Power spectrum in the Chaplygin gas model: tachyonic, fluid and scalar field representations

Abstract

The Chaplygin gas model, characterized by an equation of state of the type p = − A ρ 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 BornInfeld 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 close to that obtained in the CDM model.

Scalar models for the generalized Chaplygin gas and the structure formation constraints

“…We have shown initially that, for the GCG model, the fluid representation is equivalent to the tachyonic representation of the generalized DBI action, at background and perturbative levels, extending the results of reference [17]. Hence, in order to consider the possibility of negative values for α in a perturbative analysis, we must use another framework, which we have chosen, first, that one represented by a canonical self-interacting scalar field, and later by a non-canonical scalar field inspired in the Rastall's theory of gravity.…”

“…Inserting the expressions (23,24,25) into (20,21,22), we obtain (17,18,19). Hence, the perturbation of the generalized DBI energy-momentum tensor is perfectly equivalent to its fluid counterpart.…”

“…For the moment, we ignore all these problems and consider the canonical self-interacting scalar field as an effective model which asks for a fundamental description before the decoupling between matter and radiation, as well as particular initial conditions. This possibility has been touched in [17], but fixing α = 1. But, at least for this case, it has been found that neither the unification scenario [11] nor the anti-unification scenario [16] have been resulted from this self-interacting scalar field approach: the matter density parameter was in fact very close to that predicted by the ΛCDM or the quintessential model.…”

“…The original, more fundamental, representation of the GCG model, is given by DBI action [7,10], which employs a scalar, tachyonic field. In reference [17] it has been shown that, for α = 1 (original Chaplygin gas model) the DBI action gives the same perturbative expressions as those found in the fluid representation, but that such equivalence, at perturbative level, is broken if a self-interacting scalar field is used to represent the CG model instead of the DBI action.…”

Ruling out the Modified Chaplygin Gas cosmologies

“…If the MCG model can survive the observational tests in this alternative formulation is a question we intend to address in a future work. The main difficult comes from the fact that the usual GCG gas is connected a kind of Born-Infeld , which leads to essentially the same expression for the sound speed as in the hydrodynamical formulation [20]. Hence the restrictions found here for the hydrodynamical formulation may remain.…”