Cosmology of modified (but second order) gravity

This is a brief review of modified gravity cosmologies. Generically extensions of gravity action involve higher derivative terms, which can result in ghosts and instabilities. There are three ways to circumvent this: Chern-Simons terms, first order variational principle and nonlocality. We consider recent cosmological applications of these three classes of modified gravity models, in particular to the dark energy problem. The viable parameter spaces can be very efficiently constrained by taking into account cosmological data from all epochs in addition to Solar system tests and stability considerations. We make some new remarks concerning so called algebraic scalar-tensor theories, biscalar reformulation of nonlocal actions involving the inverse d'Alembertian, and a possible covariant formulation holographic cosmology with nonperturbative gravity.Comment: 18 pages, 2 figures. Based on a talk given at the 4th Gamow conference "Astrophysics and Cosmology after Gamow: recent progress and new horizons" at Odessa, Ukraine, 17-23 August 200

Cosmological perturbations in modified teleparallel gravity models

Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(\varphi)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.Comment: 18 pages without figures. v2: added reference

A note on viability of nonminimally coupled f(R)f(R) theory

Consistency conditions for nonminimally coupled $f(R)$ theories have been derived by requiring the absence of tachyons and instabilities in the scalar fluctuations. This note confirms these results and clarifies a subtlety regarding different definitions of sound speeds.Comment: 4 pages. -added acknowledgemen