G.D. Manucharyan1, I.V. Fomin2

1, 2 Bauman Moscow State Technical University (Moscow, Russia)
1 Sternberg Astronomical Institute, Moscow State University (Moscow, Russia)
1 gdmanucharyan@bmstu.ru, 2 fomin_iv@bmstu.ru

At present there exist various modified theories of gravitation, the analytical solution of which is significantly complicated due to their nonlinear integro-differential forms. Thus there are no models allowing to extend the solutions obtained in the framework of GR to the cases of modified gravitation (in the considered case Einstein-Gauss-Bonnet gravitation) by means of the functional dependence on inflationary parameters and linear combination of the slow rolling parameters of the former.

The aim of this work is to find analytic solutions of the equations of cosmological dynamics in the framework of Einstein-Gauss-Bonnet (EGB) gravity, related to the solutions of the equations of background dynamics in the framework of GR, and to determine the parameters allowing their verification.

In the framework of the present work a new form of the connection of inflationary parameters between EGB gravity and the general theory of relativity (GTR) is presented, the functional dependences of cosmological parameters of EGB gravity through the parameters of GTR are expressed, taking into account the proposed form of connection. A specific model of cosmological inflation for the case of GR is considered, it is shown that the model is not verifiable by observational constraints.

It is shown that the proposed form of coupling allows to extend the solutions of the equations of cosmological dynamics of GR to the case of Einstein-Gauss-Bonnet gravitation, which in turn makes it possible to estimate quantum corrections to GR operating only with inflationary parameters of GR.

Manucharyan G.D., Fomin I.V. Analytical coupled solutions of the equations of cosmological dynamics in the framework of GR and Einstein-Gauss-Bonnet gravitation. Nonlinear World. 2024. V. 22. № 3. P. 81–90. DOI: https://doi.org/10.18127/ j20700970-202403-08 (In Russian)

1. Arun K., Gudennavar S. B., Sivaram C. Dark matter, dark energy, and alternate models: A review. Advances in Space Research. 2017. V. 60. № 1. P. 166–186.
2. Nojiri S., Odintsov S. D., Oikonomou V. K. Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution. Physics Reports. 2017. V. 692. P. 1–104.
3. Fernandes P. G. S. et al. The 4D Einstein–Gauss–Bonnet theory of gravity: a review. Classical and Quantum Gravity. 2022. V. 39. № 6. С. 063001.
4. Nojiri S., Odintsov S. D., Sasaki M. Gauss-Bonnet dark energy. Physical Review D. 2005. V. 71. № 12. P. 123509.
5. Fomin I. Gauss–Bonnet term corrections in scalar field cosmology. The European Physical Journal C. 2020. V. 80. № 12. P. 1145.
6. Chervon, Sergei, Igor Fomin, Valerian Yurov, and Artyom Yurov. Scalar field cosmology. V. 13. World Scientific, 2019.
7. Salopek D.S., Bond J.R. Nonlinear evolution of long wavelength metric fluctuations in inflationary models, Phys. Rev. D42. 1990. P. 3936–3962. DOI:10.1103/PhysRevD.42.3936.
8. Liddle A.R., Lyth D.H. COBE, gravitational waves, inflation and extended inflation, Phys. Lett. B291. 1992. P. 391–398. DOI:10.1016/ 0370-2693(92)91393-N, arXiv:astro-ph/9208007 [astro-ph].
9. Aghanim N., Akrami Y.,Ashdown M., Aumont J., Baccigalupi C., Ballardini M., Banday A., Barreiro R., Bartolo N., Basak S., et al. Planck 2018 results-VI. Cosmological parameters. Astronomy & Astrophysics. 2020. V. 641. P. A6.
10. Tristram M., Banday A.J., Górski K.M., Keskitalo R., Lawrence C., Andersen K.J., Barreiro R.B., Borrill J., Colombo L., Eriksen H., et al. Improved limits on the tensor-to-scalar ratio using BICEP and Planck data. Physical Review D. 2022. V. 105. № 8. P. 083524.
11. Koh S., Lee B. H., Tumurtushaa G. Reconstruction of the scalar field potential in inflationary models with a Gauss-Bonnet term. Physical Review D. 2017. V. 95. № 12. С. 123509.
12. Tristram M. et al. Improved limits on the tensor-to-scalar ratio using BICEP and Planck data. Physical Review D. 2022. V. 105. № 8. С. 083524.