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The Chaplygin gas model, characterized by an equation of state of the type $p = - \frac{A}{\rho}$ emerges naturally from the Nambu-Goto action of string theory. This fluid representation can be recast under the form of a tachyonic field given by a Born-Infeld type Lagrangian. At the same time, the Chaplygin gas equation of state can be obtained from a self-interacting scalar field. We show that, from the point of view of the supernova type Ia data, the three representations (fluid, tachyonic, scalar field) lead to the same results. However, concerning the matter power spectra, while the fluid and tachyonic descriptions lead to exactly the same results, the self-interacting scalar field representation implies different statistical estimations for the parameters. In particular, the estimation for the dark matter density parameter in the fluid representation favors a universe dominated almost completely by dark matter, while in the self-interacting scalar field representation the prediction is very closed to that obtained in the $\Lambda$CDM model., Comment: Latex file, 10 pages, 18 figures in EPS format

The generalized Chaplygin gas model is characterized by the equation of state $$p = - \frac{A}{{\rho ^\alpha }}$$ . It is generally stated that the case α = 0 is equivalent to a model with cosmological constant and dust (Λ C D M). In this work we show that, if this is true for the background equations, this is not true for the perturbation equations. Hence, the mass spectrum predicted for both models may differ.

We study the fate of density perturbations in a Universe dominate by the Chaplygin gas, which exhibit negative pressure. In opposition to other models of perfect fluid with negative pressure, there is no instability in the small wavelength limit, due to the fact that the sound velocity for the Chaplygin gas is positive. We show that it is possible to obtain the value for the density contrast observed in large scale structure of the Universe by fixing a free parameter in the equation of state of this gas. The negative character of pressure must be significant only very recently.

Analysing the Brans–Dicke solutions for the dust phase, we show that, for negative values of ω, they contain scenarios that display an initial subluminal expansion followed by an inflationary phase. This is due to a repulsive cosmic effect. We discuss these solutions with respect to the results of the observation of high redshift supernova as well as the age problem and structure formation. We establish possible connections of these solutions with those emerging from string effective models.

We study the problem of the behaviour of cosmological gravitational waves under conformal transformations. In spite of the apparent triviality of this question, the informations we can obtain from gravitational waves in the so-called Einstein's and Jordan's frame are not the same, mainly with respect to the choice of the initial conditions and of graviton production. The only exception seems to occur in string cosmology due to the duality properties.

The Bicknell theorem states that a non-linear Lagrangian can be recast in the form of a scalar-tensor theory, with a suitable potential, through a conformal transformation. In this paper, we first show that such classical equivalence remains valid at the level of the Wheeler—deWitt equation. Then, we consider a specific case, represented by a Lagrangian f(R) = R + l−2(l2R)4/3 whose vacuum cosmological solutions describe a non-singular Universe. The corresponding scalar-tensor theory and its cosmological solutions are written down. We find again non-singular solutions. The Wheeler—deWitt equation for this case is analyzed. The application of the Bicknell theorem leads to the interpretation of the behaviour of the scale factor in terms of the matter content, represented by the scalar field, and consequently to the energy conditions. The problem of classical and quantum regime is discussed and the classical behaviour is recovered, from the quantum solutions, near the maximum of the scale factor where the strong energy condition is satisfied.

The coupling of the Einstein-Hilbert Lagrangian with a conformal field in an arbitrary even dimension leads, after reduction to four dimensions, to the ordinary gravity coupled non-trivially to two scalar fields. The vacuum solutions display an initial singularity, but with an infinite proper distance between any two points of the space-time. There is an initial contraction phase followed by an expansion phase. This is a kind of ”anti-Big Bang” scenario. The coupling to a radiative fluid preserves this feature; however, the temperature of the radiative fluid is initially zero, increasing afterwards: its maximum value is related to the moment where the horizon crosses the radius of the Universe. The entropy in the three-dimensional space is inversely proportional to the volume of the internal space, and it can be very high today. We perform also a perturbative study of this model during the contraction phase. There is no explosive growth of the scalar perturbations.

We study some consequences of the generalized Maxwell-Einstein system in higher dimensions. This generalization is such that the Maxwell-type field constructed in an evenn-dimensional space-time preserves the conformal invariance. After dimensional reduction to four dimensions, it gives rise to scalar, electromagnetic and Kalb-Ramond fields. Specifically, we analyse here some compactification processes, including the stability of the final configuration (forn=8), and anisotropic cosmological solutions (forn=6).

We study the Einstein-Maxwell theory in five dimensions coupled to matter in two distinct ways. In the first we reduce the Lagrangian to an effective four-dimension one and then we couple it to matter; in the second, we introduce matter directly in the original five-dimensional theory. In both cases we use a non trivial configuration for the Maxwell potential. We find non singular solutions which present a repulsive gravitational phase. When this phase is absent, the initial singularity is unavoidable.