`ISRN Mathematical PhysicsVolume 2013 (2013), Article ID 651684, 9 pageshttp://dx.doi.org/10.1155/2013/651684`
Research Article

## “Critical” Cosmology in Higher Order Gravity

1Department of Information and Media Studies, Yamaguchi Junior College, Hofu-shi, Yamaguchi 747-1232, Japan
2Graduate School of Science and Engineering, Yamaguchi-shi, Yamaguchi 753-8512, Japan

Received 11 January 2013; Accepted 28 January 2013

Academic Editors: R. Parwani and A. Sanyal

Copyright © 2013 Nahomi Kan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. R. Schimming and H. J. Schmidt, “On the history of fourth order metric theories of gravitation,” NTM Schriftenreihe für Geschichte der Naturwissenschaften, Technik und Medizin, vol. 27, pp. 41–48, 1990, http://arxiv.org/abs/gr-qc/0412038/.
2. H. J. Schmidt, “Fourth order gravity: equations, history, and applications to cosmology,” International Journal of Geometric Methods in Modern Physics, vol. 4, no. 2, p. 209, 2007.
3. B. Whitt, “Fourth-order gravity as general relativity plus matter,” Physics Letters B, vol. 145, no. 3-4, pp. 176–178, 1984.
4. S. W. Hawking and J. C. Luttrell, “Higher derivatives in quantum cosmology. I. The isotropic case,” Nuclear Physics B, vol. 247, no. 1, pp. 250–260, 1984.
5. T. P. Sotiriou and V. Faraoni, “$f\left(R\right)$ theories of gravity,” Reviews of Modern Physics, vol. 82, no. 1, pp. 451–497, 2010.
6. A. de Felice and S. Tsujikawa, “f(R) theories,” Living Reviews in Relativity, vol. 13, p. 3, 2010.
7. S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from $F\left(R\right)$ theory to Lorentz non-invariant models,” Physics Reports, vol. 505, no. 2-4, pp. 59–144, 2011.
8. D. Lovelock, “The Einstein tensor and its generalizations,” Journal of Mathematical Physics, vol. 12, pp. 498–501, 1971.
9. D. Lovelock, “The four-dimensionality of space and the Einstein tensor,” Journal of Mathematical Physics, vol. 13, no. 6, article 874, 3 pages, 1972.
10. J. T. Wheeler, “Symmetric solutions to the Gauss-Bonnet extended Einstein equations,” Nuclear Physics B, vol. 268, no. 3-4, pp. 737–746, 1986.
11. C. Aragone, “Geometric stringy gravity,” Physics Letters B, vol. 186, no. 2, pp. 151–156, 1987.
12. F. Müller-Hoissen, “Spontaneous compactification with quadratic and cubic curvature terms,” Physics Letters B, vol. 163, no. 1–4, pp. 106–110, 1985.
13. F. Müller-Hoissen, “Dimensionally continued Euler forms: Kaluza-Klein cosmology and dimensional reduction,” Classical and Quantum Gravity, vol. 3, no. 4, artcile 665, 1986.
14. B. Whitt, “Spherically symmetric solutions of general second-order gravity,” Physical Review D, vol. 38, no. 10, pp. 3000–3007, 1988.
15. N. Deruelle and L. Fariña-Busto, “Lovelock gravitational field equations in cosmology,” Physical Review D, vol. 41, no. 12, pp. 3696–3708, 1990.
16. B. Zumino, “Gravity theories in more than four dimensions,” Physics Reports, vol. 137, no. 1, pp. 109–114, 1986.
17. B. Zwiebach, “Curvature squared terms and string theories,” Physics Letters B, vol. 156, no. 5-6, pp. 315–317, 1985.
18. E. A. Bergshoeff, O. Hohm, and P. K. Townsend, “Massive gravity in three dimensions,” Physical Review Letters, vol. 102, no. 20, Article ID 201301, 4 pages, 2009.
19. H. Lü and C. N. Pope, “Critical gravity in four dimensions,” Physical Review Letters, vol. 106, no. 18, Article ID 181302, 4 pages, 2011.
20. H. Lü, Y. Pang, and C. N. Pope, “Conformal gravity and extensions of critical gravity,” Physical Review D, vol. 84, no. 6, Article ID 064001, 9 pages, 2011.
21. T. Çağrı Şişman, İ. Güllü, and B. Tekin, “All unitary cubic curvature gravities in $D$ dimensions,” Classical and Quantum Gravity, vol. 28, no. 19, Article ID 195004, 22 pages, 2011.
22. M. Ibison, “On the conformal forms of the Robertson-Walker metric,” Journal of Mathematical Physics, vol. 48, no. 12, Article ID 122501, 23 pages, 2007.
23. K. A. Meissner and M. Olechowski, “Domain walls without cosmological constant in higher order gravity,” Physical Review Letters, vol. 86, no. 17, pp. 3708–3711, 2001.
24. K. A. Meissner and M. Olechowski, “Brane localization of gravity in higher derivative theory,” Physical Review D, vol. 65, no. 6, Article ID 064017, 6 pages, 2002.
25. J. Oliva and S. Ray, “Classification of six derivative Lagrangians of gravity and static spherically symmetric solutions,” Physical Review D, vol. 82, no. 12, Article ID 124030, 11 pages, 2010.
26. K. Skenderis and P. K. Townsend, “Gravitational stability and renormalization-group flow,” Physics Letters B, vol. 468, no. 1-2, pp. 46–51, 1999.
27. I. Low and A. Zee, “Naked singularity and Gauss-Bonnet term in brane world scenarios,” Nuclear Physics B, vol. 585, no. 1-2, pp. 395–404, 2000.
28. Z. Kakushadze, “Localized (super)gravity and cosmological constant,” Nuclear Physics B, vol. 589, no. 1-2, pp. 75–118, 2000.
29. O. Corradini and Z. Kakushadze, “Localized gravity and higher curvature terms,” Physics Letters B, vol. 494, no. 3-4, pp. 302–310, 2000.
30. U. Camara dS and G. M. Sotkov, “New massive gravity domain walls,” Physics Letters B, vol. 694, no. 1, pp. 94–99, 2010.
31. Y. X. Liu, Y. Q. Wang, S. F. Wu, and Y. Zhong, “Analytic solutions of Brane in critical gravity,” http://arxiv.org/abs/1201.5922.