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Phys. J. C"],"published-print":{"date-parts":[[2021,11]]},"abstract":"Abstract<\/jats:title>Loop quantum cosmology (LQC) is a theory which renders the Big Bang initial singularity into a quantum bounce, by means of short-range repulsive quantum effects at the Planck scale. In this work, we are interested in reproducing the effective Friedmann equation of LQC, by considering a generic f<\/jats:italic>(R<\/jats:italic>,\u00a0P<\/jats:italic>,\u00a0Q<\/jats:italic>) theory of gravity, where $$R=g^{\\mu \\nu }R_{\\mu \\nu }$$<\/jats:tex-math>\n \n R<\/mml:mi>\n =<\/mml:mo>\n \n g<\/mml:mi>\n \n \u03bc<\/mml:mi>\n \u03bd<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n \n R<\/mml:mi>\n \n \u03bc<\/mml:mi>\n \u03bd<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the Ricci scalar, $$P=R_{\\mu \\nu }R^{\\mu \\nu }$$<\/jats:tex-math>\n \n P<\/mml:mi>\n =<\/mml:mo>\n \n R<\/mml:mi>\n \n \u03bc<\/mml:mi>\n \u03bd<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n \n R<\/mml:mi>\n \n \u03bc<\/mml:mi>\n \u03bd<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and $$Q=R_{\\alpha \\beta \\mu \\nu }R^{\\alpha \\beta \\mu \\nu }$$<\/jats:tex-math>\n \n Q<\/mml:mi>\n =<\/mml:mo>\n \n R<\/mml:mi>\n \n \u03b1<\/mml:mi>\n \u03b2<\/mml:mi>\n \u03bc<\/mml:mi>\n \u03bd<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n \n R<\/mml:mi>\n \n \u03b1<\/mml:mi>\n \u03b2<\/mml:mi>\n \u03bc<\/mml:mi>\n \u03bd<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the Kretschmann scalar. An order reduction technique allows us to work in f<\/jats:italic>(R<\/jats:italic>,\u00a0P<\/jats:italic>,\u00a0Q<\/jats:italic>) theories which are perturbatively close to General Relativity, and to deduce a modified Friedmann equation in the reduced theory. Requiring that the modified Friedmann equation mimics the effective Friedmann equation of LQC, we are able to derive several functional forms of f<\/jats:italic>(R<\/jats:italic>,\u00a0P<\/jats:italic>,\u00a0Q<\/jats:italic>). We discuss the necessary conditions to obtain viable bouncing cosmologies for the proposed effective actions of f<\/jats:italic>(R<\/jats:italic>,\u00a0P<\/jats:italic>,\u00a0Q<\/jats:italic>) theory of gravity.<\/jats:p>","DOI":"10.1140\/epjc\/s10052-021-09767-5","type":"journal-article","created":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T12:03:13Z","timestamp":1636200193000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Effective actions for loop quantum cosmology in fourth-order gravity"],"prefix":"10.1140","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0397-2705","authenticated-orcid":false,"given":"Marcello","family":"Miranda","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4379-2549","authenticated-orcid":false,"given":"Daniele","family":"Vernieri","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4886-2024","authenticated-orcid":false,"given":"Salvatore","family":"Capozziello","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9388-8373","authenticated-orcid":false,"given":"Francisco S. 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