{"doi":"10.1103/8cx9-c642","title":"Effects of radiative corrections on Starobinsky inflation","abstract":"<jats:p>\n                    We analyze radiative corrections to the predictions of Starobinsky-like models of inflation arising from self-interactions of the inflaton, and from its Yukawa couplings,\n                    <a:math xmlns:a=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <a:mi>y</a:mi>\n                    </a:math>\n                    , to matter fermions, and dimensionful trilinear couplings,\n                    <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <c:mi>κ</c:mi>\n                    </c:math>\n                    , to scalar fields, which could be responsible for reheating the Universe after inflation. The inflaton self-interactions are found to be of higher order in the Hubble expansion rate during inflation, and hence unimportant for CMB observations. In contrast, Einstein-frame matter couplings to an inflaton generating Starobinsky-like inflation can have significant effects on the spectral index of scalar CMB perturbations,\n                    <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <e:msub>\n                        <e:mi>n</e:mi>\n                        <e:mi>s</e:mi>\n                      </e:msub>\n                    </e:math>\n                    , and on the tensor-to-scalar ratio,\n                    <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <g:mi>r</g:mi>\n                    </g:math>\n                    . Using a renormalization-group improved analysis of the effective inflationary potential, we find that the  measurement of\n                    <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <i:msub>\n                        <i:mi>n</i:mi>\n                        <i:mi>s</i:mi>\n                      </i:msub>\n                    </i:math>\n                    constrains the inflaton coupling to light fermions in the Einstein frame;\n                    <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <k:mrow>\n                        <k:mi>y</k:mi>\n                        <k:mo>&lt;</k:mo>\n                        <k:mn>4.5</k:mn>\n                        <k:mo>×</k:mo>\n                        <k:msup>\n                          <k:mrow>\n                            <k:mn>10</k:mn>\n                          </k:mrow>\n                          <k:mrow>\n                            <k:mo>−</k:mo>\n                            <k:mn>4</k:mn>\n                          </k:mrow>\n                        </k:msup>\n                      </k:mrow>\n                    </k:math>\n                    , corresponding to an upper limit on the reheating temperature\n                    <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <m:msub>\n                        <m:mi>T</m:mi>\n                        <m:mrow>\n                          <m:mi>RH</m:mi>\n                        </m:mrow>\n                      </m:msub>\n                      <m:mo>&lt;</m:mo>\n                      <m:mn>2</m:mn>\n                      <m:mo>×</m:mo>\n                      <m:msup>\n                        <m:mn>10</m:mn>\n                        <m:mn>11</m:mn>\n                      </m:msup>\n                      <m:mtext> </m:mtext>\n                      <m:mtext> </m:mtext>\n                      <m:mi>GeV</m:mi>\n                    </m:math>\n                    , whereas the ACT DR6 measurement of\n                    <o:math xmlns:o=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <o:msub>\n                        <o:mi>n</o:mi>\n                        <o:mi>s</o:mi>\n                      </o:msub>\n                    </o:math>\n                    corresponds to\n                    <q:math xmlns:q=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <q:mn>3.8</q:mn>\n                      <q:mo>×</q:mo>\n                      <q:msup>\n                        <q:mn>10</q:mn>\n                        <q:mrow>\n                          <q:mo>−</q:mo>\n                          <q:mn>4</q:mn>\n                        </q:mrow>\n                      </q:msup>\n                      <q:mo>&lt;</q:mo>\n                      <q:mi>y</q:mi>\n                      <q:mo>&lt;</q:mo>\n                      <q:mn>5.6</q:mn>\n                      <q:mo>×</q:mo>\n                      <q:msup>\n                        <q:mn>10</q:mn>\n                        <q:mrow>\n                          <q:mo>−</q:mo>\n                          <q:mn>4</q:mn>\n                        </q:mrow>\n                      </q:msup>\n                    </q:math>\n                    and\n                    <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <s:mn>1.7</s:mn>\n                      <s:mo>×</s:mo>\n                      <s:msup>\n                        <s:mn>10</s:mn>\n                        <s:mn>11</s:mn>\n                      </s:msup>\n                      <s:mtext> </s:mtext>\n                      <s:mtext> </s:mtext>\n                      <s:mi>GeV</s:mi>\n                      <s:mo>&lt;</s:mo>\n                      <s:msub>\n                        <s:mi>T</s:mi>\n                        <s:mrow>\n                          <s:mi>RH</s:mi>\n                        </s:mrow>\n                      </s:msub>\n                      <s:mo>&lt;</s:mo>\n                      <s:mn>2.8</s:mn>\n                      <s:mo>×</s:mo>\n                      <s:msup>\n                        <s:mn>10</s:mn>\n                        <s:mn>11</s:mn>\n                      </s:msup>\n                      <s:mtext> </s:mtext>\n                      <s:mtext> </s:mtext>\n                      <s:mi>GeV</s:mi>\n                    </s:math>\n                    , while the upper limits on\n                    <u:math xmlns:u=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <u:mi>r</u:mi>\n                    </u:math>\n                    provide weaker constraints.  data also imply a constraint on a trilinear inflaton coupling to light scalars in the Einstein frame:\n                    <w:math xmlns:w=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <w:mi>κ</w:mi>\n                      <w:mo>≤</w:mo>\n                      <w:mn>4</w:mn>\n                      <w:mo>×</w:mo>\n                      <w:msup>\n                        <w:mn>10</w:mn>\n                        <w:mn>12</w:mn>\n                      </w:msup>\n                      <w:mtext> </w:mtext>\n                      <w:mtext> </w:mtext>\n                      <w:mi>GeV</w:mi>\n                    </w:math>\n                    , corresponding to\n                    <y:math xmlns:y=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <y:msub>\n                        <y:mi>T</y:mi>\n                        <y:mrow>\n                          <y:mi>RH</y:mi>\n                        </y:mrow>\n                      </y:msub>\n                      <y:mo>≤</y:mo>\n                      <y:mn>4.2</y:mn>\n                      <y:mo>×</y:mo>\n                      <y:msup>\n                        <y:mn>10</y:mn>\n                        <y:mn>13</y:mn>\n                      </y:msup>\n                      <y:mtext> </y:mtext>\n                      <y:mtext> </y:mtext>\n                      <y:mi>GeV</y:mi>\n                    </y:math>\n                    . We further present constraints on inflaton couplings to massive fermions and scalars, and analyze constraints on couplings in the Jordan frame.\n                  </jats:p>","journal":"Physical Review D","year":2025,"id":658566,"datarank":0.3958585994422889,"base_score":2.639057329615259,"endowment":2.639057329615259,"self_citation_contribution":0.3958585994422889,"citation_network_contribution":0.0,"self_endowment_contribution":0.3958585994422889,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":13,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":15275,"name":"Tony Gherghetta","orcid":"0000-0002-8489-1116","position":1,"is_corresponding":false},{"id":1719177,"name":"Kunio Kaneta","orcid":"0000-0001-5391-2204","position":2,"is_corresponding":false},{"id":1719178,"name":"Wenqi Ke","orcid":"0000-0002-1683-7927","position":3,"is_corresponding":false},{"id":15266,"name":"Keith A. Olive","orcid":"0000-0001-7201-5998","position":4,"is_corresponding":false},{"id":1585499,"name":"John Ellis","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Effects of radiative corrections on Starobinsky inflation","abstract":"<jats:p>\n                    We analyze radiative corrections to the predictions of Starobinsky-like models of inflation arising from self-interactions of the inflaton, and from its Yukawa couplings,\n                    <a:math xmlns:a=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <a:mi>y</a:mi>\n                    </a:math>\n                    , to matter fermions, and dimensionful trilinear couplings,\n                    <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <c:mi>κ</c:mi>\n                    </c:math>\n                    , to scalar fields, which could be responsible for reheating the Universe after inflation. The inflaton self-interactions are found to be of higher order in the Hubble expansion rate during inflation, and hence unimportant for CMB observations. In contrast, Einstein-frame matter couplings to an inflaton generating Starobinsky-like inflation can have significant effects on the spectral index of scalar CMB perturbations,\n                    <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <e:msub>\n                        <e:mi>n</e:mi>\n                        <e:mi>s</e:mi>\n                      </e:msub>\n                    </e:math>\n                    , and on the tensor-to-scalar ratio,\n                    <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <g:mi>r</g:mi>\n                    </g:math>\n                    . Using a renormalization-group improved analysis of the effective inflationary potential, we find that the  measurement of\n                    <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <i:msub>\n                        <i:mi>n</i:mi>\n                        <i:mi>s</i:mi>\n                      </i:msub>\n                    </i:math>\n                    constrains the inflaton coupling to light fermions in the Einstein frame;\n                    <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <k:mrow>\n                        <k:mi>y</k:mi>\n                        <k:mo>&lt;</k:mo>\n                        <k:mn>4.5</k:mn>\n                        <k:mo>×</k:mo>\n                        <k:msup>\n                          <k:mrow>\n                            <k:mn>10</k:mn>\n                          </k:mrow>\n                          <k:mrow>\n                            <k:mo>−</k:mo>\n                            <k:mn>4</k:mn>\n                          </k:mrow>\n                        </k:msup>\n                      </k:mrow>\n                    </k:math>\n                    , corresponding to an upper limit on the reheating temperature\n                    <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <m:msub>\n                        <m:mi>T</m:mi>\n                        <m:mrow>\n                          <m:mi>RH</m:mi>\n                        </m:mrow>\n                      </m:msub>\n                      <m:mo>&lt;</m:mo>\n                      <m:mn>2</m:mn>\n                      <m:mo>×</m:mo>\n                      <m:msup>\n                        <m:mn>10</m:mn>\n                        <m:mn>11</m:mn>\n                      </m:msup>\n                      <m:mtext> </m:mtext>\n                      <m:mtext> </m:mtext>\n                      <m:mi>GeV</m:mi>\n                    </m:math>\n                    , whereas the ACT DR6 measurement of\n                    <o:math xmlns:o=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <o:msub>\n                        <o:mi>n</o:mi>\n                        <o:mi>s</o:mi>\n                      </o:msub>\n                    </o:math>\n                    corresponds to\n                    <q:math xmlns:q=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <q:mn>3.8</q:mn>\n                      <q:mo>×</q:mo>\n                      <q:msup>\n                        <q:mn>10</q:mn>\n                        <q:mrow>\n                          <q:mo>−</q:mo>\n                          <q:mn>4</q:mn>\n                        </q:mrow>\n                      </q:msup>\n                      <q:mo>&lt;</q:mo>\n                      <q:mi>y</q:mi>\n                      <q:mo>&lt;</q:mo>\n                      <q:mn>5.6</q:mn>\n                      <q:mo>×</q:mo>\n                      <q:msup>\n                        <q:mn>10</q:mn>\n                        <q:mrow>\n                          <q:mo>−</q:mo>\n                          <q:mn>4</q:mn>\n                        </q:mrow>\n                      </q:msup>\n                    </q:math>\n                    and\n                    <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <s:mn>1.7</s:mn>\n                      <s:mo>×</s:mo>\n                      <s:msup>\n                        <s:mn>10</s:mn>\n                        <s:mn>11</s:mn>\n                      </s:msup>\n                      <s:mtext> </s:mtext>\n                      <s:mtext> </s:mtext>\n                      <s:mi>GeV</s:mi>\n                      <s:mo>&lt;</s:mo>\n                      <s:msub>\n                        <s:mi>T</s:mi>\n                        <s:mrow>\n                          <s:mi>RH</s:mi>\n                        </s:mrow>\n                      </s:msub>\n                      <s:mo>&lt;</s:mo>\n                      <s:mn>2.8</s:mn>\n                      <s:mo>×</s:mo>\n                      <s:msup>\n                        <s:mn>10</s:mn>\n                        <s:mn>11</s:mn>\n                      </s:msup>\n                      <s:mtext> </s:mtext>\n                      <s:mtext> </s:mtext>\n                      <s:mi>GeV</s:mi>\n                    </s:math>\n                    , while the upper limits on\n                    <u:math xmlns:u=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <u:mi>r</u:mi>\n                    </u:math>\n                    provide weaker constraints.  data also imply a constraint on a trilinear inflaton coupling to light scalars in the Einstein frame:\n                    <w:math xmlns:w=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <w:mi>κ</w:mi>\n                      <w:mo>≤</w:mo>\n                      <w:mn>4</w:mn>\n                      <w:mo>×</w:mo>\n                      <w:msup>\n                        <w:mn>10</w:mn>\n                        <w:mn>12</w:mn>\n                      </w:msup>\n                      <w:mtext> </w:mtext>\n                      <w:mtext> </w:mtext>\n                      <w:mi>GeV</w:mi>\n                    </w:math>\n                    , corresponding to\n                    <y:math xmlns:y=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">\n                      <y:msub>\n                        <y:mi>T</y:mi>\n                        <y:mrow>\n                          <y:mi>RH</y:mi>\n                        </y:mrow>\n                      </y:msub>\n                      <y:mo>≤</y:mo>\n                      <y:mn>4.2</y:mn>\n                      <y:mo>×</y:mo>\n                      <y:msup>\n                        <y:mn>10</y:mn>\n                        <y:mn>13</y:mn>\n                      </y:msup>\n                      <y:mtext> </y:mtext>\n                      <y:mtext> </y:mtext>\n                      <y:mi>GeV</y:mi>\n                    </y:math>\n                    . We further present constraints on inflaton couplings to massive fermions and scalars, and analyze constraints on couplings in the Jordan frame.\n                  </jats:p>","is_dataset_classified":null,"base_score":2.639057329615259,"endowment":2.639057329615259,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"19162232","pmcid":null,"openalex_id":"https://openalex.org/W4417210687","authors":[],"funders":[{"funder_name":"Science and Technology Facilities Council","grant_id":"ST/T000759/1","title":"Pathways between Fundamental Physics and Phenomenology"},{"funder_name":"U.S. Department of Energy","grant_id":"DE-SC0011842","title":null}],"total_grants":2,"fwci":7.7988,"citation_percentile":0.97809769,"influential_citations":0,"citation_trend":[{"year":2026,"count":13}],"oa_status":"hybrid","license":"cc-by","oa_locations":[{"url":"https://doi.org/10.1103/8cx9-c642","host_type":"journal"},{"url":"https://doi.org/10.1103/8cx9-c642","host_type":"publisher"},{"url":"https://link.aps.org/article/10.1103/8cx9-c642","host_type":"publisher"},{"url":"http://harvest.aps.org/v2/journals/articles/10.1103/8cx9-c642/fulltext","host_type":"publisher"},{"url":"http://cds.cern.ch/record/2946540","host_type":"repository"},{"url":"https://dx.doi.org/10.48550/arxiv.2510.15137","host_type":""},{"url":"http://arxiv.org/abs/2510.15137","host_type":""}],"fields_of_study":["Cosmology and Gravitation Theories","Galaxies: Formation, Evolution, Phenomena","Astronomy and Astrophysical Research","0103 physical sciences","01 natural sciences"],"mesh_terms":[],"keywords":["Inflaton","Cosmic microwave background","Inflation (cosmology)","Spectral index","Hubble's law","Planck","Radiative transfer","Yukawa potential","High Energy Physics - Theory","High Energy Physics - Phenomenology","High Energy Physics - Phenomenology (hep-ph)","Cosmology and Nongalactic Astrophysics (astro-ph.CO)","High Energy Physics - Theory (hep-th)","FOS: Physical sciences","General Relativity and Quantum Cosmology (gr-qc)","Cosmology and Nongalactic Astrophysics","General Relativity and Quantum Cosmology"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-12T04:40:00.325816Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}