Modeling the potential by an inverse square law in terms of the tachyon field (V (T ) = βT −2 ) we find exact solution for spatially flat isotropic universe. We show that for β > 2 √ 3/3 the model undergoes power-law inflation. A way to construct other exact solutions is specified and exemplified.

We study spatially flat isotropic universes driven by k-essence. It is shown that Friedmann and k-field equations may be analytically integrated for arbitrary k-field potentials during evolution with a constant baryotropic index. It follows that there is an infinite number of dynamically different k-theories with equivalent kinematics of the gravitational field. We show that there is a large "window" of stable solutions, and that the dust-like behaviour separates stable from unstable expansion. Restricting to the family of power law solutions, it is argued that the linear scalar field model, with constant function F , is isomorphic to a model with divergent speed of sound and this makes them less suitable for cosmological modeling than the non-linear k-field solutions we find in this paper. †Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas.

We obtain a general exact solution of the Einstein field equations for the anisotropic Bianchi type I universes filled with an exponential-potential scalar field and study their dynamics. It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behavior of the models is that of a power-law inflating F'riedmann-Robertson-Walker (FRW) universe. This property does not hold, in contrast, when some degree of inhomogeneity is introduced, as discussed in our following paper.PACS number(s): 04.20. Jb, 98.80.Cq, 98.80.H~

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We propose a picture, within the pre-big-bang approach, in which the universe emerges from a bath of plane gravitational and dilatonic waves. The waves interact gravitationally breaking the exact plane symmetry and lead generically to gravitational collapse resulting in a singularity with the Kasner-like structure. The analytic relations between the Kasner exponents and the initial data are explicitly evaluated and it is shown that pre-big-bang inflation may occur within a dense set of initial data. Finally, we argue that plane waves carry zero gravitational entropy and thus are, from a thermodynamical point of view, good candidates for the universe to emerge from.