Abstract
Not long ago, a novel gravitational scheme i.e, \(4D-EGB\) (Einstein-Gauss-Bonnet) gravity have been proposed by Glavan and Lin 2020. They rescaled the coupling factor \(\alpha \) with \(\frac{\alpha }{D-4}\) and developed the field equations. The purpose of this paper is to workout the cosmic bounce with a cubic form of scale factor and workout the bouncing scenario under these assumptions. The flat FLRW metric is used along with the perfect fluid to study the energy conditions. The conditions are scrutinized by using different coupling factors \(\alpha \) and cosmological constant \(\Lambda \) values. The stability of the assumed scale factor model is in evidence of universal expansion and allows the universal bounce by developing the validations of energy conditions.
Similar content being viewed by others
References
Glavan, D., Lin, C.: Einstein- Gauss- Bonnet gravity in four-dimensional spacetime. Phys. Rev. Lett. 124(8), 081301 (2020)
Smolin, L.: Time reborn: From the crisis in physics to the future of the universe. HMH (2013)
Davies, P.: The Goldilocks enigma: Why is the universe just right for life?. HMH (2008)
Toulmin, S. E. and Toulmin, S.: The return to cosmology: Postmodern science and the theology of nature. Univ of California Press (1985)
Gribbin, J.: Stephen Hawking. Simon and Schuster (2016)
Hubble, E.P.: The observational approach to cosmology, vol. 30. Clarendon Press, Oxford (1937)
Kirshner, R.P.: Hubble’s diagram and cosmic expansion. Proc. Natl. Acad. Sci. 101(1), 8–13 (2004)
Maurya, S.K., Gupta, Y.K., Dayanandan, B., Ray, S.: A new model for spherically symmetric anisotropic compact star. Eur. Phys. J. C. 76, 1–9 (2016)
Capozziello, S., De Laurentis, M.: Extended theories of gravity. Phys. Rep. 509(4–5), 167–321 (2011)
Dolgov, A.D., Kawasaki, M.: Can modified gravity explain accelerated cosmic expansion? Phys. Lett. B 573, 1–4 (2003)
Baade, W., Zwicky, F.: Cosmic rays from super-novae. Proc. Natl. Acad. Sci. 20(5), 259–263 (1934)
Yousaf, Z., Bhatti, M.Z., Asad, H.: Gravastars in \(f(R, T, R_{\mu \nu }T^{\mu \nu })\) gravity. Phys. Dark Universe 28, 100527 (2020)
Yousaf, Z., Bhatti, M.Z., Aman, H., Sahoo, P.K.: Non-singular bouncing model in energy momentum squared gravity. Phys. Scr. 98, 035002 (2023)
Tomozawa, Y.: Quantum corrections to gravity. arXiv:1107.1424 (2011)
Cognola, G.., Myrzakulov, R.., Sebastiani, L.., Zerbini, S..: Einstein gravity with Gauss-Bonnet entropic corrections. Phys. Rev. D 88(2), 024006 (2013)
Fernandes, P.G.S.: Charged black holes in Ad S spaces in 4 D Einstein Gauss- Bonnet gravity. Phys. Lett. B 805, 135468 (2020)
Doneva, D.D., Yazadjiev, S.S.: Relativistic stars in 4 D Einstein- Gauss- Bonnet gravity. J. Cosmol. Astropart. Phys. 05, 024 (2021)
Konoplya, R.A., Zhidenko, A.: (in) stability of black holes in the 4 D Einstein- Gauss - Bonnet and Einstein- Lovelock gravities. Phys. Dark Universe 30, 100697 (2020)
Zhang, C.-Y., Li, P.-C., Guo, M.: Greybody factor and power spectra of the hawking radiation in the 4 D Einstein–Gauss–Bonnet de-Sitter gravity. Eur. Phys. J. C 80(9), 874 (2020)
Singh, D.V., Ghosh, S.G., Maharaj, S.D.: Clouds of strings in 4 D Einstein- Gauss- Bonnet black holes. Phys. Dark Universe 30, 100730 (2020)
Churilova, M.S.: Quasinormal modes of the Dirac field in the consistent 4 D Einstein- Gauss- Bonnet gravity. Phys. Dark Universe 31, 100748 (2021)
Mishra, A.K.: Quasinormal modes and strong cosmic censorship in the regularised 4D Einstein–Gauss–Bonnet gravity. Gen. Relativ. Gravit 52(11), 106 (2020)
Islam, S.U., Kumar, R., Ghosh, S.G.: Gravitational lensing by black holes in the 4D Einstein-Gauss-Bonnet gravity. J. Cosmol. Astropart. Phys. 2020(09), 030 (2020)
Ai, W.-Y.: A note on the novel 4D Einstein–Gauss–Bonnet gravity. Commun. Theor. Phys 72(9), 095402 (2020)
Matarrese, S., Colpi, M., Gorini, V. and Moschella, U.: Dark Matter and Dark Energy: A challenge for modern cosmology, vol. 370. Springer Science & Business Media (2011)
Myrzakulov, R.: FRW cosmology in f (R, T) gravity. Eur. Phys. J. C 72(11), 2203 (2012)
Padmanabhan, T.: Cosmological constant-the weight of the vacuum. Phys. Rep. 380(5–6), 235–320 (2003)
Del Popolo, A.: Dark matter, density perturbations, and structure formation. Astron. Rep. 51(3), 169–196 (2007)
Capozziello, S., Francaviglia, M.: Extended theories of gravity and their cosmological and astrophysical applications. Gen. Relativ. Gravit. 40, 357–420 (2008)
Kolb, E.W.: and Turner. The early universe. C R C press, M. S. (2018)
Odintsov, S.D., Paul, T., Banerjee, I., Myrzakulov, R., SenGupta, S.: Unifying an asymmetric bounce to the dark energy in chern-simons f( R) gravity. Phys. Dark Universe 33, 100864 (2021)
Cai, Y.-F.: Exploring bouncing cosmologies with cosmological surveys. Sci. China: Phys. Mech. Astron. 57, 1414–1430 (2014)
Elizalde, E., Odintsov, S.D., Oikonomou, V.K., Paul, T.: Extended matter bounce scenario in ghost free f ( R, G) gravity compatible with GW170817. Nuc. Phys. B 954, 114984 (2020)
Hoyle, F., Burbidge, G. and Narlikar, J. V.: A different approach to cosmology: from a static universe through the big bang towards reality. Cambridge University Press (2000)
Nojiri, S., Odintsov, S.D., Paul, T.: Towards a smooth unification from an ekpyrotic bounce to the dark energy era. Phys. Dark Universe 35, 100984 (2022)
Agrawal, A. S., Chakraborty, S., Mishra, B., Dutta, J. and Khyllep, W.: “Global phase space analysis for a class of single scalar field bouncing solutions in general relativity,” arXiv:2212.10272 (2022)
Ijjas, A., Steinhardt, P.J.: Classically stable nonsingular cosmological bounces. Phys. Rev. Lett. 117(12), 121304 (2016)
Ijjas, A., Steinhardt, P.J., Loeb, A.: Inflationary paradigm in trouble after Planck 2013. Phys. Lett. B 723(4–5), 261–266 (2013)
Ijjas, A., Steinhardt, P.J.: A new kind of cyclic universe. Phys. Lett. B 795, 666–672 (2019)
Zhu, M. and Cai, Y. Parity-violation in bouncing cosmology. arXiv:2301.13502 (2023)
Cai, Y.-F., Easson, D.A., Brandenberger, R.: Towards a nonsingular bouncing cosmology. J. Cosmol. Astropart. Phys. 2012(08), 020 (2012)
Cai, Y.-F., Quintin, J., Saridakis, E.N., Wilson-Ewing, E.: Nonsingular bouncing cosmologies in light of BICEP2. J. Cosmol. Astropart. Phys. 2014(07), 033 (2014)
Cai, Y.-F. and Saridakis, E. N.: Non-singular cyclic cosmology without phantom menace. arXiv:1108.6052 (2011)
Cai, Y.-F., McDonough, E., Duplessis, F., Brandenberger, R.H.: Two field matter bounce cosmology. J. Cosmol. Astropart. Phys 2013(10), 024 (2013)
Agrawal, A., Tripathy, S.K., Pal, S., Mishra, B.: Role of extended gravity theory in matter bounce dynamics. Phys. Scr. 97(2), 025002 (2022)
Odintsov, S.D., Paul, T.: Bounce universe with finite-time singularity. Universe 8(5), 292 (2022)
Nojiri, S., Odintsov, S.D., Oikonomou, V.K., Paul, T.: Nonsingular bounce cosmology from lagrange multiplier F (R) gravity. Phys. Rev. D 100(8), 084056 (2019)
Curiel, E.: The analysis of singular spacetimes. Philos. Sci. 66, S119–S145 (1999)
Shamir, M.F.: Bouncing cosmology in gravity with logarithmic trace term. Adv. Astron. 2021, 8852581 (2021)
Yousaf, Z., Bhatti, M.Z., Aman, H.: Cosmic bounce with \(\alpha (e^{-\beta {G}}- 1)+ 2\lambda \) T model. Phys. Scr. 97(5), 055306 (2022)
Konoplya, R.A., Zinhailo, A.F.: Quasinormal modes, stability and shadows of a black hole in the 4 D Einstein- Gauss- Bonnet gravity. Eur. Phys. J. C 80, 1–13 (2020)
Mansoori, S.A.H.: Thermodynamic geometry of the novel 4- D Gauss- Bonnet Ad S black hole. Phys. Dark Universe 31, 100776 (2021)
Bonifacio, J., Hinterbichler, K., Johnson, L.A.: Amplitudes and 4D Gauss-Bonnet Theory. Phys. Rev. D 102(2), 024029 (2020)
Ghosh, S.G., Kumar, R.: Generating black holes in 4 D Einstein- Gauss- Bonnet gravity. Class. Quantum Grav. 37, 245008 (2020)
Wei, S.-W., Liu, Y.-X.: Extended thermodynamics and microstructures of four-dimensional charged Gauss- Bonnet black hole inAds space. Phys. Rev. D 101, 104018 (2020)
Zubair, M., Farooq, M.: Bouncing behaviours in four dimensional einstein Gauss- Bonnet gravity with cosmography and observational constraints. Eur. Phys. J. Plus 138, 173 (2023)
Easson, D.A., Manton, T., Svesko, A.: \(d\rightarrow 4\) Einstein- Gauss- Bonnet gravity and beyond. J. Cosmol. Astropart. Phys. 10, 026 (2020)
Van Acoleyen, K., Van Doorsselaere, J.: Galileons from lovelock actions. Phys. Rev. D 83(8), 084025 (2011)
Bueno, P., Cano, P.A., Ramírez, P.F., et al.: f (lovelock) theories of gravity. J. High Energy Phys. 2016(4), 1–40 (2016)
Lovelock, D.: The einstein tensor and its generalizations. J. Math. Phys. 12(3), 498–501 (1971)
A. S. Agrawal, B. Mishra, and P. K. Agrawal, Matter bounce scenario in extended symmetric teleparallel gravity. arXiv:2206.02783 (2022)
Odintsov, S.D., Paul, T.: A non-singular generalized entropy and its implications on bounce cosmology. Phys. Dark Universe 39, 101159 (2023)
K. Bamba, A. N. Makarenko, A. N. Myagky, S. Nojiri, and S. D. Odintsov, “Bounce cosmology from f (R) gravity and f (R) bigravity,” J. Cosmol. Astropart. Phys., vol. 2014(01) 008 (2014)
Singh, J. K., Bamba, K. , et al.: Bouncing universe in Gauss-Bonnet gravity. arXiv e-prints, arXiv–2204 (2022)
Yousaf, Z., Bhatti, M.Z., Aman, H.: The bouncing cosmic behavior with logarithmic law \(f ( {G, T})\) model. Chin. J. Phys. 79, 275–286 (2022)
Ford, L.H., Roman, T.A.: Averaged energy conditions and quantum inequalities. Phys. Rev. D 51(8), 4277 (1995)
Visser, M., Kar, S., Dadhich, N.: Traversable wormholes with arbitrarily small energy condition violations. Phys. Rev. Lett. 90(20), 201102 (2003)
Creminelli, P., Luty, M.A., Nicolis, A., Senatore, L.: Starting the universe: stable violation of the null energy condition and non-standard cosmologies. J. High Energy Phys. 2006(12), 080 (2006)
Santos, J., Alcaniz, J.S., Reboucas, M.J., Carvalho, F.C.: Energy conditions in f (R) gravity. Phys. Rev. D 76(8), 083513 (2007)
O. Galkina, J. C. Fabris, F. T. Falciano, and N. Pinto-Neto: Regular bouncing solutions, energy conditions, and the brans “dicke theory”, J E T P Letters, 110(8), 523–528 (2019)
Giovannini, M.: Averaged energy conditions and bouncing universes. Phys. Rev. D 96(10), 101302 (2017)
Capozziello, S., Lobo, F.S.N., Mimoso, J.P.: Generalized energy conditions in extended theories of gravity. Phys. Rev. D 91(12), 124019 (2015)
Cattoen, C., Visser, M.: Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities and extremality events, Class. Quantum Gravity 22(23), 4913 (2005)
Martin, J., Peter, P.: On the “causality argument” in bouncing cosmologies. Phys. Rev. Lett. 92(6),(2004)
Pinto-Neto, N., Fabris, J.C., Toniato, J.D., Vicente, G.S., Vitenti, S.D.: Vector perturbations in bouncing cosmology. Phys. Rev. D 101(12), 123519 (2020)
Coussaert, O., Henneaux, M., van Driel, P.: The asymptotic dynamics of three-dimensional einstein gravity with a negative cosmological constant. Class. Quantum Gravity 12(12), 2961 (1995)
Biswas, T., Mazumdar, A.: Inflation with a negative cosmological constant. Phys. Rev. D 80(2), 023519 (2009)
Sahni, V., Starobinsky, A.: The case for a positive cosmological \( {L}ambda\)-term. Int. J. Mod. Phys. D 9(04), 373–443 (2000)
Fernandes, P.G.S., Carrilho, P., Clifton, T., Mulryne, D.J.: The 4 D Einstein- Gauss- Bonnet theory of gravity: a review. Class, Quantum Gravity (2022)
Singh, J.K., Bamba, K., Nagpal, R., Pacif, S.K.J.: Bouncing cosmology in f( R, T) gravity. Phys. Rev. D 97(12), 123536 (2018)
Cai, Y.-F., Qiu, T., Zhang, X., Piao, Y.-S., Li, M.: Bouncing universe with quintom matter. J. High Energy Phys. 2007, 071 (2007)
Cai, Y.-F., Qiu, T., Brandenberger, R., Zhang, X.: Nonsingular cosmology with a scale-invariant spectrum of cosmological perturbations from Lee-Wick theory. Phys. l Rev. D 80(2), 023511 (2009)
Agrawal, A.S., Tello-Ortiz, F., Mishra, B., Tripathy, S.K.: Bouncing cosmology in extended gravity and its reconstruction as dark energy model. Fortschr. Phys. 70(1), 2100065 (2022)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix A
For the flat FLRW metric (3), the non vanishing Christoffel symbols for this study are obtained as
here, \(\delta \) shows the Kronecker symbol. The non vanishing Ricci tensor components are
The Ricci scalar turns out to be
Hence the Einstein tensor becomes
Here, \(i,j=1,2,3,...,D-1\). The mathematical forms of are as follows
Appendix B
The energy conditions plots.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Yousaf, Z., Bhatti, M.Z., Aman, H. et al. Bouncing Cosmology with 4D-EGB Gravity. Int J Theor Phys 62, 155 (2023). https://doi.org/10.1007/s10773-023-05409-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10773-023-05409-6