The tachyonic inflationary universe model in the context of intermediate inflation is studied.General conditions for this model to be realizable are discussed. In the slow-roll approximation, we describe in great details the characteristics of this model.

A coupling between the spacetime geometry and a scalar field involving the Euler four-form can have important consequences in General Relativity. The coupling is a four-dimensional version of the Jackiw-Teitelboim action, in which a scalar couples to the Euler two-form in two dimensions. In this case the first order formalism, in which the vierbein (or the metric) and the spin connection (or the affine connection) are varied independently, is not equivalent to the second order one, where the geometry is completely determined by the metric. This is because the torsion postulate T a ≡ 0 is not valid now and one cannot algebraically solve the spin connection from its own field equation. The direct consequence of this obstruction is that the torsion becomes a new source for the metric curvature, and even if the scalar field is very slowly varying over cosmic scales so as to have no observable astronomical effects at the galactic scale, it has important dynamical effects that can give rise to a cosmological evolution radically different from the standard FRWL model.

Some of the assumptions of cosmology, as based on the simplest version of General Relativity, are discussed. It is argued that by slight modifications of standard gravitation theory, our notion of the sources of gravity -the right hand side of Einstein's equations-, could be something radically different from what is usually expected. One example is exhibited to prove the point, and some consequences are discussed.

We propose a generalization of Chiral Gravity, which follows from considering a Chern-Simons action for the spin connection with anti-symmetric contorsion. The theory corresponds to Topologically Massive Gravity at the chiral point non-minimally coupled to an additional scalar mode that gathers the torsion degree of freedom. In this setup, the effective cosmological constant (the inverse of the curvature radius of maximally symmetric solutions) is either negative or zero, and it enters as an integration constant associated to the value of the contorsion at infinity. We explain how this is not in conflict with the Zamolodchikov's c-theorem holding in the dual boundary theory. In fact, we conjecture that the theory formulated about three-dimensional Anti-de Sitter space is dual to a two-dimensional conformal field theory whose right-and left-moving central charges are given by cR = 24k and cL = 0, respectively, being k the level of the Chern-Simons action. We study the classical theory both at the linear and non-linear level. In particular, we show how Chiral Gravity is included as a special sector. In addition, the theory has other sectors, which we explore; we exhibit analytic exact solutions that are not solutions of Topologically Massive Gravity (and, consequently, neither of General Relativity) and still satisfy Brown-Henneaux asymptotically AdS3 boundary conditions.