Research PapersNo Access

FOURTH-ORDER GRAVITY AS THE INFLATIONARY MODEL REVISITED

SHO KANEDA

Department of Physics, Tokyo Metropolitan University, Japan

Search for more papers by this author

SERGEI V. KETOV

Department of Physics, Tokyo Metropolitan University, Japan

IPMU, University of Tokyo, Japan

Search for more papers by this author

, and

NATSUKI WATANABE

Department of Physics, Tokyo Metropolitan University, Japan

Search for more papers by this author

https://doi.org/10.1142/S0217732310033918Cited by:31 (Source: Crossref)

Abstract

We revisit the old (fourth-order or quadratically generated) gravity model of Starobinsky in four spacetime dimensions, and derive the (inflaton) scalar potential in the equivalent scalar–tensor gravity model. The inflaton scalar potential is used to compute the (CMB) observables of inflation, associated with curvature perturbations (namely, the scalar and tensor spectral indices, and the tensor-to-scalar ratio), including the new next-to-leading order terms with respect to the inverse number of e-foldings. The results are compared to the recent (WMAP5) experimental bounds. We confirm both mathematical and physical equivalence between f(R) gravity theories and the corresponding scalar–tensor gravity theories.

Keywords:

References

A. H. Guth, Phys. Rev. D 23, 347 (1981), DOI: 10.1103/PhysRevD.23.347. Crossref, Web of Science, ADS, Google Scholar
A. D. Linde, Phys. Lett. B 175, 395 (1986). Crossref, Web of Science, ADS, Google Scholar
D. N. Spergelet al., Astrophys. J. Suppl. 170, 377 (2007), DOI: 10.1086/513700. Crossref, Web of Science, ADS, Google Scholar
A. R. Liddle and D. H. Lyth , Cosmological Inflation and Large-Scale Structure ( Cambridge Univ. Press , 2000 ) . Crossref, Google Scholar
E. Hand, Nature 458, 820 (2009), DOI: 10.1038/458820a. Crossref, Web of Science, Google Scholar
A. A. Starobinsky, Phys. Lett. B 91, 99 (1980). Crossref, Web of Science, ADS, Google Scholar
S. Capoziello, V. F. Cardone and A. Troisi, Phys. Rev. D 71, 043503 (2005), DOI: 10.1103/PhysRevD.71.043503. Crossref, Web of Science, Google Scholar
S. Nojiri and S. D. Odintsov, Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007), DOI: 10.1142/S0219887807001928. Link, Web of Science, Google Scholar
T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010), DOI: 10.1103/RevModPhys.82.451. Crossref, Web of Science, ADS, Google Scholar
A. De Felice and S. Tsujikawa , arXiv:1002.4928 . Google Scholar
B. Whitt, Phys. Lett. B 145, 176 (1984). Crossref, Web of Science, ADS, Google Scholar
V. Müller, H.-J. Schmidt and A. A. Starobinsky, Phys. Lett. B 202, 198 (1988). Crossref, Web of Science, ADS, Google Scholar
J. D. Barrow and S. Cotsakis, Phys. Lett. B 214, 515 (1988). Crossref, Web of Science, ADS, Google Scholar
K.-I. Maeda, Phys. Rev. D 39, 3159 (1989), DOI: 10.1103/PhysRevD.39.3159. Crossref, Web of Science, ADS, Google Scholar
V. F. Mukhanov and G. V. Chibisov, JETP Lett. 33, 532 (1981). Web of Science, ADS, Google Scholar
A. A. Starobinsky, Sov. Astron. Lett. 9, 302 (1983). Web of Science, Google Scholar
S. V. Ketov , Quantum Non-Linear Sigma-Models ( Springer-Verlag , 2000 ) . Crossref, Google Scholar
L. D. Landau and E. M. Lifshitz , The Classical Theory of Fields ( Pergamon Press , 2002 ) . Google Scholar
E. Komatsuet al., Astrophys. J. Suppl. 180, 330 (2009), DOI: 10.1088/0067-0049/180/2/330. Crossref, Web of Science, ADS, Google Scholar
A. O. Barvinsky, A. Yu. Kamenshchik and A. A. Starobinsky, J. Cosmol. Astropart. Phys. 0811, 021 (2008). ADS, Google Scholar
M. Iihoshi and S. V. Ketov, Adv. High Energy Phys. 2008, 521389 (2008). Google Scholar
M. Iihoshi and S. V. Ketov, Int. J. Mod. Phys. A 23, 2153 (2008), DOI: 10.1142/S0217751X0804069X. Link, Web of Science, ADS, Google Scholar
S. Kaneda, S. V. Ketov and N. Watanabe, Class. Quantum Grav. 27, 145016 (2010), DOI: 10.1088/0264-9381/27/14/145016. Crossref, Web of Science, ADS, Google Scholar
T. Saidov and A. Zhuk , arXiv:1002.4138 . Google Scholar
S. James Gates Jr. and S. V. Ketov, Phys. Lett. B 674, 59 (2009). Crossref, Web of Science, ADS, Google Scholar
S. V. Ketov, Class. Quantum Grav. 26, 135006 (2009), DOI: 10.1088/0264-9381/26/13/135006. Crossref, Web of Science, ADS, Google Scholar
S. V. Ketov, arXiv:0910.1165 in Proc. of the Int. Conf. on Invisible Universe, Paris, Palais de l'UNESCO, June 29–July 3, 2009; AIP Conf. Proc. 1241, 613 (2010) . Google Scholar
S. James Gates Jr., S. V. Ketov and N. Yunes, Phys. Rev. D 80, 065003 (2009), DOI: 10.1103/PhysRevD.80.065003. Crossref, Web of Science, Google Scholar