Abstract
Inflationary era of our Universe can be characterized as semi-classical because it can be described in the context of four-dimensional Einstein’s gravity involving quantum corrections. These string motivated corrections originate from quantum theories of gravity such as superstring theories and include higher gravitational terms as, Gauss–Bonnet and Chern–Simons terms. In this paper we investigated inflationary phenomenology coming from a scalar field, with quadratic curvature terms in the view of GW170817. Firstly, we derived the equations of motion, directly from the gravitational action. As a result, formed a system of differential equations with respect to Hubble’s parameter and the inflaton field which was very complicated and cannot be solved analytically, even in the minimal coupling case. Based on the observations from GW170817 event, which have shown that the speed of the primordial gravitational wave is equal to the speed of light, \(c_{\mathcal {T}}^2=1\) in natural units, our equations of motion where simplified after applying the constraint \(c_{\mathcal {T}}^2=1\), the slow-roll approximations and neglecting the string corrections. We described the dynamics of inflationary phenomenology and proved that theories with Gauss–Bonnet term can be compatible with recent observations. Also, the Chern–Simons term leads to asymmetric generation and evolution of the two circular polarization states of gravitational wave. Finally, viable inflationary models are presented, consistent with the observational constraints. The possibility of a blue tilted tensor spectral index is briefly investigated.
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Nojiri, S., Odintsov, S.D., Oikonomou, V.K.: Phys. Rep. 692, 1–104 (2017). https://doi.org/10.1016/j.physrep.2017.06.001
Capozziello, S., Laurentis, M.De: Phys. Rep. 509, 167–321 (2011). https://doi.org/10.1016/j.physrep.2011.09.003
Faraoni, V., Capozziello, S.: https://doi.org/10.1007/978-94-007-0165-6
Nojiri ,S., Odintsov,S. D.: eConf C0602061 (2006), 06 https://doi.org/10.1142/S0219887807001928[arXiv:hep-th/0601213 [hep-th]]
Nojiri, S., Odintsov, D.: Phys. Rep. 505, 59–144 (2011). https://doi.org/10.1016/j.physrep.2011.04.001
Olmo, G.J.: Int. J. Mod. Phys. D 20, 413–462 (2011). https://doi.org/10.1142/S0218271811018925
Kanti, P., Gannouji, R., Dadhich, N.: Phys. Rev. D 92(4), 041302 (2015). https://doi.org/10.1103/PhysRevD.92.041302
Yi, Z., Gong, Y., Sabir, M.: Phys. Rev. D 98(8), 083521 (2018). https://doi.org/10.1103/PhysRevD.98.083521
Guo, Z.K., Schwarz, D.J.: Phys. Rev. D 81, 123520 (2010). https://doi.org/10.1103/PhysRevD.81.123520
Jiang, P.X., Hu, J.W., Guo, Z.K.: Phys. Rev. D 88, 123508 (2013). https://doi.org/10.1103/PhysRevD.88.123508
Guo, Z.K., Schwarz, D.J.: Phys. Rev. D 80, 063523 (2009). https://doi.org/10.1103/PhysRevD.80.063523
De Laurentis, M., Paolella, M., Capozziello, S.: Phys. Rev. D 91(8), 083531 (2015). https://doi.org/10.1103/PhysRevD.91.083531
Fomin, I.: Eur. Phys. J. C 80(12), 1145 (2020). https://doi.org/10.1140/epjc/s10052-020-08718-w
Pozdeeva, E.O., Gangopadhyay, M.R., Sami, M., Toporensky, A.V., Vernov, S.Y.: Phys. Rev. D 102(4), 043525 (2020). https://doi.org/10.1103/PhysRevD.102.043525
Yi, Z., Gong, Y.: Universe 5(9), 200 (2019). https://doi.org/10.3390/universe5090200
van de Bruck, C., Dimopoulos, K., Longden, C.: Phys. Rev. D 94(2), 023506 (2016). https://doi.org/10.1103/PhysRevD.94.023506
Odintsov, S.D., Oikonomou, V.K.: Phys. Rev. D 98(4), 044039 (2018). https://doi.org/10.1103/PhysRevD.98.044039
Nozari, K., Rashidi, N.: Phys. Rev. D 95(12), 123518 (2017). https://doi.org/10.1103/PhysRevD.95.123518
Chakraborty, S., Paul, T., SenGupta, S.: Phys. Rev. D 98(8), 083539 (2018). https://doi.org/10.1103/PhysRevD.98.083539
Kawai, S., Soda, J.: Phys. Lett. B 460, 41–46 (1999). https://doi.org/10.1016/S0370-2693(99)00736-4
van de Bruck, C., Dimopoulos, K., Longden, C., Owen, C.: arXiv:1707.06839 [astro-ph.CO]
Bakopoulos, A., Kanti, P., Pappas, N.: Phys. Rev. D 101(8), 084059 (2020). https://doi.org/10.1103/PhysRevD.101.084059
Kleihaus, B., Kunz, J., Kanti, P.: Phys. Lett. B 804, 135401 (2020). https://doi.org/10.1016/j.physletb.2020.135401
Bakopoulos, A., Kanti, P., Pappas, N.: Phys. Rev. D 101(4), 044026 (2020). https://doi.org/10.1103/PhysRevD.101.044026
Kanti, P., Mavromatos, N.E., Rizos, J., Tamvakis, K., Winstanley, E.: Phys. Rev. D 54, 5049–5058 (1996). https://doi.org/10.1103/PhysRevD.54.5049
Bajardi, F., Dialektopoulos, K.F., Capozziello, S.: Symmetry 12(3), 372 (2020). https://doi.org/10.3390/sym12030372
Geng, C.Q., Lee, C.C., Sami, M., Saridakis, E.N., Starobinsky, A.A.: JCAP 06, 011 (2017). https://doi.org/10.1088/1475-7516/2017/06/011
Pozdeeva, E.O.: Universe 7(6), 181 (2021). https://doi.org/10.3390/universe7060181
Pozdeeva, E.O., Vernov, Y.: arXiv:2104.04995 [gr-qc]
Granda, L.N., Jimenez, D.F.: Eur. Phys. J. C 81(1), 10 (2021). https://doi.org/10.1140/epjc/s10052-020-08789-9
Aoki, K., Gorji, M.A., Mizuno, S., Mukohyama, S.: JCAP 01, 054 (2021). https://doi.org/10.1088/1475-7516/2021/01/054
Rashidi, N., Nozari, K.: Astrophys. J. 890, 58 https://doi.org/10.3847/1538-4357/ab6a10
Nojiri, S., Odintsov, S.D., Oikonomou, V.K., Popov, A.A.: Phys. Dark Univ. 28, 100514 (2020). https://doi.org/10.1016/j.dark.2020.100514
Nojiri, S., Odintsov, S.D., Oikonomou, V.K., Popov, A.A.: Phys. Rev. D 100(8), 084009 (2019). https://doi.org/10.1103/PhysRevD.100.084009
Odintsov, S.D., Oikonomou, V.K.: Phys. Rev. D 99(10), 104070 (2019). https://doi.org/10.1103/PhysRevD.99.104070
Odintsov, S.D., Oikonomou, V.K.: Phys. Rev. D 99(6), 064049 (2019). https://doi.org/10.1103/PhysRevD.99.064049
Alexander, S., Yunes, N.: Phys. Rep. 480, 1–55 (2009). https://doi.org/10.1016/j.physrep.2009.07.002
Qiao, J., Zhu, T., Zhao, W., Wang, A.: Phys. Rev. D 101(4), 043528 (2020). https://doi.org/10.1103/PhysRevD.101.043528
Nishizawa, A., Kobayashi, T.: Phys. Rev. D 98(12), 124018 (2018). https://doi.org/10.1103/PhysRevD.98.124018
Wagle, P., Yunes, N., Garfinkle, D., Bieri, L.: Class. Quant. Gravit. 36(11), 115004 (2019). https://doi.org/10.1088/1361-6382/ab0eed
Yagi, K., Yunes, N., Tanaka, T.: Phys. Rev. Lett. 109,251105 (2012) [erratum: Phys. Rev. Lett. 116(16), 169902 (2016); erratum: Phys. Rev. Lett. 124(2), 029901 (2020)]. https://doi.org/10.1103/PhysRevLett.116.169902
Yagi, K., Yunes, N., Tanaka, T.: Phys. Rev. D 86, 044037 (2012) [erratum: Phys. Rev. D 89 , 049902 (2014)] https://doi.org/10.1103/PhysRevD.86.044037
Molina, C., Pani, P., Cardoso, V., Gualtieri, L.: Phys. Rev. D 81, 124021 (2010). https://doi.org/10.1103/PhysRevD.81.124021
Izaurieta, F., Rodriguez, E., Minning, P., Salgado, P., Perez, A.: Phys. Lett. B 678, 213–217 (2009). https://doi.org/10.1016/j.physletb.2009.06.017
Smith, T.L., Erickcek, A.L., Caldwell, R.R., Kamionkowski, M.: Phys. Rev. D 77, 024015 (2008). https://doi.org/10.1103/PhysRevD.77.024015
Konno, K., Matsuyama, T., Tanda, S.: Prog. Theor. Phys. 122, 561–568 (2009). https://doi.org/10.1143/PTP.122.561
Sopuerta, C.F., Yunes, N.: Phys. Rev. D 80, 064006 (2009). https://doi.org/10.1103/PhysRevD.80.064006
Matschull, H.J.: Class. Quant. Grav. 16, 2599–2609 (1999). https://doi.org/10.1088/0264-9381/16/8/303
Haghani, Z., Harko, T., Shahidi, S.: Eur. Phys. J. C 77(8), 514 (2017). https://doi.org/10.1140/epjc/s10052-017-5078-0
Kawai, S., Kim, J.: Phys. Lett. B 789, 145–149 (2019). https://doi.org/10.1016/j.physletb.2018.12.019
Satoh, M., Kanno, S., Soda, J.: Phys. Rev. D 77, 023526 (2008). https://doi.org/10.1103/PhysRevD.77.023526
Nair, R., Perkins, S., Silva, H.O., Yunes, N.: Phys. Rev. Lett. 123(19), 191101 (2019). https://doi.org/10.1103/PhysRevLett.123.191101
Satoh, M., Soda, J.: JCAP 09, 019 (2008). https://doi.org/10.1088/1475-7516/2008/09/019
Satoh, M.: JCAP 11, 024 (2010). https://doi.org/10.1088/1475-7516/2010/11/024
Antoniadis, I., Rizos, J., Tamvakis, K.: Nucl. Phys. B 415, 497–514 (1994). https://doi.org/10.1016/0550-3213(94)90120-1
Abbott, B.P., et al.: Multi-messenger observations of a binary neutron star merger. Astrophys. J. 848(2), L12 (2017). https://doi.org/10.3847/2041-8213/aa91c9
Ezquiaga, J.M., Zumalacarregui, M.: Phys. Rev. Lett. 119(25), 251304 (2017). https://doi.org/10.1103/PhysRevLett.119.251304
Odintsov, S.D., Oikonomou, V.K., Fronimos, F.P.: Nucl. Phys. B 958, 115135 (2020). https://doi.org/10.1016/j.nuclphysb.2020.115135
Oikonomou, V.K., Fronimos, F.P.: Class. Quant. Grav. 38(3), 035013 (2021). https://doi.org/10.1088/1361-6382/abce47
Odintsov, S.D., Oikonomou, V.K., Fronimos, F.P.: Ann. Phys. 420, 168250 (2020). https://doi.org/10.1016/j.aop.2020.168250
Oikonomou, V.K., Fronimos, F.P.: EPL 131(3), 30001 (2020). https://doi.org/10.1209/0295-5075/131/30001
Odintsov, S.D., Oikonomou, V.K., Fronimos, F.P., Venikoudis, S.A.: Phys. Dark Univ. 30, 100718 (2020). https://doi.org/10.1016/j.dark.2020.100718
Oikonomou, V.K., Fronimos, F.P.: Eur. Phys. J. Plus 135(11), 917 (2020). https://doi.org/10.1140/epjp/s13360-020-00926-3
Venikoudis, S.A., Fronimos, F.P.: Eur. Phys. J. Plus 136(3), 308 (2021). https://doi.org/10.1140/epjp/s13360-021-01298-y
Akrami, Y., et al.: Planck. Astron. Astrophys. 641, A10 (2020). https://doi.org/10.1051/0004-6361/201833887
Hwang, J.C., Noh, H.: Phys. Rev. D 71, 063536 (2005). https://doi.org/10.1103/PhysRevD.71.063536
Karydas, S., Papantonopoulos, E., Saridakis, E.N.: arXiv:2102.08450 [gr-qc]
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Venikoudis, S.A., Fronimos, F.P. Inflation with Gauss–Bonnet and Chern–Simons higher-curvature-corrections in the view of GW170817. Gen Relativ Gravit 53, 75 (2021). https://doi.org/10.1007/s10714-021-02846-8
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DOI: https://doi.org/10.1007/s10714-021-02846-8