We present a model for an inhomogeneous and anisotropic early universe filled with a nonlinear electromagnetic field of Born-Infeld (BI) type. The effects of the BI field are compared with the linear case (Maxwell). Since the curvature invariants are well behaved then we conjecture that our model does not present an initial big bang singularity. The existence of the BI field modifies the curvature invariants at t = 0 as well as sets bounds on the amplitude of the conformal metric function.

An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's issue is then revealed: these transformations relate complementary geometrical pictures of a same physical reality, so that, the question about which is the physical conformal frame, does not arise. In addition, arguments are given which point out that, unless a clear statement of what is understood by "equivalence of frames" is made, the issue is a semantic one. For definiteness, an intuitively "natural" statement of conformal equivalence is given, which is associated with conformal invariance of the field equations. Under this particular reading, equivalence can take place only if the metric is defined up to a conformal equivalence class. A concrete example of a conformal-invariant theory of gravity is then explored. Since Brans-Dicke theory is not conformally invariant, then the Jordan's and Einstein's frames of the theory are not equivalent. Otherwise, in view of the alternative approach proposed here, these frames represent complementary geometrical descriptions of a same phenomenon. The different points of view existing in the literature are critically scrutinized on the light of the new arguments.

Here we investigate the cosmic dynamics of Friedmann-Robertson-Walker universes -flat spatial sections -which are driven by nonlinear electrodynamics (NLED) Lagrangians. We pay special attention to the check of the sign of the square sound speed since, whenever the latter quantity is negative, the corresponding cosmological model is classically unstable against small perturbations of the background energy density. Besides, based on causality arguments, one has to require that the mentioned small perturbations of the background should propagate at most at the local speed of light. We also look for the occurrence of curvature singularities. Our results indicate that several cosmological models which are based in known NLED Lagrangians, either are plagued by curvature singularities of the sudden and/or big rip type, or are violently unstable against small perturbations of the cosmological background -due to negative sign of the square sound speedor both. In addition, causality issues associated with superluminal propagation of the background perturbations may also arise.

We investigate in detail the asymptotic properties of tachyon cosmology for a broad class of selfinteraction potentials. The present approach relies in an appropriate re-definition of the tachyon field, which, in conjunction with a method formerly applied in the bibliography in a different context, allows to generalize the dynamical systems study of tachyon cosmology to a wider class of self-interaction potentials beyond the (inverse) square-law one. It is revealed that independent of the functional form of the potential, the matter-dominated solution and the ultra-relativistic (also matter-dominated) solution, are always associated with equilibrium points in the phase space of the tachyon models. The latter is always the past attractor, while the former is a saddle critical point. For inverse power-law potentials V ∝ φ −2λ the late-time attractor is always the de Sitter solution, while for sinh-like potentials V ∝ sinh −α (λφ), depending on the region of parameter space, the late-time attractor can be either the inflationary tachyon-dominated solution or the matter-scaling (also inflationary) phase. In general, for most part of known quintessential potentials, the late-time dynamics will be associated either with de Sitter inflation, or with matter-scaling, or with scalar field-dominated solutions.

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a DGP brane. The simplest kinds of self-interaction potentials are investigated: a) constant potential, and b) exponential potential. It is shown that the dynamics of DGP models can be very rich and complex. One of the most interesting results of this study shows that dynamical screening of the scalar field self-interaction potential, occuring within the Minkowski cosmological phase of the DGP model and mimetizing 4D phantom behaviour, is an attractor solution for a constant self-interaction potential but not for the exponential one. In the latter case gravitational screening is not even a critical point of the corresponding autonomous system of ordinary differential equations. 11.25.Wx, 95.36.+x, 98.80.Bp, 98.80.Cq, 98.80.Jk DGP model; the so called "self-accelerating" branch, or selfaccelerating cosmological phase [9]. 3 Regarding the so called "normal" branch, or Minkowski cosmological phase [9] of DGP model, this is just a particular member in the wider class of models of reference [15].