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Register a new userInflationary cosmology with Chaplygin gas in Palatini formalism
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We present a simple generalisation of the $Lambda$CDM model which on the one hand reaches very good agreement with the present day experimental data and provides an internal inflationary mechanism on the other hand. It is based on Palatini modified gravity with quadratic Starobinsky term and generalized Chaplygin gas as a matter source providing, besides a current accelerated expansion, the epoch of endogenous inflation driven by type III freeze singularity. It follows from our statistical analysis that astronomical data favors negative value of the parameter coupling quadratic term into Einstein-Hilbert Lagrangian and as a consequence the bounce instead of initial Big-Bang singularity is preferred.
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We study new FRW type cosmological models of modified gravity treated on the background of Palatini approach. These models are generalization of Einstein gravity by the presence of a scalar field non-minimally coupled to the curvature. The models employ Starobinskys term in the Lagrangian and dust matter. Therefore, as a by-product, an exhausted cosmological analysis of general relativity amended by quadratic term is presented. We investigate dynamics of our models, confront them with the currently available astrophysical data as well as against LCDM model. We have used the dynamical system methods in order to investigate dynamics of the models. It reveals the presence of a final sudden singularity. Fitting free parameters we have demonstrated by statistical analysis that this class of models is in a very good agreement with the data (including CMB measurements) as well as with the standard LCDM model predictions. One has to use statefinder diagnostic in order to discriminate among them. Therefore Bayesian methods of model selection have been employed in order to indicate preferred model. Only in the light of CMB data the concordance model remains invincible.
We classify singularities in FRW cosmologies, which dynamics can be reduced to the dynamical system of the Newtonian type. This classification is performed in terms of geometry of a potential function if it has poles. At the sewn singularity, which is of a finite scale factor type, the singularity in the past meets the singularity in the future. We show, that such singularities appear in the Starobinsky model in $f(hat{R})=hat{R}+gamma hat{R}^2$ in the Palatini formalism, when dynamics is determined by the corresponding piece-wise smooth dynamical system. As an effect we obtain a degenerated singularity. Analytical calculations are given for the cosmological model with matter and the cosmological constant. The dynamics of model is also studied using dynamical system methods. From the phase portraits we find generic evolutionary scenarios of the evolution of the Universe. For this model, the best fit value of $Omega_gamma=3gamma H_0^2$ is equal $9.70times 10^{-11}$. We consider model in both Jordan and Einstein frames. We show that after transition to the Einstein frame we obtain both form of the potential of the scalar field and the decaying Lambda term.
Unification of dark matter and dark energy as short- and long-range manifestations of a single cosmological substance is possible in models described by the generalized Chaplygin gas equation of state. We show it admits halo-like structures and discuss their density profiles, the resulting space-time geometry and the rotational velocity profiles expected in these models.
We study flat FLRW $alpha$-attractor $mathrm{E}$- and $mathrm{T}$-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of $e$-folds, is associated with a solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this `inflationary attractor solution. A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.
We investigate the Tolman-Oppenheimer-Volkoff equations for the generalized Chaplygin gas with the aim of extending the findings of V. Gorini, U. Moschella, A. Y. Kamenshchik, V. Pasquier, and A. A. Starobinsky [Phys. Rev. D {bf 78}, 064064 (2008)]. We study both the standard case, where we reproduce some previous results, and the phantom case. In the phantom case we show that even a superluminal group velocity arising for $alpha > 1$ cannot prevent the divergence of the pressure at a finite radial distance. Finally, we investigate how a modification of the generalized Chaplygin gas equation of state, required by causality arguments at densities very close to $Lambda$, affects the results found so far.
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