- Open Access
Uniqueness of conformal Killing gravity cosmology
APS Open Sci. 1, 000203 – Published 4 November, 2026
DOI: https://doi.org/10.1103/75zr-9kwq
Abstract
We investigate an extension of Harada gravity, a third-order theory proposed as an alternative to general relativity that preserves energy-momentum conservation and in which the cosmological constant arises as an integration constant. Our aim is to determine whether Harada gravity is unique under the principles that motivated its construction. We show that imposing both the existence of all Einstein solutions and energy-momentum conservation restricts the theory to only two distinct branches: general relativity and Harada gravity. We then relax each of these assumptions independently and demonstrate that, within the class of symmetric theories considered, Harada gravity remains the unique extension of general relativity.
Physics Subject Headings (PhySH)
Article Text
References (13)
- J. Harada, Gravity at cosmological distances: Explaining the accelerating expansion without dark energy, Phys. Rev. D 108, 044031 (2023).
- J. Harada, Emergence of the Cotton tensor for describing gravity, Phys. Rev. D 103, L121502 (2021).
- C. A. Mantica and L. G. Molinari, Note on Harada’s conformal Killing gravity, Phys. Rev. D 108, 124029 (2023).
- A. Barnes, Vacuum static spherically symmetric spacetimes in Harada’s theory, arXiv:2309.05336.
- J. T. S. S. Junior, F. S. N. Lobo, and M. E. Rodrigues, Black bounces in conformal Killing gravity, Eur. Phys. J. C 84, 557 (2024).
- C. A. Mantica and L. G. Molinari, Note on conserved currents in static conformal Killing gravity, Phys. Rev. D 112, 024070 (2025).
- E. L. Junior, J. T. S. Junior, F. S. Lobo, M. E. Rodrigues, L. F. D. da Silva, and H. A. Vieira, Novel charged black hole solutions in conformal Killing gravity, arXiv:2502.00589.
- Y. Ladghami, B. Asfour, F. S. Lobo, and T. Ouali, Thermodynamics and information recovery of Schwarzschild AdS black holes in conformal Killing gravity, Eur. Phys. J. C 86, 526 (2026).
- C. A. Mantica and L. G. Molinari, Conformal Killing cosmology: Geometry, dark sector, growth of structures, and a big rip, Phys. Rev. D 110, 064041 (2024).
- S. Capozziello, C. A. Mantica, L. G. Molinari, and G. Sarracino, Constraints on cosmological parameters and CMB first acoustic peak in conformal Killing gravity, Phys. Rev. D 113, 015006 (2026).
- H. Chaudhary, S. Capozziello, C. A. Mantica, L. Guido Molinari, D. Jyoti Gogoi, and G. Mustafa, Conformal Killing gravity: New constraints from DESI DR2 BAO datasets, Phys. Dark Universe 54 102444 (2026).
- D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12, 498 (1971).
- S. Capozziello, C. A. Mantica, and L. G. Molinari, Non conservative conformal Killing gravity: Coupling the dark sector with curvature and matter, arXiv:2606.08213.
