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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 651684, 9 pages
http://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.

Abstract

We construct the higher order terms of curvatures in Lagrangians of the scale factor in the D-dimensional Robertson-Walker metric, which are linear in the second derivative of the scale factor with respect to cosmic time. It is shown that they are composed of the Lovelock tensors at the first step; iterative construction yields arbitrarily high order terms. The relation to the former work on higher order gravity is discussed. Despite the absence of scalar degrees of freedom in cosmological models which come from our Lagrangian, it is shown that an inflationary behavior of the scale factor can be found. The application to the thick brane solutions is also studied.