- Open Access
Lorentz Violation in Emergent Gravity and Its Cosmological Consequences
Phys. Rev. Lett. 136, 231501 – Published 8 June, 2026
DOI: https://doi.org/10.1103/tvmx-qk3k
Abstract
We show that general relativity and other geometrical theories can be viewed as a degenerate Otto cycle with only heat-exchange legs in emergent gravity. Including work-producing legs yields controlled violations of local Lorentz invariance and energy-momentum conservation, which produce late-time cosmological acceleration. Implications for the cosmological constant problem, structure formation, and local observations are discussed.
Physics Subject Headings (PhySH)
Article Text
References (53)
- T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995).
- C. Eling, R. Guedens, and T. Jacobson, Phys. Rev. Lett. 96, 121301 (2006).
- A. Paranjape, S. Sarkar, and T. Padmanabhan, Phys. Rev. D 74, 104015 (2006).
- T. Padmanabhan, Mod. Phys. Lett. A 25, 1129 (2010).
- T. Padmanabhan, Res. Astron. Astrophys. 12, 891 (2012).
- T. Padmanabhan, Int. J. Mod. Phys. D 23, 1430011 (2014).
- E. P. Verlinde, J. High Energy Phys. 04 (2011) 029.
- E. P. Verlinde, SciPost Phys. 2, 016 (2017).
- T. Jacobson, Phys. Rev. Lett. 116, 201101 (2016).
- J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).
- S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).
- C. V. Johnson, Classical Quantum Gravity 31, 205002 (2014).
- C. V. Johnson, Classical Quantum Gravity 37, 034001 (2020).
- N. Lilani and M. R. Visser, Commun. Phys. 8, 379 (2025).
- S. A. Hayward, Classical Quantum Gravity 15, 3147 (1998).
- R. G. Cai and L. M. Cao, Phys. Rev. D 75, 064008 (2007).
To be published.
- L. Bombelli, J. Lee, D. Meyer, and R. D. Sorkin, Phys. Rev. Lett. 59, 521 (1987).
- R. D. Sorkin, Causal sets: Discrete gravity, in Lectures on Quantum Gravity, edited by A. Gomberoff and D. Marolf (Springer, Boston, 2005).
- S. Surya, Living Rev. Relativity 22, 5 (2019).
- A. Ashtekar and J. Lewandowski, Classical Quantum Gravity 21, R53 (2004).
- T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2007).
- C. Rovelli and F. Vidotto, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory (Cambridge University Press, Cambridge, England, 2014).
- A. Perez, Living Rev. Relativity 16, 3 (2013).
- G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002).
- J. Magueijo and L. Smolin, Phys. Rev. Lett. 88, 190403 (2002).
- J. Kowalski-Glikman, Introduction to doubly special relativity, in Planck Scale Effects in Astrophysics and Cosmology, Lecture Notes in Physics Vol. 669 (Springer, New York, 2005), p. 131.
Therefore, if when we change the temperature at the entry and exit of a causal diamond, we are not claiming that the surface gravity on and are different at the same external time.
The theories that we will develop have a passing resemblance to previous work on preferred frames, with or without violations of energy conservation (e.g., Refs. [30, 31, 32, 33]).
- J. W. Moffat, Int. J. Mod. Phys. D 02, 351 (1993).
- A. Albrecht and J. Magueijo, Phys. Rev. D 59, 043516 (1999).
- T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001).
- D. Blas, O. Pujolàs, and S. Sibiryakov, Phys. Rev. Lett. 104, 181302 (2010).
Our argument should not be confused with that in Ref. [9], which focuses on the spatial . We adopt the view that all entropy resides on the null surfaces.
The derivation in this paragraph can be redone with the conformal KV, writing and evaluating geodesic deviation from , where [resulting in ] is the geodesic deviation before matter flows across (describing a zeroth order entropy, to be subtracted). Dropping the isochoric assumption on is examined in Ref. [17]. Note that even within the isochoric assumption one could make other choices for the relation between curvature and entropy, e.g., based on the Wald entropy functional, leading to theories considered “GR-like” in this Letter; see Ref. [3].
See End Matter, Appendix B.
See End Matter, Appendix A.
The extra minus signs account for and .
- T. Jacobson and M. R. Visser, SciPost Phys. 15, 023 (2023).
A specie dependent makes sense because thermodynamics is generally nonlinear and is a nonlinear function of just as is a nonlinear function of .
See End Matter, Appendix C.
- B. Wang, E. Abdalla, F. Atrio-Barandela, and D. Pavón, Rep. Prog. Phys. 87, 036901 (2024).
- Y. Zhai, M. de Cesare, C. van de Bruck, E. Di Valentino, and E. Wilson-Ewing, J. Cosmol. Astropart. Phys. 11 (2025) 010.
- S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).
- A. Padilla, arXiv:1502.05296.
- Y. J. Ng and H. van Dam, J. Math. Phys. (N.Y.) 32, 1337 (1991).
- L. Smolin, Phys. Rev. D 80, 084003 (2009).
- A. Padilla and I. D. Saltas, Eur. Phys. J. C 75, 561 (2015).
- J. Magueijo and L. Smolin, Classical Quantum Gravity 21, 1725 (2004).
See End Matter, Appendix D.
- Y. Bonder, J. E. Herrera, and A. M. Rubiol, Phys. Rev. D 107, 084032 (2023).
- M. Carrera and D. Giulini, Rev. Mod. Phys. 82, 169 (2010).
- K. O. Friedrichs, Math. Ann. 98, 566 (1928).