Perfect fluid in Lagrangian formulation due to generalized three-form field

Abstract

A Lagrangian formulation of perfect fluid due to a noncanonical three-form field is investigated.The thermodynamic quantities such as energy density, pressure and the four velocity are obtained and then analyzed by comparing with the k-essence scalar field. The nonrelativistic matter due to the generalized three-form field with the equation of state parameter being zero is realized while it might not be possible for the k-essence scalar field. We also found that nonadiabatic pressure perturbations can be possibly generated. The fluid dynamics of the perfect fluid due to the threeform field corresponds to the system in which the number of particles is not conserved.We argue that it is interesting to use this three-form field to represent the dark matter for the classical interaction theory between dark matter and dark energy.

Generalized Three-Form Field

“…In this section, we will review the generalized three-form field model by considering a Lagrangian of the three-form field, A αβγ , as a function of the kinetic and mass terms as follows, [18]…”

“…From this expression, the description of non-relativistic matter can be obtained by choosing a proper parameters to yield w X = 0, for example, µ = 1, ν = −1/2. Therefore, the Lagrangian of the three-form is still finite and then the model can avoid the caustic problem which is found in the k-essence scalar field case [18]. Moreover, one can relax the assumption of constant w by assuming w X = w X (y).…”

“…Moreover, one can relax the assumption of constant w by assuming w X = w X (y). As a result, one of the solutions can be written as P = P 0 K ν e (1−2ν) 2 λy [18] where w X = −1 + λy and λ is a constant. From this solution, we found that it is possible to obtain the solution which admits the dark energy model.…”

“…A scalar field model is one of simple models to describe these phenomena [1,2,3,4]. Beside the cosmological models due to the scalar field, a three-form field can be successfully used to describe both inflationary phase and dark energy phase [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. At the perturbation level, it is obvious to see that the three-form field can generate intrinsic vector perturbations while it is not possible for the scalar field.…”

“…At the perturbation level, it is obvious to see that the three-form field can generate intrinsic vector perturbations while it is not possible for the scalar field. In the present work, by mimicking the k-essence scalar field, we investigate a generalized version of the three-form field by considering a Lagrangian as a function of kinetic and mass terms [18]. We briefly review the important ingredients of the three-form field including energy momentum tensor and the equation of motion in covariant form.…”