{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:08:55Z","timestamp":1790878135655,"version":"4.1.0"},"reference-count":52,"publisher":"American Physical Society (APS)","issue":"23","license":[{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000271","name":"Science and Technology Facilities Council","doi-asserted-by":"publisher","award":["ST\/T000791\/1"],"award-info":[{"award-number":["ST\/T000791\/1"]}],"id":[{"id":"10.13039\/501100000271","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,5,14]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1103\/tvmx-qk3k","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T12:08:02Z","timestamp":1778760482000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Lorentz Violation in Emergent Gravity and Its Cosmological Consequences"],"prefix":"10.1103","volume":"136","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8937-1527","authenticated-orcid":true,"given":"Raymond","family":"Isichei","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/009gyvm78","id-type":"ROR","asserted-by":"publisher"}],"name":"Abdus Salam Centre for Theoretical Physics"},{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1408-3313","authenticated-orcid":true,"given":"Jo\u00e3o","family":"Magueijo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/009gyvm78","id-type":"ROR","asserted-by":"publisher"}],"name":"Abdus Salam Centre for Theoretical Physics"},{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,6,8]]},"reference":[{"key":"tvmx-qk3kCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.1260","type":"journal-article"},{"key":"tvmx-qk3kCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.121301","type":"journal-article"},{"key":"tvmx-qk3kCc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.74.104015","type":"journal-article"},{"key":"tvmx-qk3kCc4R1","doi-asserted-by":"publisher","DOI":"10.1142\/S021773231003313X","type":"journal-article"},{"key":"tvmx-qk3kCc5R1","doi-asserted-by":"publisher","DOI":"10.1088\/1674-4527\/12\/8\/003","type":"journal-article"},{"key":"tvmx-qk3kCc6R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218271814300110","type":"journal-article"},{"key":"tvmx-qk3kCc7R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP04(2011)029","type":"journal-article"},{"key":"tvmx-qk3kCc8R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.2.3.016","type":"journal-article"},{"key":"tvmx-qk3kCc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.201101","type":"journal-article"},{"key":"tvmx-qk3kCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.7.2333","type":"journal-article"},{"key":"tvmx-qk3kCc11R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02345020","type":"journal-article"},{"key":"tvmx-qk3kCc12R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/31\/20\/205002","type":"journal-article"},{"key":"tvmx-qk3kCc13R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/ab5ba9","type":"journal-article"},{"key":"tvmx-qk3kCc14R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-025-02291-y","type":"journal-article"},{"key":"tvmx-qk3kCc15R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/15\/10\/017","type":"journal-article"},{"key":"tvmx-qk3kCc16R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.75.064008","type":"journal-article"},{"key":"tvmx-qk3kCc17R1","unstructured":"To be published.","type":"other"},{"key":"tvmx-qk3kCc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.59.521","type":"journal-article"},{"key":"tvmx-qk3kCc19R1","volume-title":"Lectures on Quantum Gravity","author":"R.\u2009D. Sorkin","year":"2005","type":"book"},{"key":"tvmx-qk3kCc20R1","doi-asserted-by":"publisher","DOI":"10.1007\/s41114-019-0023-1","type":"journal-article"},{"key":"tvmx-qk3kCc21R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/21\/15\/R01","type":"journal-article"},{"key":"tvmx-qk3kCc22R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511755682","type":"book","volume-title":"Modern Canonical Quantum General Relativity","author":"T. Thiemann","year":"2007"},{"key":"tvmx-qk3kCc23R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107706910","type":"book","volume-title":"Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory","author":"C. Rovelli","year":"2014"},{"key":"tvmx-qk3kCc24R1","doi-asserted-by":"publisher","DOI":"10.12942\/lrr-2013-3","type":"journal-article"},{"key":"tvmx-qk3kCc25R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218271802001330","type":"journal-article"},{"key":"tvmx-qk3kCc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.190403","type":"journal-article"},{"key":"tvmx-qk3kCc27R1","doi-asserted-by":"crossref","DOI":"10.1007\/b105189","type":"book","volume-title":"Planck Scale Effects in Astrophysics and Cosmology","author":"J. Kowalski-Glikman","year":"2005"},{"key":"tvmx-qk3kCc28R1","unstructured":"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 \u2110+ and \u2110\u2212 are different at the same external time.","type":"other"},{"key":"tvmx-qk3kCc29R1","unstructured":"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.\u00a0[30, 31, 32, 33]).","type":"other"},{"key":"tvmx-qk3kCc30R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218271893000246","type":"journal-article"},{"key":"tvmx-qk3kCc31R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.59.043516","type":"journal-article"},{"key":"tvmx-qk3kCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.64.024028","type":"journal-article"},{"key":"tvmx-qk3kCc33R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.181302","type":"journal-article"},{"key":"tvmx-qk3kCc34R1","unstructured":"Our argument should not be confused with that in Ref.\u00a0[9], which focuses on the spatial \u03a3. We adopt the view that all entropy resides on the null surfaces.","type":"other"},{"key":"tvmx-qk3kCc35R1","unstructured":"The derivation in this paragraph can be redone with the conformal KV, writing \u03b4U=\u03b4Q=T\u03bc\u03bd\u03b6\u03bcd\u03a3\u03bd and evaluating geodesic deviation from \u03b4\u03b8=\u03b8\u2212\u03b80, where \u03b80=1\/(\u2213\u2113+\u03bb\/2) [resulting in A0=4\u03c0(\u2113\u2213\u03bb\/2)2] is the geodesic deviation before matter flows across \u2110\u00b1 (describing a zeroth order entropy, to be subtracted). Dropping the isochoric assumption on \u2110\u00b1 is examined in Ref.\u00a0[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 \u201cGR-like\u201d in this Letter; see Ref.\u00a0[3].","type":"other"},{"key":"tvmx-qk3kCc36R1","unstructured":"See End Matter, Appendix\u00a0B.","type":"other"},{"key":"tvmx-qk3kCc37R1","unstructured":"See End Matter, Appendix\u00a0A.","type":"other"},{"key":"tvmx-qk3kCc38R1","unstructured":"The extra minus signs account for \u03b60&lt;0 and n0&lt;0.","type":"other"},{"key":"tvmx-qk3kCc39R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.15.1.023","type":"journal-article"},{"key":"tvmx-qk3kCc40R1","unstructured":"A specie dependent L2 makes sense because thermodynamics is generally nonlinear and U is a nonlinear function of S just as R\u03bc\u03bd is a nonlinear function of T\u03bc\u03bd.","type":"other"},{"key":"tvmx-qk3kCc41R1","unstructured":"See End Matter, Appendix\u00a0C.","type":"other"},{"key":"tvmx-qk3kCc42R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/ad2527","type":"journal-article"},{"key":"tvmx-qk3kCc43R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2025\/11\/010","type":"journal-article"},{"key":"tvmx-qk3kCc44R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.61.1","type":"journal-article"},{"key":"tvmx-qk3kCc46R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.529283","type":"journal-article"},{"key":"tvmx-qk3kCc47R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.80.084003","type":"journal-article"},{"key":"tvmx-qk3kCc48R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjc\/s10052-015-3767-0","type":"journal-article"},{"key":"tvmx-qk3kCc49R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/21\/7\/001","type":"journal-article"},{"key":"tvmx-qk3kCc50R1","unstructured":"See End Matter, Appendix\u00a0D.","type":"other"},{"key":"tvmx-qk3kCc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.084032","type":"journal-article"},{"key":"tvmx-qk3kCc52R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.82.169","type":"journal-article"},{"key":"tvmx-qk3kCc53R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01451608","type":"journal-article"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/tvmx-qk3k","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/tvmx-qk3k\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T17:46:36Z","timestamp":1790876796000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/tvmx-qk3k"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,8]]},"references-count":52,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2026,6]]}},"URL":"https:\/\/doi.org\/10.1103\/tvmx-qk3k","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2511.22221","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,8]]},"assertion":[{"value":"2025-11-27","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"231501"}}