Mod. Phys. A. 36 (8n09, 2130006): 2130006–2130831. arXiv:2012.11608. Bibcode:2021IJMPA..3630006S. doi:10.1142/S0217751X21300064. S2CID 229349013.
  4. ^ Stelle, K. S. (15 August 1977). "Renormalization of higher-derivative quantum gravity". Physical Review D. 16 (4): 953–969. doi:10.1103/PhysRevD.16.953. ISSN 0556-2821.
  5. ^ a b c d Wood, Charlie (17 November 2025). "Old 'Ghost' Theory of Quantum Gravity Makes a Comeback". Quanta Magazine. Retrieved 18 November 2025.
  6. ^ Falls, Kevin; Ohta, Nobuyoshi; Percacci, Roberto (2020). "Towards the determination of the dimension of the critical surface in asymptotically safe gravity". Physics Letters B. 810 (135773) 135773. arXiv:2004.04126. Bibcode:2020PhLB..81035773F. doi:10.1016/j.physletb.2020.135773.
  7. ^ a b Kubo, Jisuke; Kuntz, Jeffrey (21 December 2022). "Spontaneous conformal symmetry breaking and quantum quadratic gravity". Physical Review D. 106 (12). doi:10.1103/PhysRevD.106.126015. ISSN 2470-0010.
  8. ^ Donoghue, John F.; Menezes, Gabriel (3 May 2022). "On quadratic gravity". Il Nuovo Cimento C. 45 (2): 1–11. doi:10.1393/ncc/i2022-22026-7.
  9. ^ Daas, Jesse; Kuijpers, Kolja; Saueressig, Frank; Wondrak, Michael F.; Falcke, Heino (May 2023). "Probing quadratic gravity with the Event Horizon Telescope". Astronomy & Astrophysics. 673: A53. arXiv:2204.08480. Bibcode:2023A&A...673A..53D. doi:10.1051/0004-6361/202244080. ISSN 0004-6361.


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