{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T05:40:58Z","timestamp":1777614058879,"version":"3.51.4"},"reference-count":106,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,3,9]],"date-time":"2015-03-09T00:00:00Z","timestamp":1425859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We review inflationary cosmology in modified gravity such as R2 gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the R2 term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of scalar modes of the density perturbations and the tensor-to-scalar ratio can be consistent with the Planck results. Bounce cosmology in F(R) gravity is also explained.<\/jats:p>","DOI":"10.3390\/sym7010220","type":"journal-article","created":{"date-parts":[[2015,3,9]],"date-time":"2015-03-09T11:47:19Z","timestamp":1425901639000},"page":"220-240","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":319,"title":["Inflationary Cosmology in Modified Gravity Theories"],"prefix":"10.3390","volume":"7","author":[{"given":"Kazuharu","family":"Bamba","sequence":"first","affiliation":[{"name":"Leading Graduate School Promotion Center, Ochanomizu University, Tokyo 112-8610, Japan"},{"name":"Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, Tokyo 112-8610, Japan"}]},{"given":"Sergei","family":"Odintsov","sequence":"additional","affiliation":[{"name":"Consejo Superior de Investigaciones Cient\u00edficas, ICE\/CSIC-IEEC, Campus UAB, Facultat de Ci\u00e8ncies, Torre C5-Parell-2a pl, E-08193 Bellaterra (Barcelona), Spain"},{"name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats (ICREA), Passeig Llu\u00eds Companys,23-08010 Barcelona, Spain"},{"name":"Tomsk State Pedagogical University, 634061 Tomsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ade, P.A.R., Aikin, R.W., Barkats, D., Benton, S.J., Bischoff, C.A., Bock, J.J., Brevik, J.A., Buder, I., Bullock, E., and Dowell, C.D. (2014). Detection of B-Mode Polarization at Degree Angular Scales by BICEP2. Phys. Rev. Lett, 112.","DOI":"10.1103\/PhysRevLett.112.241101"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1086\/377226","article-title":"First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters","volume":"148","author":"Spergel","year":"2003","journal-title":"Astrophys. J. Suppl"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1086\/513700","article-title":"Wilkinson Microwave Anisotropy Probe (WMAP) three year results: Implications for cosmology","volume":"170","author":"Spergel","year":"2007","journal-title":"Astrophys. J. Suppl"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1088\/0067-0049\/180\/2\/330","article-title":"Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation","volume":"180","author":"Komatsu","year":"2009","journal-title":"Astrophys. J. Suppl"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Komatsu, E., Smith, K.M., Dunkley, J., Bennett, C.L., Gold, B., Hinshaw, G., Jarosik, N., Larson, D., Nolta, M.R., and Page, L. (2011). Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. Astrophys. J. Suppl, 192.","DOI":"10.1088\/0067-0049\/192\/2\/18"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Hinshaw, G., Larson, D., Komatsu, E., Spergel, D.N., Bennett, C.L., Dunkley, J., Nolta, M.R., Halpern, M., Hill, R.S., and Odegard, N. (2013). Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results. Astrophys. J. Suppl, 208.","DOI":"10.1088\/0067-0049\/208\/2\/19"},{"key":"ref_7","unstructured":"Ade, P.A.R., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A.J., and Barreiro, R.B. (2014). Planck 2013 results. XVI. Cosmological parameters. Astron. Astrophys, 571."},{"key":"ref_8","unstructured":"Ade, P.A.R., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A.J., and Barreiro, R.B. (2014). Planck 2013 results. XXII. Constraints on inflation. Astron. Astrophys, 571."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0370-2693(83)90837-7","article-title":"Chaotic Inflation","volume":"129","author":"Linde","year":"1983","journal-title":"Phys. Lett. B"},{"key":"ref_10","unstructured":"Linde, A. arXiv:1402.0526, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1402.0526."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gorbunov, D.S., and Rubakov, V.A. (2011). Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory, World Scientific.","DOI":"10.1142\/9789814322232"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.physrep.2011.04.001","article-title":"Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models","volume":"505","author":"Nojiri","year":"2011","journal-title":"Phys. Rep"},{"key":"ref_13","first-page":"115","article-title":"Introduction to modified gravity and gravitational alternative for dark energy","volume":"4","author":"Nojiri","year":"2007","journal-title":"ECONF"},{"key":"ref_14","unstructured":"Bamba, K., Nojiri, S., and Odintsov, S.D. arXiv:1302.4831, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1302.4831."},{"key":"ref_15","unstructured":"Bamba, K., and Odintsov, S.D. arXiv:1402.7114, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1402.7114."},{"key":"ref_16","unstructured":"Capozziello, S., and Faraoni, V. (2010). Beyond Einstein Gravity, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.physrep.2011.09.003","article-title":"Extended Theories of Gravity","volume":"509","author":"Capozziello","year":"2011","journal-title":"Phys. Rep"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.3390\/e14091717","article-title":"Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modified gravity theories","volume":"14","year":"2012","journal-title":"Entropy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10509-012-1181-8","article-title":"Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests","volume":"342","author":"Bamba","year":"2012","journal-title":"Astrophys. Space Sci"},{"key":"ref_20","unstructured":"Joyce, A., Jain, B., Khoury, J., and Trodden, M. arXiv:1407.0059, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1407.0059."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0370-2693(80)90670-X","article-title":"New Type of Isotropic Cosmological Models Without Singularity","volume":"91","author":"Starobinsky","year":"1980","journal-title":"Phys. Lett. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1103\/PhysRevD.32.2511","article-title":"Classical and Quantum Cosmology of the Starobinsky Inflationary Model","volume":"32","author":"Vilenkin","year":"1985","journal-title":"Phys. Rev. D"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.physletb.2010.12.035","article-title":"Screening of cosmological constant in non-local gravity","volume":"696","author":"Nojiri","year":"2011","journal-title":"Phys. Lett. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1007\/s10714-012-1342-7","article-title":"Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities","volume":"44","author":"Bamba","year":"2012","journal-title":"Gen. Rel. Grav"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, Y.L., and Sasaki, M. (2012). Screening of cosmological constant in non-local cosmology. Int. J. Mod. Phys. D, 21.","DOI":"10.1142\/S021827181250006X"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Sebastiani, L., Cognola, G., Myrzakulov, R., Odintsov, S.D., and Zerbini, S. (2014). Nearly Starobinsky inflation from modified gravity. Phys. Rev. D, 89.","DOI":"10.1103\/PhysRevD.89.023518"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bamba, K., Myrzakulov, R., Odintsov, S.D., and Sebastiani, L. (2014). Trace-anomaly driven inflation in modified gravity and the BICEP2 result. Phys. Rev. D, 90.","DOI":"10.1103\/PhysRevD.90.043505"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Amor\u00f3s, J., de Haro, J., and Odintsov, S.D. (2014). R + \u03b1R2 Loop Quantum Cosmology. Phys. Rev. D, 89.","DOI":"10.1103\/PhysRevD.89.104010"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5227","DOI":"10.1103\/PhysRevLett.86.5227","article-title":"Absence of singularity in loop quantum cosmology","volume":"86","author":"Bojowald","year":"2001","journal-title":"Phys. Rev. Lett"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Bojowald, M. (2002). Inflation from quantum geometry. Phys. Rev. Lett, 89.","DOI":"10.1103\/PhysRevLett.89.261301"},{"key":"ref_31","first-page":"135","article-title":"An Introduction to Loop Quantum Gravity Through Cosmology","volume":"122","author":"Ashtekar","year":"2007","journal-title":"Nuovo Cim. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1088\/0264-9381\/23\/2\/008","article-title":"Quantum geometry and the Schwarzschild singularity","volume":"23","author":"Ashtekar","year":"2006","journal-title":"Class. Quant. Grav"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ashtekar, A., Corichi, A., and Singh, P. (2008). Robustness of key features of loop quantum cosmology. Phys. Rev. D, 77.","DOI":"10.1103\/PhysRevD.77.024046"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/978-3-540-45230-0_3","article-title":"Lectures on loop quantum gravity","volume":"631","author":"Thiemann","year":"2003","journal-title":"Lect. Notes Phys"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"233","DOI":"10.4310\/ATMP.2003.v7.n2.a2","article-title":"Mathematical structure of loop quantum cosmology","volume":"7","author":"Ashtekar","year":"2003","journal-title":"Adv. Theor. Math. Phys"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Bojowald, M. (2005). Loop quantum cosmology. Living Rev. Relativ, 8.","DOI":"10.12942\/lrr-2005-11"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Thiemann, T. (2007). Modern Canonical Quantum General Relativity, Cambridge University Press.","DOI":"10.1017\/CBO9780511755682"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Bojowald, M. (2008). Loop quantum cosmology. Living Rev. Relativ, 11.","DOI":"10.12942\/lrr-2008-4"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ashtekar, A., and Singh, P. (2011). Loop Quantum Cosmology: A Status Report. Class. Quant. Grav, 28.","DOI":"10.1088\/0264-9381\/28\/21\/213001"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Bojowald, M. (2012). Quantum Cosmology: Effective Theory. Class. Quant. Grav, 29.","DOI":"10.1088\/0264-9381\/29\/21\/213001"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Odintsov, S.D., and Oikonomou, V.K. (2014). Matter Bounce Loop Quantum Cosmology from F(R) Gravity. Phys. Rev. D, 90.","DOI":"10.1103\/PhysRevD.90.064047"},{"key":"ref_42","unstructured":"Odintsov, S.D., Oikonomou, V.K., and Saridakis, E.N. arXiv:1501.06591, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1501.06591."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Bamba, K., Geng, C.Q., Nojiri, S., and Odintsov, S.D. (2009). Crossing of the phantom divide in modified gravity. Phys. Rev. D, 79.","DOI":"10.1103\/PhysRevD.79.083014"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3159","DOI":"10.1103\/PhysRevD.39.3159","article-title":"Towards the Einstein-Hilbert Action via Conformal Transformation","volume":"39","author":"Maeda","year":"1989","journal-title":"Phys. Rev. D"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Fujii, Y., and Maeda, K.I. (2003). The Scalar-Tensor Theory of Gravitation, Cambridge University Press.","DOI":"10.1017\/CBO9780511535093"},{"key":"ref_46","first-page":"532","article-title":"Quantum Fluctuation and Nonsingular Universe","volume":"33","author":"Mukhanov","year":"1981","journal-title":"JETP Lett"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Liddle, A.R., and Lyth, D.H. (2000). Cosmological Inflation and Large-Scale Structure, Cambridge University Press.","DOI":"10.1017\/CBO9781139175180"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1103\/RevModPhys.69.373","article-title":"Reconstructing the inflation potential: An overview","volume":"69","author":"Lidsey","year":"1997","journal-title":"Rev. Mod. Phys"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Sebastiani, L., and Zerbini, S. A. (2008). Class of viable modified f(R) gravities describing inflation and the onset of accelerated expansion. Phys. Rev. D, 77.","DOI":"10.1103\/PhysRevD.77.046009"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Linder, E.V. (2009). Exponential Gravity. Phys. Rev. D, 80.","DOI":"10.1103\/PhysRevD.80.123528"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Elizalde, E., Nojiri, S., Odintsov, S.D., Sebastiani, L., and Zerbini, S. (2011). Non-singular exponential gravity: A simple theory for early- and late-time accelerated expansion. Phys. Rev. D, 83.","DOI":"10.1103\/PhysRevD.83.086006"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2467","DOI":"10.1007\/s10714-013-1597-7","article-title":"An Exponential F(R) Dark Energy Model","volume":"45","author":"Oikonomou","year":"2013","journal-title":"Gen. Rel. Grav"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.physletb.2014.09.014","article-title":"Reconstruction of scalar field theories realizing inflation consistent with the Planck and BICEP2 results","volume":"737","author":"Bamba","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Bamba, K., Nojiri, S., Odintsov, S.D., and S\u00e1ez-G\u00f3mez, D. (2014). Inflationary universe from perfect fluid and F(R) gravity and its comparison with observational data. Phys. Rev. D, 90.","DOI":"10.1103\/PhysRevD.90.124061"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Bamba, K., Cognola, G., Odintsov, S.D., and Zerbini, S. (2014). One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result. Phys. Rev. D, 90.","DOI":"10.1103\/PhysRevD.90.023525"},{"key":"ref_56","unstructured":"Cognola, G., Elizalde, E., and Zerbini, S. arXiv:1408.1766, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1408.1766."},{"key":"ref_57","unstructured":"Rinaldi, M., Cognola, G., Vanzo, L., and Zerbini, S. arXiv:1410.0631, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1410.0631."},{"key":"ref_58","unstructured":"Ade, P.A.R., Aghanim, N., Alina, D., Alves, M.I.R., Armitage-Caplan, C., Arnaud, M., Arzoumanian, D., Ashdown, M., Atrio-Barandela, F., and Aumont, J. arXiv:1405.0871, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1405.0871."},{"key":"ref_59","unstructured":"Ade, P.A.R., Alves, M.I.R., Aniano, G., Armitage-Caplan, C., Arnaud, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A.J., and Barreiro, R.B. Planck intermediate results. XXII. Frequency dependence of thermal emission from Galactic dust in intensity and polarization. arXiv:1405.0874, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1405.0874."},{"key":"ref_60","unstructured":"Adam, R., Ade, P.A.R., Aghanim, N., Arnaud, M., Aumont, J., Baccigalupi, C., Banday, A.J., Barreiro, R.B., Bartlett, J.G., and Bartolo, N. arXiv:1409.5738, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1409.5738."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Mortonson, M.J., and Seljak, U. (2014). A joint analysis of Planck and BICEP2 B modes including dust polarization uncertainty. JCAP, 1410.","DOI":"10.1088\/1475-7516\/2014\/10\/035"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Kamionkowski, M., and Kovetz, E.D. (2014). Statistical diagnostics to identify Galactic foregrounds in B-mode maps. Phys. Rev. Lett, 113.","DOI":"10.1103\/PhysRevLett.113.191303"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"2034","DOI":"10.1093\/mnras\/stu2547","article-title":"Genus Topology and Cross-Correlation of BICEP2 and Planck 353 GHz B-Modes: Further Evidence Favoring Gravity Wave Detection","volume":"447","author":"Colley","year":"2015","journal-title":"Mon. Not. Roy. Astron. Soc"},{"key":"ref_64","unstructured":"Ade, P.A.R., Aghanim, N., Ahmed, Z., Aikin, R.W., Alexander, K.D., Arnaud, M., Aumont, J., Baccigalupi, C., Banday, A.J., and Barkats, D. arXiv:1502.00612, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1502.00612."},{"key":"ref_65","unstructured":"Motohashi, H. arXiv:1411.2972, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1411.2972."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Prokopec, T., and Weenink, J. (2012). Uniqueness of the gauge invariant action for cosmological perturbations. JCAP, 1212.","DOI":"10.1088\/1475-7516\/2012\/12\/031"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"George, D.P., Mooij, S., and Postma, M. (2014). Quantum corrections in Higgs inflation: The real scalar case. JCAP, 1402.","DOI":"10.1088\/1475-7516\/2014\/02\/024"},{"key":"ref_68","unstructured":"Kaiser, D.I. arXiv:astro-ph\/9507048, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/astro-ph\/9507048."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.physletb.2009.09.045","article-title":"Cosmological reconstruction of realistic modified F(R) gravities","volume":"681","author":"Nojiri","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Nojiri, S., and Odintsov, S.D. (2006). Modified f(R) gravity consistent with realistic cosmology: From matter dominated epoch to dark energy universe. Phys. Rev. D, 74.","DOI":"10.1103\/PhysRevD.74.086009"},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Nojiri, S., and Odintsov, S.D. (2007). Modified gravity and its reconstruction from the universe expansion history. J. Phys. Conf. Ser, 66.","DOI":"10.1088\/1742-6596\/66\/1\/012005"},{"key":"ref_72","first-page":"207","article-title":"Cyclic, ekpyrotic and little rip universe in modified gravity","volume":"1458","author":"Nojiri","year":"2011","journal-title":"J. Phys. Conf. Ser"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"De la Cruz-Dombriz, A., and Dobado, A. (2006). f(R) gravity without cosmological constant. Phys. Rev. D, 74.","DOI":"10.1103\/PhysRevD.74.087501"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.physletb.2014.02.041","article-title":"Trace-anomaly driven inflation in f(T) gravity and in minimal massive bigravity","volume":"731","author":"Bamba","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0550-3213(76)90480-6","article-title":"Nonlocal Conformal Anomalies","volume":"111","author":"Deser","year":"1976","journal-title":"Nucl. Phys. B"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/0550-3213(77)90410-2","article-title":"Observations on Conformal Anomalies","volume":"125","author":"Duff","year":"1977","journal-title":"Nucl. Phys. B"},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Birell, N.D., and Davies, P.C.W. (1982). Quantum Fields in Curved Space, Cambridge University Press.","DOI":"10.1017\/CBO9780511622632"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1088\/0264-9381\/11\/6\/004","article-title":"Twenty years of the Weyl anomaly","volume":"11","author":"Duff","year":"1994","journal-title":"Class. Quant. Grav"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/S0370-2693(98)01351-3","article-title":"Conformal anomaly for dilaton coupled theories from AdS\/CFT correspondence","volume":"444","author":"Nojiri","year":"1998","journal-title":"Phys. Lett. B"},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Hawking, S.W., Hertog, T., and Reall, H.S. (2001). Trace anomaly driven inflation. Phys. Rev. D, 63.","DOI":"10.1103\/PhysRevD.63.083504"},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Bamba, K., Geng, C.Q., and Lee, C.C. (2010). Cosmological evolution in exponential gravity. JCAP, 1008.","DOI":"10.1088\/1475-7516\/2010\/08\/021"},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Nojiri, S., Odintsov, S.D., and Tsujikawa, S. (2005). Properties of singularities in (phantom) dark energy universe. Phys. Rev. D, 71.","DOI":"10.1103\/PhysRevD.71.063004"},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Bamba, K., Nojiri, S., and Odintsov, S.D. (2008). The future of the universe in modified gravitational theories: Approaching a finite-time future singularity. JCAP, 10.","DOI":"10.1088\/1475-7516\/2008\/10\/045"},{"key":"ref_84","doi-asserted-by":"crossref","unstructured":"Bamba, K., de Haro, J., and Odintsov, S.D. (2013). Future Singularities and Teleparallelism in Loop Quantum Cosmology. JCAP, 1302.","DOI":"10.1088\/1475-7516\/2013\/02\/008"},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Amor\u00f3s, J., de Haro, J., and Odintsov, S.D. (2013). Bouncing loop quantum cosmology from F (T) gravity. Phys. Rev. D, 87.","DOI":"10.1103\/PhysRevD.87.104037"},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Haro, J., and Amor\u00f3s, J. (2014). Viability of the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology for general potentials. JCAP, 1412.","DOI":"10.1088\/1475-7516\/2014\/12\/031"},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"Zhang, X., and Ma, Y. (2011). Extension of loop quantum gravity to f(R) theories. Phys. Rev. Lett, 106.","DOI":"10.1103\/PhysRevLett.106.171301"},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Zhang, X., and Ma, Y. (2011). Loop quantum f(R) theories. Phys. Rev. D, 84.","DOI":"10.1103\/PhysRevD.84.104045"},{"key":"ref_89","first-page":"80","article-title":"Loop quantum modified gravity and its cosmological application","volume":"8","author":"Zhang","year":"2013","journal-title":"Front. Phys. China"},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Gupt, B., and Singh, P. (2012). Contrasting features of anisotropic loop quantum cosmologies: The Role of spatial curvature. Phys. Rev. D, 85.","DOI":"10.1103\/PhysRevD.85.044011"},{"key":"ref_91","doi-asserted-by":"crossref","unstructured":"Singh, P. (2009). Are loop quantum cosmos never singular?. Class. Quant. Grav, 26.","DOI":"10.1088\/0264-9381\/26\/12\/125005"},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Corichi, A., and Singh, P. (2008). Is loop quantization in cosmology unique?. Phys. Rev. D, 78.","DOI":"10.1103\/PhysRevD.78.024034"},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Ashtekar, A., Pawlowski, T., and Singh, P. (2006). Quantum Nature of the Big Bang: Improved dynamics. Phys. Rev. D, 74.","DOI":"10.1103\/PhysRevD.74.084003"},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Haro, J., and Elizalde, E. (2010). Loop cosmology: Regularization vs. quantization. Europhys. Lett, 89.","DOI":"10.1209\/0295-5075\/89\/69001"},{"key":"ref_95","doi-asserted-by":"crossref","unstructured":"Dzierzak, P., Malkiewicz, P., and Piechocki, W. (2009). Turning big bang into big bounce. 1. Classical dynamics. Phys. Rev. D, 80.","DOI":"10.1103\/PhysRevD.80.104001"},{"key":"ref_96","doi-asserted-by":"crossref","unstructured":"Bojowald, M. (2009). Consistent Loop Quantum Cosmology. Class. Quant. Grav, 26.","DOI":"10.1088\/0264-9381\/26\/7\/075020"},{"key":"ref_97","unstructured":"De Haro, J., and Amor\u00f3s, J. arXiv:1411.7611, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1411.7611."},{"key":"ref_98","unstructured":"Elizalde, E., Haro, J., and Odintsov, S.D. arXiv:1411.3475, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1411.3475."},{"key":"ref_99","doi-asserted-by":"crossref","unstructured":"De Haro, J., and Amor\u00f3s, J. (2014). Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data. JCAP, 1408.","DOI":"10.1088\/1475-7516\/2014\/08\/025"},{"key":"ref_100","unstructured":"Bamba, K., Makarenko, A.N., Myagky, A.N., and Odintsov, S.D. arXiv:1411.3852, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1411.3852."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.physletb.2014.04.004","article-title":"Bouncing cosmology in modified Gauss-Bonnet gravity","volume":"732","author":"Bamba","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_102","doi-asserted-by":"crossref","unstructured":"Bamba, K., Makarenko, A.N., Myagky, A.N., Nojiri, S., and Odintsov, S.D. (2014). Bounce cosmology from F(R) gravity and F(R) bigravity. JCAP, 1401.","DOI":"10.1088\/1475-7516\/2014\/01\/008"},{"key":"ref_103","doi-asserted-by":"crossref","unstructured":"Koehn, M., Lehners, J.L., and Ovrut, B.A. (2014). Cosmological super-bounce. Phys. Rev. D, 90.","DOI":"10.1103\/PhysRevD.90.025005"},{"key":"ref_104","doi-asserted-by":"crossref","unstructured":"Cai, Y.F., Easson, D.A., and Brandenberger, R. (2012). Towards a Nonsingular Bouncing Cosmology. JCAP, 1208.","DOI":"10.1088\/1475-7516\/2012\/08\/020"},{"key":"ref_105","doi-asserted-by":"crossref","unstructured":"Khoury, J., Ovrut, B.A., Steinhardt, P.J., and Turok, N. (2001). The Ekpyrotic universe: Colliding branes and the origin of the hot big bang. Phys. Rev. D, 64.","DOI":"10.1103\/PhysRevD.64.123522"},{"key":"ref_106","unstructured":"Myrzakulov, R., Odintsov, S.D., and Sebastiani, L. arXiv:1412.1073, arXiv.org e-Print archive. Available online: http:\/\/arxiv.org\/abs\/1412.1073."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/7\/1\/220\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:43:15Z","timestamp":1760215395000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/7\/1\/220"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,9]]},"references-count":106,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,3]]}},"alternative-id":["sym7010220"],"URL":"https:\/\/doi.org\/10.3390\/sym7010220","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,9]]}}}