Abstract
We focus on the large field of a hyperbolic potential form, which is characterized by a parameter f, in the framework of the brane-world inflation in Randall-Sundrum-II model. From the observed form of the power spectrum P R (k), the parameter f should be of order 0.1m p to 0.001m p , the brane tension must be in the range λ ~ (1−10)×1057 GeV4, and the energy scale is around V0 1/4 ~ 1015 GeV. We find that the inflationary parameters (n s , r, and dn s /d(ln k) depend only on the number of e-folds N. The compatibility of these parameters with the last Planck measurements is realized with large values of N.
Similar content being viewed by others
References
A. Linde, “Inflationary Cosmology after Planck 2013”, arXiv: 1402.0526.
A. H. Guth, Phys. “Inflationary universe: A possible solution to the horizon and flatness problems,” Phys. Rev. D 23, 347 (1981).
A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University, Cambridge, 2000).
D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation,” Phys. Rep. 314, 1–146 (1999).
J. Martin, C. Ringeval, and V. Vennin, “Encyclopaedia inflationaris, ” arXiv: 1303.3787.
R. Kallosh, A. Linde, and A. Westphal, “Chaotic inflation in supergravity after Planck and BICEP2,” Phys. Rev. D 90, 023534 (2014).
T. Kobayashi and O. Seto, “Polynomial inflationmodels after BICEP2,” Phys. Rev. D 89, 103524 (2014).
T. Li, Z. Li, and D. V. Nanopoulos, “Supergravity inflation with broken shift symmetry and large tensorto- scalar ratio,” JCAP 02, 028 (2014).
K. Freese and W. H. Kinney, “Natural inflation: consistency with cosmic microwave background observations of Planck and BICEP2,” JCAP 03, 044 (2015).
Takeshi Chiba and Kazunori Kohri, “Consistency relations for large field inflation,” Prog. Theor. Exp. Phys. 093, E01 (2014).
S. Antuscha and D. Noldea, “BICEP2 implications for single-field slow-roll inflation revisited,” JCAP 05, 035 (2014).
K. Nakayama, F. Takahashi, and Ts. T. Yanagida, “Chaotic inflation with right-handed sneutrinos after Planck,” Phys. Lett. B 730, 24 (2014).
C. Rubano and J. D. Barrow, “Scaling solutions and reconstruction of scalar field potentials,” Phys. Rev. D 64 (12), 127301 (2001).
S. Basilakos and J. D. Barrow, “Hyperbolic inflation in the light of Planck 2015 data,” Phys. Rev. D 91, 103517 (2015).
R. Maartens and K. Koyama, “Brane-world gravity,” Living Rev. Rel. 13, 1004–3962 (2010).
L. Randall and R. Sundrum, “An alternative to compactification,” Phys. Rev. Lett. 83, 4690 (1999)
M. J. Duff and J. T. Liu, “Complementarity of the Maldacena and Randall-Sundrum pictures,” Phys. Rev. Lett. 85, 2052 (2000).
R. Maartens and K. Koyama, “Brane-world gravity” Living Rev. Rel. 7, 7 (2004).
G. Calcagni, S. Kuroyanagi, J. Ohashi, and S. Tsujikaw, “Strong Planck constraints on brane world and non-commutative inflation,” J. Cosmol. Astropart. Phys. 03, 052 (2014).
R. Adam et al. (Planck Collaboration), “Planck 2015 results. XIII. Cosmological parameters,” arXiv: 1502.01589.
J. Polchinski, String Theory I & II (Cambridge University, Cambridge, 1998).
N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, “Phenomenology, astrophysics, and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,” Phys. Rev. D 59, 086004 (1999).
J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, “Ekpyrotic universe: Colliding branes and the origin of the hot big bang,” Phys. Rev. D 64, 123522 (2001).
L. Battarra and J. L. Lehners, “Quantum-to-classical transition for ekpyrotic perturbations,” Phys. Rev. D 89, 063516 (2014).
J. E. Lidsey, “Inflation and braneworlds. “The early Universe and observational cosmology,” Lect. Notes Phys. 646, 357–379 (2004).
D. Langlois, R. Maartens and D. Wands, “Gravitational waves from inflation on the brane,” Phys. Lett. B 489, 259 (2000).
R. Maartens, D. Wands, B. Basset, and I. Heard, “Chaotic inflation on the brane,” Phys. Rev. D 62, 041301 (2000).
R. G. Felipe, “Natural brane world inflation and baryogenesis,” Phys. Lett. B 618, 7–13 (2005).
R. Herrera, “Tachyon-Chaplygin inflation on the brane,” Gen. Rel. Grav. 41, 1259 (2009).
M. Bastero-Gil, S. King, and Q. Shafi, “Supersymmetric hybrid inflation with non-minimal K‘`ahler potential,” Phys. Lett. B 651, 345–351 (2007).
M. Ferricha-Alami, A. Safsasfi, A. Bouaouda, R. Zarrouki, and M. Bennai, “K‘`ahler potential braneworld inflation in supergravity after Planck 2015,” Int. J. Mod. Phys. A 30, 1550208 (2015).
A. Safsafi, A. Bouaouda, H. Chakir, J. Inchaouh, and M. Bennai, “On cosmic strings in supergravity braneworld inflation,” Gen. Rel. Grav. 29, 215006 (2012).
G. Panotopoulos, “Assisted chaotic inflation in braneworld cosmology,” Phys. Rev. D 75, 107302 (2007).
R. Easther, J. Frazer, H. V. Peiris, and L. C. Price, “Simple predictions from multifield inflationary models,” Phys. Rev. Lett. 112, 161302 (2014); L. C. Price, H. V. Peiris, J. Frazer, and R. Easther, “Designing and testing inflationary models with Bayesian networks, ” arXiv: 1511.00029.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mounzi, Z., Ferricha-Alami, M., Safsafi, A. et al. Observational constraints on a hyperbolic potential in brane-world inflation. Gravit. Cosmol. 23, 84–89 (2017). https://doi.org/10.1134/S020228931701011X
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S020228931701011X