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Rev. Lett."],"accepted":{"date-parts":[[2026,2,25]]},"abstract":"<jats:p>We present a quantum quadratic gravity inflationary scenario that can accommodate the new cosmological constraints, which have disfavored Starobinsky inflation. The theory is asymptotically free in the ultraviolet, but 1-loop running is found to dynamically lead to slow-roll inflation toward the infrared. When a large number of matter fields contribute to the beta functions, the spectral index and the tensor-to-scalar ratio can be phenomenologically viable. We find that as inflation ends, the theory approaches its strong coupling regime and general relativity must emerge, as an effective field theory, as the universe must reheat and enter its standard radiation era. In order to avoid strong coupling, a minimum tensor-to-scalar ratio of 0.01 is predicted for this theory. Our framework offers a laboratory for connecting a concrete ultraviolet completion (quantum quadratic gravity) with inflationary dynamics, reheating, and precise cosmological observations.<\/jats:p>","DOI":"10.1103\/6gtx-j455","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T12:52:06Z","timestamp":1772023926000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Ultraviolet Completion of the Big Bang in Quadratic Gravity"],"prefix":"10.1103","volume":"136","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7385-3071","authenticated-orcid":true,"given":"Ruolin","family":"Liu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01aff2v68","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Waterloo"},{"id":[{"id":"https:\/\/ror.org\/013m0ej23","id-type":"ROR","asserted-by":"publisher"}],"name":"Perimeter Institute for Theoretical Physics"},{"id":[{"id":"https:\/\/ror.org\/01aff2v68","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Waterloo"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4532-7026","authenticated-orcid":true,"given":"Jerome","family":"Quintin","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0020snb74","id-type":"ROR","asserted-by":"publisher"}],"name":"\u00c9cole de technologie sup\u00e9rieure"},{"id":[{"id":"https:\/\/ror.org\/01pxwe438","id-type":"ROR","asserted-by":"publisher"}],"name":"McGill University"},{"id":[{"id":"https:\/\/ror.org\/01aff2v68","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Waterloo"},{"id":[{"id":"https:\/\/ror.org\/013m0ej23","id-type":"ROR","asserted-by":"publisher"}],"name":"Perimeter Institute for Theoretical Physics"},{"id":[{"id":"https:\/\/ror.org\/01aff2v68","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Waterloo"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9940-7040","authenticated-orcid":true,"given":"Niayesh","family":"Afshordi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01aff2v68","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Waterloo"},{"id":[{"id":"https:\/\/ror.org\/013m0ej23","id-type":"ROR","asserted-by":"publisher"}],"name":"Perimeter Institute for Theoretical Physics"},{"id":[{"id":"https:\/\/ror.org\/01aff2v68","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Waterloo"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,3,18]]},"reference":[{"key":"6gtx-j455Cc1R1","doi-asserted-by":"publisher","DOI":"10.12942\/lrr-2004-5","type":"journal-article"},{"key":"6gtx-j455Cc2R1","unstructured":"We use the mostly positive metric signature. We contract tensor indices with the metric g\u03bc\u03bd, whose determinant is g and Ricci scalar R. Finally, we use natural units, and MPl denotes the reduced Planck mass.","type":"other"},{"key":"6gtx-j455Cc3R1","first-page":"69","type":"journal-article","volume":"20","author":"G. \u2019t Hooft","year":"1974","journal-title":"Ann. Inst. 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Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/6gtx-j455 for details of the calculations pertaining to the renormalization group equations, the cosmological evolution in the Jordan frame, the cosmological perturbations in the Einstein frame, and reheating.","type":"other"},{"key":"6gtx-j455Cc57R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP02(2024)039","type":"journal-article"},{"key":"6gtx-j455Cc58R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP09(2025)202","type":"journal-article"},{"key":"6gtx-j455Cc59R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02748300","type":"journal-article"},{"key":"6gtx-j455Cc60R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/11\/6\/004","type":"journal-article"},{"key":"6gtx-j455Cc61R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.28.2960","type":"journal-article"},{"key":"6gtx-j455Cc62R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(82)90866-8","type":"journal-article"},{"key":"6gtx-j455Cc63R1","unstructured":"The natural possibility of a \u201ccreation out of nothing\u201d is a compelling one here, but it certainly deserves further investigation. In particular, finding proper instanton solutions and analyzing the path integral of QQG would constitute interesting follow-up work.","type":"other"},{"key":"6gtx-j455Cc64R1","unstructured":"One may question how large N can reasonably be. In theoretical settings, such as holography, N is often taken to be arbitrarily large, to ensure perturbative gravity in the bulk. Here, we remain agnostic about whether or not a very large N represents a fine-tuning problem. We should further note that these matter fields would probably end up being confined to the UV, together with all the degrees of freedom of QQG, in a similar fashion to quarks and gluons in QCD.","type":"other"},{"key":"6gtx-j455Cc65R1","unstructured":"Here, we ignore the impact of the running of the coupling to Gauss-Bonnet\u2019s invariant G, which is not widely studied due to its topological nature. However, this may affect cosmological evolution\u2014as in f(R,G) theories, which are widely studied in the literature, e.g., [66]\u2014but we defer that consideration to future work.","type":"other"},{"key":"6gtx-j455Cc66R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.73.084007","type":"journal-article"},{"key":"6gtx-j455Cc67R1","volume-title":"Effective Action in Quantum Gravity","author":"I.\u2009L. Buchbinder","year":"1992","type":"book"},{"key":"6gtx-j455Cc68R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(93)91427-O","type":"journal-article"},{"key":"6gtx-j455Cc69R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01957780","type":"journal-article"},{"key":"6gtx-j455Cc70R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.91.083529","type":"journal-article"},{"key":"6gtx-j455Cc71R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP10(2023)063","type":"journal-article"},{"key":"6gtx-j455Cc72R1","unstructured":"Note that during the slow-roll phase of inflation, due to the near de Sitter nature of spacetime, different choices of curvature invariants for the RG scale are generically equivalent to the Ricci scalar. However, they will start to differ as we approach the end of inflation, and thus, they could lead to different reheating mechanisms in the strongly coupled regime.","type":"other"},{"key":"6gtx-j455Cc73R1","unstructured":"The contribution from the Weyl tensor vanishes on a homogeneous and isotropic background. This is not true once cosmological perturbations are introduced. Still, contributions from the Weyl tensor to, e.g., tensor perturbations are usually highly suppressed [34], and we do not expect this result to be affected by small logarithmic running.","type":"other"},{"key":"6gtx-j455Cc74R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dark.2014.01.003","type":"journal-article"},{"key":"6gtx-j455Cc75R1","doi-asserted-by":"publisher","DOI":"10.1051\/0004-6361\/201321569","type":"journal-article"},{"key":"6gtx-j455Cc76R1","doi-asserted-by":"publisher","DOI":"10.1051\/0004-6361\/201833887","type":"journal-article"},{"key":"6gtx-j455Cc77R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2025\/11\/062","type":"journal-article"},{"key":"6gtx-j455Cc79R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.151301","type":"journal-article"},{"key":"6gtx-j455Cc80R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2025\/02\/021","type":"journal-article"},{"key":"6gtx-j455Cc81R1","doi-asserted-by":"publisher","DOI":"10.1103\/lq71-b84v","type":"journal-article"},{"key":"6gtx-j455Cc82R1","unstructured":"Cold dark matter with a cosmological constant (\u039bCDM) refers to the standard model of cosmology, while the Chevallier-Polarski-Linder [83, 84] parametrization for dynamical dark energy (often called w0waCDM) stands as an alternative where the dark-energy equation of state depends linearly on the cosmological scale factor. The recent BAO data of DESI point toward a slight preference for the latter [80].","type":"other"},{"key":"6gtx-j455Cc83R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218271801000822","type":"journal-article"},{"key":"6gtx-j455Cc84R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.90.091301","type":"journal-article"},{"key":"6gtx-j455Cc85R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.118.041301","type":"journal-article"},{"key":"6gtx-j455Cc86R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.81.021301","type":"journal-article"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/6gtx-j455","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/6gtx-j455\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T15:01:09Z","timestamp":1773846069000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/6gtx-j455"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,18]]},"references-count":81,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2026,3]]}},"URL":"https:\/\/doi.org\/10.1103\/6gtx-j455","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2510.18733","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,18]]},"assertion":[{"value":"2025-11-04","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":"111501"}}