Gravity with Higher Derivatives in D-Dimensions

The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations of motion, (3) derivation of approximate equations in the presence of a small parameter in the system, and (4) the method of test functions. Some applications are presented to illustrate each method. The unification of two necessary elements of a future theory is also kept in mind - the extra dimensions and the extended form of the gravity.Comment: 22 pages, 9 figures, this article belongs to the Special Issue Selected Papers from the 17th Russian Gravitational Conference - International Conference on Gravity, Cosmology and Astrophysics (RUSGRAV-17

Sub-Planckian scale and limits for f(R)f(R) models

We study the Universe evolution starting from the sub-Planckian scale to present times. The requirement for an exponential expansion of the space with the observed metric as a final stage leads to significant restrictions on the parameter values of a $f(R)$-function. An initial metric of the Universe is supposed to be maximally symmetric with the positive curvature