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Exact inflationary solutions in exponential gravity

  • Joseph P. Johnson
  • Jose MathewEmail author
  • S. Shankaranarayanan
Research Article
  • 67 Downloads

Abstract

We consider a modified gravity model of the form \( f(R,\phi )=R e^{h(\phi )R} \), where the strong gravity corrections are taken to all orders and \(\phi \) is a self-interacting massless scalar field. We show that the conformal transformation of this model to Einstein frame leads to non-canonical kinetic term and negates the advantage of the Einstein frame. We obtain exact solutions for the background in the Jordan frame without performing conformal transformations and show that the model leads to inflation with exit. We obtain scalar and tensor power-spectrum in Jordan frame and show that the model leads to red-tilt. We discuss the implications of the same in the light of cosmological observations.

Keywords

Inflation \(f(R, \phi )\) gravity Exponential gravity Power spectrum 

Notes

Acknowledgements

We thank Debottam Nandi for fruitful discussions and suggestions. JM thank Prof. L. Sriramkumar for supporting him during his visit at IITM. JPJ is supported by CSIR Junior Research Fellowship, India and JM was supported by UGC Senior Research Fellowship, India. The work is supported by DST-Max Planck Partner Group on Gravity and Cosmology.

References

  1. 1.
    Lyth, D.H., Liddle, A.R.: Cosmological Inflation and Large-Scale Structure. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  2. 2.
    Linde, A.D.: Contemp. Concepts Phys. 5, 1 (1990). arXiv:hep-th/0503203 [hep-th]Google Scholar
  3. 3.
    Mukhanov, V.: Physical Foundations of Cosmology. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  4. 4.
    Weinberg, S.: Cosmology. Oxford University Press, Oxford (2008)zbMATHGoogle Scholar
  5. 5.
    Mukhanov, V.F., Feldman, H.A., Brandenberger, R.H.: Phys. Rep. 215, 203 (1992)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Donoghue, J.F.: Phys. Rev. Lett. 72, 2996 (1994). arXiv:gr-qc/9310024 [gr-qc]ADSCrossRefGoogle Scholar
  7. 7.
    Donoghue, J.: Recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories. In: Proceedings, 8th Marcel Grossmann Meeting, MG8, Jerusalem, Israel, June 22–27, 1997. Pts. A, B (1997) pp. 26–39. arXiv:gr-qc/9712070 [gr-qc]
  8. 8.
    Hamber, H.W., Liu, S.: Phys. Lett. B357, 51 (1995). arXiv:hep-th/9505182 [hep-th]ADSCrossRefGoogle Scholar
  9. 9.
    Barth, N.H., Christensen, S.M.: Phys. Rev. D28, 1876 (1983)ADSGoogle Scholar
  10. 10.
    Myrzakulov, R., Sebastiani, L., Vagnozzi, S.: Eur. Phys. J. C75, 444 (2015). arXiv:1504.07984 [gr-qc]ADSCrossRefGoogle Scholar
  11. 11.
    Calcagni, G., Nardelli, G.: Phys. Rev. D82, 123518 (2010). arXiv:1004.5144 [hep-th]ADSGoogle Scholar
  12. 12.
    Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010). arXiv:0805.1726 [gr-qc]ADSCrossRefGoogle Scholar
  13. 13.
    De Felice, A., Tsujikawa, S.: Living Rev. Rel. 13, 3 (2010). arXiv:1002.4928 [gr-qc]CrossRefGoogle Scholar
  14. 14.
    Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Phys. Rep. 513, 1 (2012). arXiv:1106.2476 [astro-ph.CO]ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011a). arXiv:1011.0544 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Woodard, R.P.: 3rd Aegean Summer School: The Invisible Universe: Dark Matter and Dark Energy, vol. 720, pp. 403–433 (2007). arXiv:astro-ph/0601672 [astro-ph]
  17. 17.
    Faraoni, V., Gunzig, E., Nardone, P.: Fund. Cosm. Phys. 20, 121 (1999). arXiv:gr-qc/9811047 [gr-qc]ADSGoogle Scholar
  18. 18.
    Magnano, G., Sokołowski, L.M.: Phys. Rev. D. 50, 5039 (1994). arXiv:gr-qc/9312008 ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Brooker, D.J., Odintsov, S.D., Woodard, R.P.: Nucl. Phys. B911, 318 (2016). arXiv:1606.05879 [gr-qc]ADSCrossRefGoogle Scholar
  20. 20.
    Järv, L., Kannike, K., Marzola, L., Racioppi, A., Raidal, M., Rünkla, M., Saal, M., Veermäe, H.: Phys. Rev. Lett. 118, 151302 (2017). arXiv:1612.06863 [hep-ph]ADSCrossRefGoogle Scholar
  21. 21.
    Kuusk, P., Rünkla, M., Saal, M., Vilson, O.: Class. Quantum Gravity 33, 195008 (2016). arXiv:1605.07033 [gr-qc]ADSCrossRefGoogle Scholar
  22. 22.
    Mathew, J., Shankaranarayanan, S.: Astropart. Phys. 84, 1 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    Mathew, J., Johnson, J.P., Shankaranarayanan, S.: Gen. Relativ. Gravit. 50, 90 (2018). arXiv:1705.07945 [gr-qc]ADSCrossRefGoogle Scholar
  24. 24.
    Linder, E.V.: Phys. Rev. D 80, 123528 (2009). arXiv:0905.2962 [astro-ph.CO]ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Odintsov, S.D., Sáez-Chillón Gómez, D., Sharov, G.S.: Eur. Phys. J. C77, 862 (2017). arXiv:1709.06800 [gr-qc]ADSCrossRefGoogle Scholar
  26. 26.
    Xu, Q., Chen, B.: Commun. Theor. Phys. 61, 141 (2014). arXiv:1203.6706 [astro-ph.CO]ADSCrossRefGoogle Scholar
  27. 27.
    Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Sebastiani, L., Zerbini, S.: Phys. Rev. D77, 046009 (2008). arXiv:0712.4017 [hep-th]ADSGoogle Scholar
  28. 28.
    Capozziello, S., Faraoni, V.: Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics, vol. 170. Springer, Berlin (2010)zbMATHGoogle Scholar
  29. 29.
    Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011b). arXiv:1011.0544 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Nojiri, S., Odintsov, S.D., Oikonomou, V.K.: Phys. Rep. 692, 1 (2017). arXiv:1705.11098 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Elizalde, E., Nojiri, S., Odintsov, S.D., Sebastiani, L., Zerbini, S.: Phys. Rev. D83, 086006 (2011). arXiv:1012.2280 [hep-th]ADSGoogle Scholar
  32. 32.
    Odintsov, S.D., Oikonomou, V.K.: Nucl. Phys. B929, 79 (2018). arXiv:1801.10529 [gr-qc]ADSCrossRefGoogle Scholar
  33. 33.
    Kaiser, D.I.: Phys. Rev. D 81, 084044 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Kallosh, R., Linde, A.: JCAP 1310, 033 (2013). arXiv:1307.7938 [hep-th]ADSCrossRefGoogle Scholar
  35. 35.
    Abedi, H., Abbassi, A.M.: J. Cosmol. Astropart. Phys. 2015, 026 (2015)CrossRefGoogle Scholar
  36. 36.
    Hwang, J.-c., Noh, H.: Phys. Rev. D61, 043511 (2000). arXiv:astro-ph/9909480 [astro-ph]
  37. 37.
    Capozziello, S., Nojiri, S., Odintsov, S.D., Troisi, A.: Phys. Lett. B639, 135 (2006). arXiv:astro-ph/0604431 [astro-ph]ADSCrossRefGoogle Scholar
  38. 38.
    Bahamonde, S., Odintsov, S.D., Oikonomou, V.K., Tretyakov, P.V.: Phys. Lett. B766, 225 (2017). arXiv:1701.02381 [gr-qc]ADSCrossRefGoogle Scholar
  39. 39.
    Akrami, Y., et al.: (Planck) (2018). arXiv:1807.06211 [astro-ph.CO]
  40. 40.
    Gordon, C., Wands, D., Bassett, B.A., Maartens, R.: Phys. Rev. D63, 023506 (2001). arXiv:astro-ph/0009131 [astro-ph]ADSGoogle Scholar
  41. 41.
    Odintsov, S.D., Saez-Chillon Gomez, D., Sharov, G.S.: Phys. Rev. D99, 024003 (2019). arXiv:1807.02163 [gr-qc]ADSGoogle Scholar

Copyright information

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Authors and Affiliations

  1. 1.Department of PhysicsIndian Institute of Technology BombayMumbaiIndia
  2. 2.Department of PhysicsIndian Institute of Technology MadrasChennaiIndia

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