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Advances in High Energy Physics
Volume 2008 (2008), Article ID 521389, 27 pages
Research Article

On the Superstrings-Induced Four-Dimensional Gravity and Its Applications to Cosmology

Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi, Tokyo 192–0397, Japan

Received 17 June 2008; Revised 19 October 2008; Accepted 21 October 2008

Academic Editor: Anastasios Petkou

Copyright © 2008 Masao Iihoshi and Sergei V. Ketov. 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.


We review the status of the fourth-order (quartic in the spacetime curvature) terms induced by superstrings/M-theory (compactified on a warped torus) in the leading order with respect to the Regge slope parameter, and study their (nonperturbative) impact on the evolution of the Hubble scale in the context of the four-dimensional FRW cosmology. After taking into account the quantum ambiguities in the definition of the off-shell superstring effective action, we propose the generalized Friedmann equations, find the existence of their (de Sitter) exact inflationary solutions without a spacetime singularity, and constrain the ambiguities by demanding stability and the scale factor duality invariance of our solutions. The most naive (Bel-Robinson tensor squared) quartic terms are ruled out, thus giving the evidence for the necessity of extra quartic (Ricci tensor-dependent) terms in the off-shell gravitational effective action for superstrings. Our methods are generalizable to the higher orders in the spacetime curvature.