Cosmology in 5D and 4D Einstein-Gauss-Bonnet gravity

We consider the five-dimensional Einstein-Gauss-Bonnet gravity, which can be obtained by means of an appropriate choice of coefficients in the five-dimensional Lanczos-Lovelock gravity theory. The Einstein-Gauss-Bonnet field equations for the Friedmann-Lemaitre-Robertson-Walker metric are found as well as some of their solutions. The hyperbolicity of the corresponding equations of motion is discussed. A four-dimensional gravity action is obtained from the Gauss-Bonnet gravity using the Randall-Sundrum compactification procedure and then it is studied the implications of the compactification procedure in the cosmological solutions. The same procedure is used to obtain gravity in four dimensions from the five-dimensional AdS-Chern-Simons gravity to then study some cosmological solutions. Some aspects of the construction of the four-dimensional action gravity, as well as a brief review of Lovelock gravity in 5D are considered in an Appendix.

Automated summary

We consider the five-dimensional Einstein-Gauss-Bonnet gravity and derive the corresponding field equations and solutions by choosing appropriate coefficients in the five-dimensional Lanczos-Lovelock gravity theory. The hyperbolicity of the equations of motion is discussed, and the implications of the compactification procedure in the cosmological solutions are studied. The same procedure is also applied to obtain four-dimensional gravity from five-dimensional AdS-Chern-Simons gravity and study its cosmological solutions. Some aspects of the construction of the four-dimensional gravity action, as well as a brief review of Lovelock gravity in 5D, are considered in an Appendix.