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Inflation from an E-Model Potential of \(\alpha \)-Attractors

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Abstract

In this paper, we study the \(\alpha \)-attractors in the framework of the Randall–Sundrum type II braneworld model. We consider the simplest E-model of \(\alpha \)-attractors and apply the slow-roll approximation in high energy limit. In this scenario, we numerically investigate the inflationary parameters and show that high-energy brane corrections have significant effect on the parameter \(\alpha \); namely, lower values of \(\alpha \) are observationally preferred in this limit. The latter substantially reduces the tensor-to-scalar ratio of perturbations making the braneworld inflation compatible with observational data.

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References

  1. Weinberg, S.: Gravitation and cosmology. Wiley, New York (1972)

    Google Scholar 

  2. Kolb, E.W.; Turner, M.S.: The early universe. Addison-Wesley, Redwood City, CA (1990)

    MATH  Google Scholar 

  3. Pati, J.G.; Salam, A.: Is baryon number conserved? Phys. Rev. Lett. 31, 661 (1973)

    Article  Google Scholar 

  4. Smoot, G.F.; et al.: Structure in the COBE differential microwave radiometer first-year maps. Astrophys. J. Lett. 396, L1 (1992)

    Article  Google Scholar 

  5. Georgi, H.; Glashow, S.: Unity of all elementary-particle forces. Phys. Rev. Lett. 32, 438 (1974)

    Article  Google Scholar 

  6. Bennett, C.L.; et al.: Four-year COBE* DMR cosmic microwave background observations: maps and basic results. Astrophys. J. Lett. 464, 1 (1996)

    Article  Google Scholar 

  7. Hooft, G.: Magnetic monopoles in unified theories. Nucl. Phys. B. 79, 276 (1974)

    Article  MathSciNet  Google Scholar 

  8. Polyakov, A.: Particle spectrum in quantum field theory. JETP Lett. 20, 194, 1974

  9. Preskill, J.P.: Cosmological production of superheavy magnetic monopoles. Phys. Rev. Lett. 43, 1365, 1979

  10. Peebles, P.J.E.: The large-scale structure of the universe. Princeton University Press, Princeton (1980)

    MATH  Google Scholar 

  11. G. Efstathiou: Cosmological perturbations. In: , J.A. Peacock, A.F. Heavens, A.T. Davies (ed) The Physics of the Early Universe. (Adam-Higler, Bristol 1990) pp. 361-463.

  12. Guth, A.H.: Cosmological consequences of a first-order phase transition in the S U 5 grand unified model. Phys. Rev. D 23, 347 (1981)

    Article  Google Scholar 

  13. Linde, A.D.: Particle physics and inflationary cosmology. Harwood Academic Publishers, London (1990)

    Book  Google Scholar 

  14. G. Lazarides: PRHEP-corfu98/014 (hepph/9904502), hep-ph/0111328 G.S. Watson: astro-ph/0005003.

  15. Martin, J.; Ringeval, C.; Vennin, V.: Encyclopaedia inflationaris. Phys. Dark Univ. 5, 75–235 (2014)

    Article  Google Scholar 

  16. Es-Sobbahi, H.; Nach, M.: IJMPA. On braneworld inverse power-law inflation 33(10), 1850058 (2018)

    Google Scholar 

  17. Ahl-laamara, R.; Es-Sobbahi, H.; Ennadifi, S.E.: On braneworld monomial inflation. IJMPA 3325, 1850147 (2018)

    Article  MathSciNet  Google Scholar 

  18. Yi, Z.; Gong, Y.: On the constant-roll inflation. JCAP 1803(03), 052 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gao, Q.: The observational constraint on constant-roll inflation. Sci. China Phys. Mech. Astron. 61(7), 070411 (2018)

    Article  Google Scholar 

  20. Gao, Q.; Gong, Y.; Fei, Q.: Constant-roll tachyon inflation and observational constraints. JCAP 1805(05), 005 (2018)

    Article  MATH  Google Scholar 

  21. Gao, Q.; Gong, Y.; Yi, Z.: On the constant-roll inflation with large and small \(\eta \)H. Universe 5(11), 215 (2019)

    Article  Google Scholar 

  22. Akrami, Y.; et al., Planck 2018 results. X. Constraints on inflation. arXiv:1807.06211.

  23. Ade, P.A.R.; et al.: BICEP2 / Keck Array x: Constraints on primordial gravitational waves using Planck, WMAP, and New BICEP2/Keck observations through the 2015 Season. Phys. Rev. Lett. 121, 221301 (2018)

    Article  Google Scholar 

  24. Goncharov, A.S.; Linde, A.D.: Chaotic inflation of the universe in supergravity. Sov. Phys. JETP 59, 930 (1984)

    Google Scholar 

  25. Goncharov, A.B.; Linde, A.D.: Chaotic inflation in supergravity. Phys. Lett. B 139, 27 (1984)

    Article  Google Scholar 

  26. Linde, A.: Does the first chaotic inflation model in supergravity provide the best fit to the Planck data?, JCAP 1502, no. 02, 030 (2015) [arXiv:1412.7111 [hep-th]].

  27. Salopek, D.S.; Bond, J.R.; Bardeen, J.M.: Designing density fluctuation spectra in inflation. Phys. Rev. D 40, 1753 (1989)

    Article  Google Scholar 

  28. Bezrukov, F.L., Shaposhnikov, M.: The Standard Model Higgs boson as the inflaton. Phys. Lett. B 659, 703 (2008). ([arXiv:0710.3755 [hep-th]])

  29. Kallosh, R.; Linde, A.; Roest, D.: Universal attractor for inflation at strong coupling. Phys. Rev. Lett. 112(1), 011303 (2014)

    Article  Google Scholar 

  30. Galante, M.; Kallosh, R.; Linde, A.; Roest, D.: Unity of cosmological inflation attractors. Phys. Rev. Lett. 114(14), 141302 (2015)

    Article  Google Scholar 

  31. Kallosh, R.; Linde, A.: Escher in the sky. Comptes Rendus Phys 16(10), 914–927 (2015)

    Article  Google Scholar 

  32. Carrasco, J.J.M.; Kallosh, R.; Linde, A.: Cosmological attractors and initial conditions for inflation. Phys. Rev. D 92(6), 063519 (2015)

    Article  Google Scholar 

  33. Randall, L.; Sundrum, R.: An alternative to compactification. Phys. Rev. Lett. 83, 4690 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  34. Maartens, R.; Wands, D.; Bassett, B.A.; Heard, I.: Chaotic inflation on the brane. Phys. Rev. D 62, 041301 (2000)

    Article  Google Scholar 

  35. Galante, M.; Kallosh, R.; Linde, A.; Roest, D.: Unity of cosmological inflation attractors. Physical review letters 114(14), 141302 (2015)

    Article  Google Scholar 

  36. Kallosh, R.; Linde, A.; Roest, D.: Superconformal inflationary \( \alpha \)-attractors. J. High Energy Phys. 2013(11), 198 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  37. Randall, L.; Sundrum, R.: An alternative to compactification. Phys. Rev. Lett. 83(23), 4690 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  38. Shiromizu, T.; Maeda, K.I.; Sasaki, M.: The Einstein equations on the 3-brane world. Phys. Rev. D 62(2), 024012 (2000)

    Article  MathSciNet  Google Scholar 

  39. Sahni, V.; Sami, M.; Souradeep, T.: Relic gravity waves from braneworld inflation. Phys. Rev. D 65(2), 023518 (2001)

    Article  Google Scholar 

  40. Sami, M.; Sahni, V.: Quintessential inflation on the brane and the relic gravity wave background. Phys. Rev. D 70(8), 083513 (2004)

    Article  Google Scholar 

  41. Tsujikawa, S.; Liddle, A. R.: Constraints on braneworld inflation from CMB anisotropies. J. Cosmol. Astropart. Phys. 2004(3), 001 (2004)

  42. Maartens, R.; Wands, D.; Bassett, B.A.; Heard, I.P.: Chaotic inflation on the brane. Phys. Rev. D 62(4), 041301 (2000)

    Article  Google Scholar 

  43. Langlois, D.; Maartens, R.; Wands, D.: Gravitational waves from inflation on the brane. Phys. Lett. B 489(3–4), 259–267 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  44. Roest, D.; Scalisi, M.: Cosmological attractors from \(\alpha \) -scale supergravity. Phys. Rev. D 92(4), 043525 (2015)

    Article  MathSciNet  Google Scholar 

  45. Linde, A.: Single-field \(\alpha \)-attractors. J. Cosmol. Astropart. Phys. 2015(5), 003 (2015)

  46. Starobinsky, A. A. A: new type of isotropic cosmological models without singularity. In 30 Years Of The Landau Institute—Selected Papers (pp. 771–774) (1996).

  47. Mukhanov, V.F.; Chibisov, G.V.: Quantum fluctuations and a nonsingular universe. JETP Lett. 33(10), 532–535 (1981)

    Google Scholar 

  48. Kallosh, R.; Linde, A.: Superconformal generalizations of the Starobinsky model. J. Cosmol. Astropart. Phys. 2013(6), 028 (2013)

  49. Carrasco, J. J. M.; Kallosh, R.; Linde, A.: \(\alpha \) -attractors: Planck, LHC and dark energy. J. High Energy Phys. 2015, 147 (2015). https://doi.org/10.1007/JHEP10(2015)147

  50. Sabir, M.; Ahmed, W.; Gong, Y.; Lu, Y.: \(\alpha \)-attractor from superconformal E-models in brane inflation. Eur. Phys. J. C 80(1), 1–7 (2020)

    Article  Google Scholar 

  51. Ferrara, S.; Kallosh, R.; Linde, A.; Porrati, M.: Minimal supergravity models of inflation. Phys. Rev. D 88(8), 085038 (2013)

    Article  Google Scholar 

  52. Bunn, E.F.; White, M.: The 4 year COBE normalization and large-scale structure. Astrophys. J. 480(1), 6 (1997)

    Article  Google Scholar 

  53. Jaman, N.; Myrzakulov, K.: Braneworld inflation with an effective \(\alpha \)-attractor potential. Phys. Rev. D 99(10), 103523 (2019)

    Article  MathSciNet  Google Scholar 

  54. Lyth, D.H.; Liddle, A.R.: The primordial density perturbation: cosmology, inflation and the origin of structure. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  55. Baleanu, D.; Vacaru, S.: Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics. CEJP 9(5), 1267–1279 (2011)

    Google Scholar 

  56. Baleanu, D.; Vacaru, S.: Fractional almost Kahler-Lagrange geometry. Nonlin. Dynam. 64(4), 365–373 (2011)

    Article  Google Scholar 

  57. Baleanu, D.; Vacaru, S.: Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics. JMP. 52(5), 053514 (2011)

    MathSciNet  MATH  Google Scholar 

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The authors are grateful to their families for support.

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Es-sobbahi, H., Ennadifi, S.E. Inflation from an E-Model Potential of \(\alpha \)-Attractors. Arab J Sci Eng 47, 379–385 (2022). https://doi.org/10.1007/s13369-021-05484-z

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