Scalar Cosmological Models Research Articles

Slow-roll inflation in the k-essence model with a periodic scalar field function

In this paper, a periodic cosmological model is considered. Previously, it was assumed that the expansion of the universe slows down over time. Theorists proceeded from the assumption that the main part of the mass of the Universe is matter - both visible and invisible (dark matter). On the basis of new observations indicating the acceleration of expansion, it was found that in the Universe there is a previously unknown energy with negative pressure (equation of state). They called it "dark energy". In this paper, a scalar cosmological model is considered. The Lagrangian is derived and the system of equations of motion is obtained. To study the model, a scalar field in the form of a periodic function was chosen. The Hubble parameter, the scale factor, which has the meaning of the radius of the Universe, and in the case of a periodic function of the scalar field, which has an exponential dependence, the density of dark energy, the pressure and the potential of the scalar field are calculated, and their graphs are plotted in the time dependence section from 0 to 2p. To study the inflationary model, the potential is introduced in a power-law form. From it, the parameters of slow rolling through e-folding are derived and a plot of spectral indices for this model is plotted. The results obtained are consistent with the Planck observational data and confirm the correspondence of the model under study with the previously proposed ones.

Application of the form invariance transformations of the scalar cosmological model in inflation theory

In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry, which is arising from the form invariance transformation. Form invariance transformation is defined by linear function ρ = n 2 ρ in general case. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at exponent of the scale factor α > 1, but stability of the transformation model depends on index n. Slow roll parameters and spectral induces is obtained and at large α they agree with Planck observation data.

Self-similar scalar cosmologies

We study several scalar cosmological models under the self-similar approach. We deduce, by stating and proving general theorems, which is the exact form that must follow the scalar field and the potential in the frameworks of a single scalar field and non-interacting (with a perfect fluid) models. The proofs are carried out by two methods: the matter collineation approach and the Lie group method. The results obtained are absolutely general and valid for all Bianchi models and the flat FRW one. In order to study how the “constant” G may vary we propose, in a phenomenological way, how to incorporate a variable G in the framework of scalar models by modifying the Klein-Gordon equation. This approach is more general than the usual one in the context of the FRW symmetries. We deduce the exact form to be followed by each quantity in these new models. Therefore, to study how the “constants” G and Λ may vary, we propose three scenarios where such constants are considered as time functions: modified general relativity with a perfect fluid, the scalar cosmological models (“quintessence”) in the non-interacting case and a scalar-tensor model with a dynamical Λ. As an example, we study the case of Bianchi VI0 geometry.

Bianchi I in scalar and scalar-tensor cosmologies

Abstract We study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants $G$ and $\Lambda$ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (\textquotedblleft quintessence\textquotedblright) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical $\Lambda$) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi \textrm{V}, \textrm{VII}$_{0}$ and \textrm{IX}, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive to the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.